%% Journal articles or Book chapters PUBLISHED @article{fds235787, Author = {Calderbank, AR and Wales, DB}, Title = {A global code invariant under the Higman-Sims group}, Journal = {Journal of Algebra}, Volume = {75}, Number = {1}, Pages = {233-260}, Year = {1982}, ISSN = {0021-8693}, Key = {fds235787} } @article{fds235788, Author = {Calderbank, AR and Mazo, JE and Shapiro, HM}, Title = {UPPER BOUNDS ON THE MINIMUM DISTANCE OF TRELLIS CODES.}, Journal = {The Bell System technical journal}, Volume = {62}, Number = {8 pt 1}, Pages = {2617-2646}, Year = {1983}, url = {http://dx.doi.org/10.1002/j.1538-7305.1983.tb03197.x}, Abstract = {A trellis code is a 'sliding window' method of encoding a binary data stream into a sequence of real numbers that are input to a noisy transmission channel. When a trellis code is used to encode data at the rate of k bits/channel symbol, each channel input will depend not only on the most recent block of k data bits to enter the encoder but will also depend on, say, the nu bits preceding this block. The performance of trellis codes, like that of block codes, depends on a suitably defined minimum-distance property of the code. This paper obtains upper bounds on this minimum distance that are simple functions of k and nu . These results also provide a lower bound on the number of states required to achieve a specific coding gain.}, Doi = {10.1002/j.1538-7305.1983.tb03197.x}, Key = {fds235788} } @article{fds235789, Author = {Bremner, A and Calderbank, R and Hanlon, P and Morton, P and Wolfskill, J}, Title = {Two-weight ternary codes and the equation y^{2}= 4 × 3^{a}+ 13}, Journal = {Journal of Number Theory}, Volume = {16}, Number = {2}, Pages = {212-234}, Year = {1983}, ISSN = {0022-314X}, Abstract = {This paper determines the parameters of all two-weight ternary codes C with the property that the minimum weight in the dual code C⊥ is at least 4. This yields a characterization of uniformly packed ternary [n, k, 4] codes. The proof rests on finding all integer solutions of the equation y2 = 4 × 3a + 13. © 1983.}, Key = {fds235789} } @article{fds236006, Author = {CALDERBANK, R}, Title = {A SQUARE ROOT BOUND ON THE MINIMUM WEIGHT IN QUASI-CYCLIC CODES}, Journal = {IEEE Transactions on Information Theory}, Volume = {29}, Number = {3}, Pages = {332-337}, Year = {1983}, Abstract = {The author establishes a square root bound on the minimum weight in the quasi-cyclic binary codes constructed by V. K. Bhargava, S. E. Tavares, and S. G. S. Shiva. The proof rests on viewing the codes as ideas in a group algebra over GF.}, Key = {fds236006} } @article{fds235790, Author = {Calderbank, AR and Goethals, J-M}, Title = {THREE-WEIGHT CODES AND ASSOCIATION SCHEMES.}, Journal = {Philips Journal of Research}, Volume = {39}, Number = {4-5}, Pages = {143-152}, Year = {1984}, Abstract = {Three-weight projective codes C are considered for which the restriction to C of the Hamming association scheme H//n(q) is an association scheme with three classes. Sufficient conditions are established and restrictions on the three weights of C are obtained. It is shown in the binary case that the three-weight subcodes of the shortened second-order Reed-Muller codes provide a large class of examples, Previously known examples were the duals of perfect 3-error-correcting or uniformly packed 2-error-correcting codes.}, Key = {fds235790} } @article{fds235791, Author = {Calderbank, AR and Sloane, NJA}, Title = {NEW FAMILY OF CODES FOR DIAL-UP VOICE LINES.}, Pages = {673-676}, Year = {1984}, Abstract = {Using a certain 4-dimensional lattice, a new family of codes has been constructed that has a very low error rate. Two particular codes in this family appear to be excellent candidates for use in modems operating at 9. 6 and 14. 4 kb/s, respectively, on dial-up voice telephone lines. The new codes are trellis codes; the output of the encoder is a 4-tuple of odd integers that depends on the input data and the state of the encoder.}, Key = {fds235791} } @article{fds235792, Author = {Calderbank, R and Wales, DB}, Title = {The Haemers partial geometry and the Steiner system S(5, 8, 24)}, Journal = {Discrete Mathematics}, Volume = {51}, Number = {2}, Pages = {125-136}, Year = {1984}, ISSN = {0012-365X}, url = {http://dx.doi.org/10.1016/0012-365X(84)90066-9}, Abstract = {Haemers has constructed a partial geometry with parameters s = 4, t = 17, and α = 2, using properties of the Hoffman-Singleton graph. We describe this geometry in terms of the Steiner system S(5, 8, 24). © 1984.}, Doi = {10.1016/0012-365X(84)90066-9}, Key = {fds235792} } @article{fds235793, Author = {Calderbank, AR and Chung, FRK and Sturtevant, DG}, Title = {Increasing sequences with nonzero block sums and increasing paths in edge-ordered graphs}, Journal = {Discrete Mathematics}, Volume = {50}, Number = {C}, Pages = {15-28}, Year = {1984}, ISSN = {0012-365X}, Abstract = {Consider the maximum length f(k) of a (lexicographically) increasing sequence of vectors in GF(2)k with the property that the sum of the vectors in any consecutive subsequence is nonzero modulo 2. We prove that 23 48 · 2k ≤ f(k) ≤ ( 1 2 + o(1))2k. A related problem is the following. Suppose the edges of the complete graph Kn are labelled by the numbers 1,2,..., (2n). What is the minimum α(n), over all edge labellings, of the maximum length of a simple path with increasing edge labels? We prove that α(n) ≤ ( 1 2 + o(1))n. © 1984.}, Key = {fds235793} } @article{fds235794, Author = {Calderbank, AR and Jr, EGC and Flatto, L}, Title = {OPTIMUM HEAD SEPARATION IN A DISK SYSTEM WITH TWO READ/WRITE HEADS.}, Journal = {Journal of the ACM}, Volume = {31}, Number = {4}, Pages = {826-838}, Year = {1984}, url = {http://dx.doi.org/10.1145/1634.1638}, Abstract = {A mathematical model of computer disk storage devices having two movable read/write heads is studied. Storage addresses are approximated by points in the continuous interval left bracket 0,1 right bracket , and requests for information on the disk are processed first-come-first-served. We assume that the disk heads are maintained a fixed distance d apart; that is, in procesing a request, both heads are moved the same distance in the same direction. Assuming that successive requested locations are independently and uniformly distributed over left bracket 0,1 right bracket , we calculate the invariant measure of a Markov chain representing successive head positions under the nearer-server rule: Requests in left bracket 0,d right bracket are processed by the left head, those in left bracket 1 minus d, 1 right bracket by the right head, and those in left bracket d, 1- minus d right bracket by the nearer of the two heads. Our major objective is the equilibrium expected distance E(d) that the heads are moved in processing a request. For the problem of designing the separation distance d, we show that E (0. 44657) equals 0. 16059 equals min//dE(d). Thus, a basic insight of the analysis is that a system with two heads performs more than twice as well as a system with a single head.}, Doi = {10.1145/1634.1638}, Key = {fds235794} } @article{fds235795, Author = {CALDERBANK, R and MAZO, JE}, Title = {A NEW DESCRIPTION OF TRELLIS CODES}, Journal = {IEEE Transactions on Information Theory}, Volume = {30}, Number = {6}, Pages = {784-791}, Year = {1984}, Abstract = {A trellis code is a 'sliding window' method of encoding a binary data stream as a sequence of real or complex numbers that are input to a noisy transmission channel. Ungerboeck has constructed simple trellis codes that provide the same noise immunity as is given by increasing the power of uncoded transmission by factors ranging from two to four. His method is to specify an underlying convolutional code and a rule (mapping by set partitioning) that maps the output of this code onto a fixed signal constellation. A new description of a trellis code is given that combines these two steps into one. The new description is analytic rather than graphical. Many practical codes can be described very simply, and strict bounds on performance can be obtained. A method for differential encoding trellis codes is presented that was suggested by the authors' representation.}, Key = {fds235795} } @article{fds235796, Author = {Calderbank, AR and Mazo, JE and Wei, VK}, Title = {ASYMPTOTIC UPPER BOUNDS ON THE MINIMUM DISTANCE OF TRELLIS CODES.}, Journal = {IEEE Transactions on Communications}, Volume = {COM-33}, Number = {4}, Pages = {305-309}, Year = {1985}, Abstract = {A trellis code is a 'sliding window' method of encoding a binary data stream as a sequence of signal points. When a trellis code is used to encode data at the rate of k bits/channel symbol, each channel input depends not only on the most recent block of k bits to enter the encoder, but will also depend on a set of upsilon bits preceding this block. The upsilon bits determine the state of the encoder and the most recent block of k bits generates the channel symbol conditional on the encoder state. The performance of a trellis code depends on a suitably defined minimum distance property of that code. This paper obtained upper bounds on this minimum distance that are better than any previously known.}, Key = {fds235796} } @article{fds235797, Author = {Calderbank, AR and Coffman, EG and Flatto, L}, Title = {SEQUENCING PROBLEMS IN TWO-SERVER SYSTEMS.}, Journal = {Mathematics of Operations Research}, Volume = {10}, Number = {4}, Pages = {585-598}, Year = {1985}, Abstract = {We analyze a service system in which two identical servers move one at a time along a linear array of N positions. Requests for service, each designating one of the N positions, join a first-in-first queue, where processing of the nth request does not begin until processing of the (n-1)th requested is completed. Processing the nth request entails determining which server to move, moving this server to the requested position, and then performing the service. Several potential applications of the model are mentioned, the most notable being the design of computer storage systems with multiple access devices. Within a simple probability model we compare server-selection policies in terms of the equilibrium expected distance a server is moved in processing a request. Distance is measured under two regimes, both assigning a unit distance between adjacent positions.}, Key = {fds235797} } @article{fds235798, Author = {Calderbank, AR and Sloane, NJA}, Title = {FOUR-DIMENSIONAL MODULATION WITH AN EIGHT-STATE TRELLIS CODE.}, Journal = {AT&T Technical Journal}, Volume = {64}, Number = {5}, Pages = {1005-1018}, Year = {1985}, Abstract = {A trellis code is a 'sliding window' method for encoding a binary data stream left brace a**i right brace , a**i equals 0, 1, as a sequence of signal points drawn from R**n. The rule for assigning signal points depends on the state of the encoder. In this paper n equals 4, and the signal points are 4-tuples of odd integers. The authors describe an infinite family of eight-state trellis codes. For k equals 3, 4, 5, . . . they construct a trellis encoder with a rate of k bits/four-dimensional signal. They propose that the codes with rates k equals 8 and 12 be considered for use in modems designed to achieve data rates of 9. 6 kb/s and 14. 4 kb/s, respectively.}, Key = {fds235798} } @article{fds331066, Author = {Calderbank, AR and Coffman, EG and Flatto, L}, Title = {Sequencing two servers on a sphere}, Journal = {Communications in Statistics. Part C: Stochastic Models}, Volume = {1}, Number = {1}, Pages = {17-28}, Year = {1985}, Month = {January}, url = {http://dx.doi.org/10.1080/15326348508807002}, Doi = {10.1080/15326348508807002}, Key = {fds331066} } @article{fds331065, Author = {Calderbank, A and Goethals, J-M}, Title = {On a Pair of Dual Subschemes of the Hamming Scheme Hn(q)}, Journal = {European Journal of Combinatorics}, Volume = {6}, Number = {2}, Pages = {133-147}, Year = {1985}, Month = {June}, url = {http://dx.doi.org/10.1016/S0195-6698(85)80004-4}, Doi = {10.1016/S0195-6698(85)80004-4}, Key = {fds331065} } @article{fds235799, Author = {Calderbank, AR and Sloane, NJA}, Title = {EIGHT-DIMENSIONAL TRELLIS CODE.}, Journal = {Proceedings of the IEEE}, Volume = {74}, Number = {5}, Pages = {757-759}, Year = {1986}, Abstract = {A family of eight-state, eight-dimensional trellis codes based on the E//8 lattice that can be used at 9. 6, 14. 4, or 19. 2 kb/s is presented. The nominal coding gain is close to 6 dB. The relatively high path multiplicity of 382 per dimension can be reduced by increasing the memory of the code.}, Key = {fds235799} } @article{fds236007, Author = {Calderbank, AR and Heegard, C and Lee, T-A}, Title = {BINARY CONVOLUTIONAL CODES WITH APPLICATION TO MAGNETIC RECORDING.}, Pages = {42-}, Year = {1986}, Abstract = {Summary form only given. A. R. Calderbank et. al. have suggested a method of designing codes for channels with intersymbol interference, such as the magnetic recording channel. They considered an idealized model of the magnetic recording channel that leads to the problem of designing codes for a partial response channel with transfer function (1 - D**N)/2 where the channel inputs are constrained to be plus or minus 1. This problem is considered here. Channel inputs are generated using a nontrivial coset of a binary convolution code. The coset is chosen to limit the zero-run length of the output of the channel and so maintain clock synchronization. The minimum squared Euclidean distance between outputs corresponding to distinct inputs is bounded below by the free distance of a second convolutional code called the magnitude code. An interesting feature of the analysis is that magnitude codes that are catastrophic may perform better than those that are noncatastrophic.}, Key = {fds236007} } @article{fds236008, Author = {Calderbank, AR and Hanlon, P}, Title = {The extension to root systems of a theorem on tournaments}, Journal = {Journal of Combinatorial Theory, Series A}, Volume = {41}, Number = {2}, Pages = {228-245}, Year = {1986}, ISSN = {0097-3165}, Abstract = {M. G. Kendall and B. Babington-Smith proved that if a tournament p′ is obtained from a tournament p by reversing the edges of a 3-cycle then p and p′ contain the same number of 3-cycles. This theorem is the basis of a cancellation argument used by D. Zeilberer and D. M. Bressoud in their recent proof of the q-analog of Dyson's conjecture. The theorem may be restated in terms of the root system An and the main result of this paper is the extension of this theorem to arbitrary root systems. As one application we give a combinatorial proof of a special case of the Macdonald conjecture for root systems using the method of Zeilberger and Bressoud. A second application is a combinatorial proof of the Weyl denominator formula. © 1986.}, Key = {fds236008} } @article{fds236009, Author = {Calderbank, AR and Sloane, NJA}, Title = {NEW TRELLIS CODES.}, Pages = {59-}, Year = {1986}, Abstract = {Summary form only given. A technique is proposed for constructing multidimensional trellis codes that provides an alternative to Ungerboeck's method of 'set partitioning. ' The new codes use a signal constellation consisting of points from an n-dimensional lattice LAMBDA , with an equal number of points from each coset of a sublattice LAMBDA prime . One part of the input stream drives a generalized convolutional code whose outputs are cosets of LAMBDA prime , while the other part selects points from these cosets. This technique allows the path multiplicity to be calculated easily. It is also possible to describe methods of differential encoding very simply.}, Key = {fds236009} } @article{fds236010, Author = {Calderbank, AR}, Title = {70,58,5.}, Journal = {IEEE Transactions on Information Theory}, Volume = {IT-32}, Number = {6}, Pages = {828-833}, Year = {1986}, url = {http://dx.doi.org/10.1109/TIT.1986.1057232}, Abstract = {Uniformly packed, linear e-error-correcting codes are considered. In particular, it is shown that the nonexistence of a uniformly packed left bracket 70,58,5 right bracket code C PERPEND is proved by examining geometries associated with the 3-weight code C.}, Doi = {10.1109/TIT.1986.1057232}, Key = {fds236010} } @article{fds236012, Author = {Brouwer, AE and Calderbank, AR}, Title = {An Erdös-Ko-Rado theorem for regular intersecting families of octads}, Journal = {Graphs and Combinatorics}, Volume = {2}, Number = {1}, Pages = {309-316}, Year = {1986}, ISSN = {0911-0119}, url = {http://dx.doi.org/10.1007/BF01788105}, Abstract = {Codewords of weight 8 in the [24, 12] binary Golay code are called octads. A family ℱ of octads is said to be a regular intersecting family if ℱ is a 1-design and |x ∩ y| ≠ 0 for all x, y ∈ ℱ. We prove that if ℱ is a regular intersecting family of octads then |ℱ| ≤ 69. Equality holds if and only if ℱ is a quasi-symmetric 2-(24, 8, 7) design. We then apply techniques from coding theory to prove nonexistence of this extremal configuration. © 1986 Springer-Verlag.}, Doi = {10.1007/BF01788105}, Key = {fds236012} } @article{fds236013, Author = {Calderbank, AR and Heegard, C and Lee, T-A}, Title = {BINARY CONVOLUTIONAL CODES WITH APPLICATION TO MAGNETIC RECORDING.}, Journal = {IEEE Transactions on Information Theory}, Volume = {IT-32}, Number = {6}, Pages = {797-815}, Year = {1986}, url = {http://dx.doi.org/10.1109/TIT.1986.1057245}, Abstract = {Motivated by an idealized model of the magnetic recording channel, codes were designed for a partial response channel with transfer function (1-D**N)/2 where the channel inputs are constrained to be plus or minus 1. Channel inputs are generated using a nontrivial coset of a binary convolutional code called the sign code. The probability of decoder error is determined by the minimum squared Euclidean distance between outputs corresponding to distinct inputs. This Euclidean distance is bounded below by the free distance of a second binary convolutional code called the magnitude code. The coset of the sign code is chosen to limit the zero-run length of the output of the channel and so maintain clock synchronization. The performance of rate k/k plus 1) codes on the (1-D)/2 and (1-D**2 )/2 channels was analyzed. It was found that magnitude codes that are catastrophic may perform better than those that are noncatastrophic.}, Doi = {10.1109/TIT.1986.1057245}, Key = {fds236013} } @article{fds326909, Author = {CALDERBANK, R and KANTOR, WM}, Title = {THE GEOMETRY OF 2-WEIGHT CODES}, Journal = {Bulletin of the London Mathematical Society}, Volume = {18}, Pages = {97-122}, Year = {1986}, Month = {March}, url = {http://dx.doi.org/10.1112/blms/18.2.97}, Doi = {10.1112/blms/18.2.97}, Key = {fds326909} } @article{fds331064, Author = {Calderbank, A and Fishburn, P and Spencer, J}, Title = {Functions that Never Agree}, Journal = {European Journal of Combinatorics}, Volume = {7}, Number = {3}, Pages = {207-210}, Year = {1986}, Month = {July}, url = {http://dx.doi.org/10.1016/S0195-6698(86)80023-3}, Doi = {10.1016/S0195-6698(86)80023-3}, Key = {fds331064} } @article{fds331063, Author = {Calderbank, AR and Hanlon, P and Robinson, RW}, Title = {Partitions into Even and Odd Block Size and Some Unusual Characters of the Symmetric Groups}, Journal = {Proceedings of the London Mathematical Society}, Volume = {s3-53}, Number = {2}, Pages = {288-320}, Year = {1986}, Month = {September}, url = {http://dx.doi.org/10.1112/plms/s3-53.2.288}, Doi = {10.1112/plms/s3-53.2.288}, Key = {fds331063} } @article{fds236011, Author = {Calderbank, AR}, Title = {The application of invariant theory to the existence of quasi-symmetric designs}, Journal = {Journal of Combinatorial Theory, Series A}, Volume = {44}, Number = {1}, Pages = {94-109}, Year = {1987}, ISSN = {0097-3165}, Abstract = {Gleason and Mallows and Sloane characterized the weight enumerators of maximal self-orthogonal codes with all weights divisible by 4. We apply these results to obtain a new necessary condition for the existence of 2 - (v, k, λ) designs where the intersection numbers s1...,sn satisfy s1 ≡ s2 ≡ ... ≡ sn (mod 2). Non-existence of quasi-symmetric 2-(21, 18, 14), 2-(21, 9, 12), and 2-(35, 7, 3) designs follows directly from the theorem. We also eliminate quasi-symmetric 2-(33, 9, 6) designs. We prove that the blocks of quasi-symmetric 2-(19, 9, 16), 2-(20, 10, 18), 2-(20,8, 14), and 2-(22, 8, 12) designs are obtained from octads and dodecads in the [24, 12] Golay code. Finally we eliminate quasi-symmetric 2-(19,9, 16) and 2-(22, 8, 12) designs. © 1987.}, Key = {fds236011} } @article{fds236015, Author = {Calderbank, AR and Sloane, NJA}, Title = {NEW TRELLIS CODES BASED ON LATTICES AND COSETS.}, Journal = {IEEE Transactions on Information Theory}, Volume = {IT-33}, Number = {2}, Pages = {177-195}, Year = {1987}, Abstract = {A new technique is proposed for constructing trellis codes, which provides an alternative to Ungerboeck's method of set partitioning. The new codes use a signal constellation consisting of points from an n-dimensional lattice LAMBDA , with an equal number of points from each coset of a sublattice LAMBDA '. One part of the input stream drives a generalized convolutional code whose outputs are cosets of LAMBDA ', while the other part selects points from these cosets. Several of the new codes are better than those previously known.}, Key = {fds236015} } @article{fds236014, Author = {Calderbank, AR and Sloane, NJA}, Title = {Linear inequalities for covering codes}, Volume = {25 n 13}, Pages = {33-}, Year = {1988}, Abstract = {Summary form only given, as follows. Any code C with covering radius R must satisfy a set of linear inequalities that involve the Lloyd polynomial LR(x); these generalize the sphere bound. The syndrome graphs associated with a linear code C help to keep track of low weight vectors in the same coset of C (if there are too many such vectors C cannot exist). As illustrations it is shown that t[17, 10] = 3 and t[23, 15] = 3, where t[n, k] is the smallest covering radius of any [n, k] code.}, Key = {fds236014} } @article{fds236016, Author = {Herro, MA and Telang, V and Calderbank, AR}, Title = {Construction of trellis-decodable error-correcting line codes}, Volume = {25 n 13}, Pages = {63-64}, Year = {1988}, Abstract = {Summary form only given, as follows. The design of balanced error-correcting codes has received a lot of attention in recent literature. Besides their error-control capability, these codes also have power spectral densities that make them attractive for use on the fiber optic channel and for data storage on magnetic tape. Since these codes are balanced, the number of ones in every code word equals the number of zeros. This property guarantees a null at DC in the power spectral densities of these codes. The authors show ways of constructing single error-correcting balanced codes with dmi n = 4. They construct code words by a two-layered method. They first define a set of balanced symbols consisting of a sequence of zeros and ones (with the number of ones equal to the number of zeros). Thus any sequence of these symbols will be balanced. The code words are constructed by concatenating these symbols in a way that guarantees the minimum distance of the code to be 4, i.e., dm in = 4.}, Key = {fds236016} } @article{fds236017, Author = {Calderbank, AR}, Title = {Multi-level trellis codes for the Gaussian channel and for channels subject to impulsive noise}, Journal = {Proceedings - IEEE Military Communications Conference}, Volume = {2}, Pages = {673-678}, Year = {1988}, Abstract = {The author designs multilevel trellis codes based on lattices and cosets that provide greater immunity to Gaussian noise and/or greater resistance to impulse noise than previous approaches. He shows how to calculate minimum-squared distance and path multiplicity in terms of the norms and multiplicities of the different cosets. The multilevel structure allows the redundancy in the coset selection procedure to be allocated efficiently among the different levels. The proposed codes admit a staged decoding procedure that requires very few trellis states and has performance/complexity advantages over maximum-likelihood decoding.}, Key = {fds236017} } @article{fds236018, Author = {Calderbank, AR and Jr, EGC and Flatto, L}, Title = {OPTIMAL DIRECTORY PLACEMENT ON DISK STORAGE DEVICES.}, Journal = {Journal of the ACM}, Volume = {35}, Number = {2}, Pages = {433-446}, Year = {1988}, url = {http://dx.doi.org/10.1145/42282.42287}, Abstract = {Two mathematical models dealing with optimal placement of directories on disk devices are analyzed. Storage addresses on the disk are approximated by points in the interval left bracket 0, 1 right bracket . Requests for information on the disk are represented by a sequence of file names. To process a request, a read-write head is first moved to a directory kept on the disk that specifies the address of the file, and then a head is moved to the specified address. The addresses are assumed to be independent and uniform on left bracket 0, 1 right bracket . In the first model we consider a system of two heads separated by a fixed distance d and a directory situated at 0 less than equivalent to x less than equivalent to 1. In the second model we consider a system consisting of one head and n greater than equivalent to 2 directories at 0 less than equivalent to x//1 less than x//2 less than . . . less than x//n less than equivalent to 1. For both models we study the problem of finding those values of the parameters that minimize the expected head motion to process a request in statistical equilibrium.}, Doi = {10.1145/42282.42287}, Key = {fds236018} } @article{fds236019, Author = {Calderbank, AR}, Title = {Geometric invariants for quasi-symmetric designs}, Journal = {Journal of Combinatorial Theory, Series A}, Volume = {47}, Number = {1}, Pages = {101-110}, Year = {1988}, ISSN = {0097-3165}, Abstract = {Let p be an odd prime. We derive new necessary conditions for the existence of 2 - (ν, k, λ) designs where the block intersection sizes s1, s2, ..., sn satisfy s1 ≡ s2 ≡ ... ≡ sn (mod p). The method is to define a nondegenerate scalar product on a 2m-dimensional vector space and to construct an m-dimensional totally singular subspace. This result is a generalization to nonsymmetric designs of the Bruck-Ryser-Chowla theorem. © 1988.}, Key = {fds236019} } @article{fds236020, Author = {Jr, GDF and Calderbank, AR}, Title = {COSET codes for partial response; or, codes with spectral nulls}, Volume = {25 n 13}, Pages = {141-}, Year = {1988}, Abstract = {Summary form only given, as follows. Known coset codes are adapted for use on partial response channels or to generate signals with spectral nulls. By use of methods of coset precoding and running digital sum feedback, any desired tradeoff can be achieved between the power and spectra of the relevant sequences, up to the optimum tradeoff possible. A fundamental theorem specifying this optimum tradeoff is given. An MLSE decoder for the original code may be used for the adapted code, and such a decoder then attains the minimum squared distance of the original code. These methods sometimes generate codes with greater minimum squared distance than that of the original code, which can be attained by augmented decoders, although such decoders inherently require long decoding delays and may be subject to quasi-catastrophic error propagation. The general conclusion is that, at least for sequences that support large number of bits per symbol, one can obtain the same kinds of performance and complexity on partial response channels, or for sequences with spectral nulls, as can be obtained with the same coset codes in the ordinary memoryless case.}, Key = {fds236020} } @article{fds236021, Author = {Pottie, GJ and Taylor, DP and Calderbank, AR}, Title = {Multi-level channel codes based on partitioning}, Volume = {25 n 13}, Pages = {166-}, Year = {1988}, Abstract = {Summary form only given, as follows. Imai and Hirakawa have proposed a multilevel coding method based on binary block codes that admits a staged decoding procedure. This method has been extended to the design of codes for the Gaussian channel by Ginzburg and Tanner. The authors show that coset codes (including lattice, Ungerboeck, and binary codes) and indeed any codes which rely on a partitioning of the signal set may be described by one formalism, and all can be used in a multilevel scheme. The combination of such codes in a multilevel scheme often leads to reduced decoding complexity for the same performance as previously published schemes. The authors discuss some alternatives to the staged decoding structure, and the tradeoffs involved. They present as examples powerful multi-level schemes for the Gaussian channel and for channels that are subject to both Gaussian and impulsive noise.}, Key = {fds236021} } @article{fds236022, Author = {Calderbank, AR}, Title = {Inequalities for quasi-symmetric designs}, Journal = {Journal of Combinatorial Theory, Series A}, Volume = {48}, Number = {1}, Pages = {53-64}, Year = {1988}, ISSN = {0097-3165}, Abstract = {A 2-design is said to be quasi-symmetric if there are two block intersection sizes. We obtain inequalities satisfied by the parameters of a quasi-symmetric design using linear programming techniques. The same methods apply to codes with covering radius 2 with the property that the number of codewords at distance 2 from a given vector ν depends on the distance of ν from the code. © 1988.}, Key = {fds236022} } @article{fds236023, Author = {Calderbank, AR and Lee, T-A and Mazo, JE}, Title = {Baseband trellis codes with a spectral null at zero}, Journal = {IEEE Transactions on Information Theory}, Volume = {34}, Number = {3}, Pages = {425-434}, Year = {1988}, url = {http://dx.doi.org/10.1109/18.6023}, Abstract = {A method is described for modifying classical N-dimensional trellis codes to provide baseband codes that combine a spectral null at DC with significant coding gain. The information rate of the classical code is decreased by one bit, and this extra redundancy is used to keep the running digital sum bounded. Equivalently, if the rate is held constant, then twice as many signal points are needed, causing a power penalty of 6/N dB. Baseband trellis codes are presented for several information rates together with complete spectral plots and performance comparisons. A method of constructing baseband codes with multiple spectral nulls is also described.}, Doi = {10.1109/18.6023}, Key = {fds236023} } @article{fds236026, Author = {Calderbank, AR and Sloane, NJA}, Title = {Inequalities for covering codes}, Journal = {IEEE Transactions on Information Theory}, Volume = {34}, Number = {5 pt 2}, Pages = {1276-1280}, Year = {1988}, url = {http://dx.doi.org/10.1109/18.21257}, Abstract = {Any code C with covering radius R must satisfy a set of linear inequalities that involve the Lloyd polynomial LR(x); these generalize the sphere bound. Syndrome graphs associated with a linear code C are introduced to help keep track of low-weight vectors in the same coset of C (if there are too many such vectors C cannot exist). As illustrations it is shown that t[17,10]=3 nd t[23,15]=3 where t[n,k] is the smallest covering radius of any [n,k] code.}, Doi = {10.1109/18.21257}, Key = {fds236026} } @article{fds331062, Author = {Calderbank, A}, Title = {Symmetric Designs as the Solution of an Extremal Problem in Combinatorial Set Theory}, Journal = {European Journal of Combinatorics}, Volume = {9}, Number = {2}, Pages = {171-173}, Year = {1988}, Month = {March}, url = {http://dx.doi.org/10.1016/S0195-6698(88)80043-X}, Doi = {10.1016/S0195-6698(88)80043-X}, Key = {fds331062} } @article{fds236024, Author = {Calderbank, AR and Herro, MA and Telang, V}, Title = {Multilevel approach to the design of DC-free line codes}, Journal = {IEEE Transactions on Information Theory}, Volume = {35}, Number = {3}, Pages = {579-583}, Year = {1989}, url = {http://dx.doi.org/10.1109/18.30980}, Abstract = {A multilevel approach to the design of DC-free line codes is presented. The different levels can be used for different purposes, for example, to control the maximum accumulated charge or to guarantee a certain minimum distance. The advantages of codes designed by this method over similar codes are the improved run-length/accumulated-charge parameters, higher transmission rate, and the systematic nature of the code construction. The multilevel structure allows the redundancy in the signal selection procedure to be allocated efficiently among the different levels. It also allows the use of suboptimal staged decoding procedures that have performance/complexity advantages over maximum-likelihood decoding.}, Doi = {10.1109/18.30980}, Key = {fds236024} } @article{fds236025, Author = {Calderbank, AR}, Title = {Multilevel codes and multistage decoding.}, Journal = {IEEE Transactions on Communications}, Volume = {37}, Number = {3}, Pages = {222-229}, Year = {1989}, Abstract = {H. Imai and S. Hirakawa have proposed (1977) a multilevel coding method based on binary block codes that admits a staged decoding procedure. Here the coding method is extended to coset codes and it is shown how to calculate minimum squared distance and path multiplicity in terms of the norms and multiplicities of the different cosets. The multilevel structure allows the redundancy in the coset selection procedure to be allocated efficiently among the different levels. It also allows the use of suboptimal multistage decoding procedures that have performance/complexity advantages over maximum-likelihood decoding.}, Key = {fds236025} } @article{fds236027, Author = {Jr, GDF and Calderbank, AR}, Title = {Coset codes for partial response channels; or, coset codes with spectral nulls}, Journal = {IEEE Transactions on Information Theory}, Volume = {35}, Number = {5}, Pages = {925-943}, Year = {1989}, url = {http://dx.doi.org/10.1109/18.42211}, Abstract = {Known coset codes are adapted for use on partial response channels or to generate signals with spectral nulls. By using coset precoding and running digital sum feedback, any desired tradeoff can be achieved between the power and spectra of the relevant sequences, up to the optimum tradeoff possible. A fundamental theorem specifying this optimum tradeoff is given. A maximum-likelihood-sequence-estimation (MLSE) decoder for the original code may be used for the adapted code, and such a decoder then attains the minimum squared distance of the original code. These methods sometimes generate codes with greater minimum squared distance than that of the original code; this distance can be attained by augmented decoders, although such decoders inherently require long decoding delays and may be subjected to quasi-catastrophic error propagation. The authors conclude that, at least for sequences supporting large numbers of bits per symbol, coset codes can be adapted to achieve effectively the same performance and complexity on partial response channels, or for sequences with spectral nulls, as they do in the ordinary memoryless case.}, Doi = {10.1109/18.42211}, Key = {fds236027} } @article{fds236028, Author = {Calderbank, AR and Mazo, JE}, Title = {Baseband line codes via spectral factorization.}, Journal = {IEEE Journal on Selected Areas in Communications}, Volume = {7}, Number = {6}, Pages = {914-928}, Year = {1989}, url = {http://dx.doi.org/10.1109/49.29614}, Abstract = {A description is given of a methodology for designing baseband line codes with prescribed spectral nulls in the transmitted spectrum. These codes have the property that the transmitted power is adjustable (with a concomitant change in spectral shape, i.e., null width) and can be made arbitrarily close to the innovations power, while keeping the minimum distance between signal points (or sequences) constant. The essential design step requires the spectral factorization of a certain trigonometric polynomial. The line code that results can easily be used in conjunction with a large class of trellis-coded modulation schemes. Specific baseband codes are constructed using a representation of the general theory that involves a dither variable, which is used to create integer symbols and to minimize the size of the symbol alphabet. Emphasis is on the design of line codes with a double null at DC using the symbol alphabet {±1, ±3}.}, Doi = {10.1109/49.29614}, Key = {fds236028} } @article{fds236031, Author = {Calderbank, AR and Jr, EGC and Flatto, L}, Title = {Note extending the analysis of two-head disk systems to more general seek-time characteristics}, Journal = {IEEE Transactions on Computers}, Volume = {38}, Number = {11}, Pages = {1584-1586}, Year = {1989}, url = {http://dx.doi.org/10.1109/12.42130}, Abstract = {The authors analyze a model of a movable-head disk system with two read/write heads maintained a fixed distance d apart on each arm. Successive request-addresses are assumed to be independent random variables, uniformly distributed over the set of cylinders. The purpose of the analysis is to find that value of d which minimizes the expected seek time per request, assuming that seek time varies linearly with the distance z traveled by the heads. The authors extend an earlier analysis of this model to more general seek-time characteristics which take into account nonlinear acceleration effects. Detailed results, combining both analysis and simulation experiments, are presented for seek times linear in zα, 0 ≤ α ≤ 1. An unexpected result of the study was that the value of d which minimizes expected seek time is very nearly independent of α.}, Doi = {10.1109/12.42130}, Key = {fds236031} } @article{fds235800, Author = {Calderbank, AR}, Title = {Covering radius and the chromatic number of Kneser graphs}, Journal = {Journal of Combinatorial Theory, Series A}, Volume = {54}, Number = {1}, Pages = {129-131}, Year = {1990}, ISSN = {0097-3165}, url = {http://dx.doi.org/10.1016/0097-3165(90)90011-K}, Abstract = {Let C be a binary linear code with covering radius R and let C0 be a subcode of C with codimension i. We prove that the covering radius R0 of C satisfies R0 ≤ 2R + 2i - 1, by setting up a graph coloring problem involving Kneser graphs. © 1990.}, Doi = {10.1016/0097-3165(90)90011-K}, Key = {fds235800} } @article{fds235801, Author = {Calderbank, AR and Ozarow, LH}, Title = {Nonequiprobable signaling on the Gaussian channel}, Journal = {IEEE Transactions on Information Theory}, Volume = {36}, Number = {4}, Pages = {726-740}, Year = {1990}, url = {http://dx.doi.org/10.1109/18.53734}, Abstract = {Signaling schemes for the Gaussian channel based on finite-dimensional lattices are considered. The signal constellation consists of all lattice points within a region R, and the shape of this region determines the average signal power. Spherical signal constellations minimize average signal power, and in the limit as N → ∞, the shape gain of the N-sphere over the N-cube approaches πe/6 ≈ 1.53 dB. A nonequiprobable signaling scheme is described that approaches this full asymptotic shape gain in any fixed dimension. A signal constellation Ω is partitioned into T subconstellations Ω0,..., ΩT-1 of equal size by scaling a basic region R. Signal points in the same subconstellation are used equiprobably, and a shaping code selects the subconstellation Ωi with frequency fi. Shaping codes make it possible to achieve any desired fractional bit rate. The schemes presented are compared with equiprobable signaling schemes based on Voronoi regions of multidimensional lattices. For comparable shape gain and constellation expansion ratio, the peak to average power ratio of the schemes presented is superior. Furthermore, a simple table lookup is all that is required to address points in the constellations. This is not the case for Voronoi constellations. It is also shown that it is possible to integrate coding and nonequiprobable signaling within a common multilevel framework.}, Doi = {10.1109/18.53734}, Key = {fds235801} } @article{fds235804, Author = {Calderbank, AR and Frankl, P}, Title = {Binary codes and quasi-symmetric designs}, Journal = {Discrete Mathematics}, Volume = {83}, Number = {2-3}, Pages = {201-204}, Year = {1990}, ISSN = {0012-365X}, Abstract = {We obtain a new necessary condition for the existence of a 2-(υ, k, λ) design where the block intersection sizes s1,s2,...,sn satisfy s1≡s2≡...≡sn≡s( mod 2). This condition eliminates quasi-symmetric 2-(20, 10, 18) and 2-(60, 30, 58) designs. Quasi-symmetric 2- (20, 8, 14) designs are eliminated by an ad hoc coding theoretic argument. © 1990.}, Key = {fds235804} } @article{fds236029, Author = {Calderbank, AR and Ozarow, LH}, Title = {Non-equiprobable signaling on the Gaussian channel}, Pages = {145-}, Year = {1990}, Abstract = {Summary form only given, as follows. Many signaling schemes for the Gaussian channel are based on finite-dimensional lattices. The signal constellation consists of all lattice points within a region R, and the shape of this region determines the average signal power. In the limit as N → ∞, the shape gain the N-sphere over the N-cube approaches πe/6 = 1.53 dB. It is shown that the full asymptotic shape gain can be realized in any fixed dimension by nonequiprobable signaling. Shaping schemes that achieve a significant fraction of the available asymptotic shaping gain are described. The peak-to-average-power ratio of these schemes is superior to that of equiprobable signaling schemes based on Voronoi regions of multidimensional lattices. The new shaping schemes admit a simple staged demodulation procedure.}, Key = {fds236029} } @article{fds236030, Author = {Calderbank, AR and Delsarte, P and Sloane, NJA}, Title = {A strengthening of the Assmus-Mattson Theorem}, Pages = {41-}, Year = {1990}, Abstract = {Summary form only given. Let w1 = d, w2, ..., ws be the weights of the nonzero code words in a binary linear [n, k, d] code C, and let w1′, w2′, ..., ws′ be the nonzero weights in the dual code C⊥. Let t be an integer in the range 0 < t < d such that there are at most d - t weights wi′ with 0 < wi′ ≤ n - t. Assmus and Mattson proved that the words of any weight wi in C form a t-design. Let δ = 0 or 1, according to whether C is even or not, and let B denote the set of code words of weight d. The present authors have proved that if w2 ≥ d + 4, then either (1) t = 1, d is odd, and B partitions {1, 2, ..., n}, or (2) B is a (t + δ + 1)-design, or (3) B is a {1, ..., t + δ, t + δ + 2}-design. If C is a self-orthogonal binary code with all weights divisible by 4, then the result extends to code words of any given weight. The special case of code words of minimal weight in extremal self-dual codes also follows from a theorem of Venkov and Koch.}, Key = {fds236030} } @article{fds235802, Author = {Calderbank, AR and Delsarte, P and Sloane, NJA}, Title = {A strengthening of the Assmus-Mattson theorem}, Journal = {IEEE Transactions on Information Theory}, Volume = {37}, Number = {5}, Pages = {1261-1268}, Year = {1991}, url = {http://dx.doi.org/10.1109/18.133244}, Abstract = {Let w1 = d,w2,...,ws be the weights of the nonzero codewords in a binary linear [n,k,d] code C, and let w′1, w′2, ..., w′s′, be the nonzero weights in the dual code C⊥. Let t be an integer in the range 0 < t < d such that there are at most d - t weights w′i with 0 < w′i ≤ n - t. E. F. Assmus and H. F. Mattson, Jr. (1969) proved that the words of any weight wi in C form a t-design. The authors show that if w2 ≥ d + 4 then either the words of any nonzero weight wi form a (t + 1)-design or else the codewords of minimal weight d form a {1,2,...,t,t + 2}-design. If in addition C is self-dual with all weights divisible by 4 then the codewords of any given weight wi form either a (t + 1)-design or a {1,2,...,t,t + 2}-design. The proof avoids the use of modular forms.}, Doi = {10.1109/18.133244}, Key = {fds235802} } @article{fds235803, Author = {Calderbank, AR}, Title = {The mathematics of moderns}, Journal = {The Mathematical Intelligencer}, Volume = {13}, Number = {3}, Pages = {56-65}, Year = {1991}, ISSN = {0343-6993}, url = {http://dx.doi.org/10.1007/BF03023836}, Doi = {10.1007/BF03023836}, Key = {fds235803} } @article{fds235805, Author = {Calderbank, AR and Mazo, JE}, Title = {Spectral nulls and coding with large alphabets}, Journal = {IEEE Communications Magazine}, Volume = {29}, Number = {12}, Pages = {58-67}, Year = {1991}, url = {http://dx.doi.org/10.1109/35.120352}, Abstract = {Generalizations of the simple alternate-mark-inversion (AMI) line code that provide enhanced immunity to additive noise as well as spectral shaping are considered. The first technique is the extension of balanced disparity methods to multilevel signaling alphabets. This is a small step beyond simple codes such as AMI that are used to transmit binary PCM over twisted-pair cables. An important feature of this method (and later methods) is the use of suboptimal decoders. The most sophisticated technique used was Tomlinson filtering, and here it was possible to require a spectral null in the line code spectrum with a certain minimum width, and to minimize line code power subject to this requirement. This technique is compared to methods introduced by B. H. Marcus and P. H. Siegel (1987) in magnetic recording that provide spectral nulls at rational multiples of the symbol frequency. Theoretical possibilities, rather than techniques proven superior for a particular application, are addressed.}, Doi = {10.1109/35.120352}, Key = {fds235805} } @article{fds235806, Author = {Calderbank, AR and Klimesh, M}, Title = {Balanced codes and nonequiprobable signaling}, Journal = {IEEE Transactions on Information Theory}, Volume = {38}, Number = {3}, Pages = {1119-1122}, Year = {1992}, url = {http://dx.doi.org/10.1109/18.135651}, Abstract = {The problem of shaping signal constellations that are designed for the Gaussian channel is considered. The signal constellation consists of all points from some translate of a lattice Λ that lie within a region R. The signal constellation is partitioned into T annular subconstellations Ω0,...,ΩT-1 by scaling the region R. Signal points in the same subconstellation are used equiprobably, and a shaping code selects region Ωi with frequency fi. If the signal constellation is partitioned into annular subconstellations of unequal size, then the transmission rate should vary with the choice of codeword in the shaping code, and it will be necessary to queue the data in buffers. It is described how the balanced binary codes constructed by D. E. Knuth (1986) can be used to avoid a data rate that is probabilistic. The basic idea is that if symbols 0 and 1 represent constellations of unequal size, and if all shaping codewords have equally many 0's and 1's, then the data rate will be deterministic.}, Doi = {10.1109/18.135651}, Key = {fds235806} } @article{fds235807, Author = {Calderbank, AR}, Title = {Covering bounds for codes}, Journal = {Journal of Combinatorial Theory, Series A}, Volume = {60}, Number = {1}, Pages = {117-122}, Year = {1992}, ISSN = {0097-3165}, Abstract = {Given an [n, k]R code C, and a subcode H of C with codimension j, define SHj(C) = maxx∈F2n {d(x, H) + d(x, C H)}, and define the j-norm, Sj(C) to be the minimum value of SHj(C) as H ranges over the subcodes with codimension j. We prove that if k (n + 1) > R (R + 1), then S1(C) ≤ 2R + 1. © 1992.}, Key = {fds235807} } @article{fds235808, Author = {Blokhuis, A and Calderbank, AR}, Title = {Quasi-symmetric designs and the Smith Normal Form}, Journal = {Designs, Codes and Cryptography}, Volume = {2}, Number = {2}, Pages = {189-206}, Year = {1992}, ISSN = {0925-1022}, url = {http://dx.doi.org/10.1007/BF00124897}, Abstract = {We obtain necessary conditions for the existence of a 2 - (ν, k, λ) design, for which the block intersection sizes s1, s2, ..., snsatisfy s1 ≡ s2 ≡ ... ≡ sn ≡ s (mod pe),where p is a prime and the exponent e is odd. These conditions are obtained from restriction on the Smith Normal Form of the incidence matrix of the design. We also obtain restrictions on the action of the automorphism group of a 2 - (ν, k, λ) design on points and on blocks. © 1992 Kluwer Academic Publishers.}, Doi = {10.1007/BF00124897}, Key = {fds235808} } @article{fds236032, Author = {Calderbank, AR and Pottie, GJ}, Title = {Upper bounds for small trellis codes}, Journal = {IEEE Transactions on Information Theory}, Volume = {38}, Number = {6}, Pages = {1791-1795}, Year = {1992}, url = {http://dx.doi.org/10.1109/18.165452}, Abstract = {An upper bound on the minimum squared distance of trellis codes by packing Voronoi cells is derived and compared with previously known bounds. The authors focus on codes with small memory for modulation formats such as pulse amplitude modulation (PAM), m-ary quadrature amplitude modulation (QAM), and m-ary phase shift keying (PSK). The bound is tight to search results for coset codes with a small number of states.}, Doi = {10.1109/18.165452}, Key = {fds236032} } @article{fds236033, Author = {Calderbank, AR}, Title = {Covering machines}, Journal = {Discrete Mathematics}, Volume = {106-107}, Number = {C}, Pages = {105-110}, Year = {1992}, ISSN = {0012-365X}, Abstract = {We construct 2-state covering machines from binary linear codes with a sufficiently rich subcode structure. The goal is to trade multiple covering properties for increased redundancy. We explain why the expected covering properties of covering machines should be superior to those of codes obtained by iterating the ADS construction. © 1992.}, Key = {fds236033} } @article{fds331060, Author = {Calderbank, AR and Frankl, P}, Title = {Improved Upper Bounds Concerning the Erdős-Ko-Rado Theorem}, Journal = {Combinatorics, Probability and Computing}, Volume = {1}, Number = {02}, Pages = {115-122}, Year = {1992}, Month = {June}, url = {http://dx.doi.org/10.1017/S0963548300000134}, Doi = {10.1017/S0963548300000134}, Key = {fds331060} } @article{fds235809, Author = {Calderbank, AR and Fishburn, PC}, Title = {Normalized second moment of the binary lattice determined by a convolutional code}, Journal = {Proceedings of the 1993 IEEE International Symposium on Information Theory}, Pages = {137-}, Year = {1993}, Abstract = {The output of a finite state machine is a collection of codewords that can be searched efficiently to find the optimum codeword with respect to any nonnegative measure that can be calculated on a symbol by symbol basis. Applications involving trellis codes are considered. Although details are given for the convolutional code, the method can be applied to arbitrary codes.}, Key = {fds235809} } @article{fds235810, Author = {Calderbank, AR and Georghiades, CN}, Title = {Coding for the unsynchronized optical OPPM channel}, Journal = {Proceedings of the 1993 IEEE International Conference on Communications}, Pages = {557-561}, Year = {1993}, Abstract = {Random OPPM sequences result in an unrecoverable error floor on both the probability of erroneous synchronization and the probability of symbol error when only chip synchronization is present. It is known, however, that for a given sequence length M, a subset of the set of all possible sequences is synchronizable in the sense that in the absence of noise, the receiver can correctly symbol-synchronize by observing M or more symbol intervals. In this paper we design finite state machines and codes over a J-ary alphabet which produce sequences with the property that every subsequence of length L is synchronizable and introduce algorithms that utilize the memory in the encoded sequences to produce joint estimates of timing and sequences.}, Key = {fds235810} } @article{fds235811, Author = {Calderbank, AR and Fishburn, PC and Rabinovich, A}, Title = {Covering properties of convolutional codes and associated lattices}, Journal = {Proceedings of the 1993 IEEE International Symposium on Information Theory}, Pages = {141-}, Year = {1993}, Abstract = {This talk describes methods for analyzing the expected and worst-case performance of sequence based methods of quantization. We suppose that the quantization algorithm is dynamic programming, where the current step depends on a vector of path metrics, which we call a metric function. Our principal objective is a concise representation of these metric functions and the possible trajectories of the dynamic programming algorithm. We shall consider quantization of equiprobable binary data using a convolutional code. Here the additive group of the code splits the set of metric functions into a finite collection of subsets. The subsets form the vertices of a directed graph, where edges are labelled by aggregate incremental increases in mean squared error (msc). Paths in this graph correspond both to trajectories of the Viterbi algorithm, and to cosets of the code. For the rate 1/2 convolutional code [1 + D2, 1 + D + D2], this graph has only 9 vertices. In this case it is particularly simple to calculate per dimension expected and worst case mse, and performance is similar to the binary [24, 12] Colay code. Our methods also apply to quantization of arbitrary sysmmetric probability distributions on [0, 1] using convolutional codes. For the uniform distribution on [0, 1], the expected mse is the second moment of the 'Voronoi region' of an infinite dimensional lattice determined by the convolutional code. It may also be interpreted as an increase in the reliability of a transmission scheme obtained by nonequiprobable signalling. For certain convolutional codes we obtain a formula for expected mse that depends only on the distribution of differences for a single pair of path metrics.}, Key = {fds235811} } @article{fds235812, Author = {Calderbank, AR and Seshadri, N}, Title = {Multilevel codes for unequal error protection}, Journal = {Proceedings of the 1993 IEEE International Symposium on Information Theory}, Pages = {183-}, Year = {1993}, Abstract = {In many speech and image coding schemes, some of the coded bits are extremely sensitive to channel errors while some others exhibit very little sensitivity. In order to make the best use of channel redundancy, unequal error protection (UEP) codes are needed. In a bandlimited environment, such coding and the modulation should be integrated. In this paper, the authors propose two combined UEP coding and modulation schemes.}, Key = {fds235812} } @article{fds235813, Author = {Calderbank, AR and Graham, RL and Shepp, LA and Frank, P and Li, W-CW}, Title = {Sperner capacity of linear and nonlinear codes for the cyclic triangle}, Journal = {Proceedings of the 1993 IEEE International Symposium on Information Theory}, Pages = {154-}, Year = {1993}, Abstract = {Shannon introduced the concept of zero-error capacity of a discrete memoryless channel. The channel determines an undirected graph on the symbol alphabet, where adjacency means that symbols cannot be confused at the receiver. The zero-error or Shannon capacity is an invariant of this graph. Gargano, Koerner, and Vaccaro have recently extended the concept of Shannon capacity to directed graphs. Their generalization of Shannon capacity is called Sperner capacity. We resolve a problem posed by these authors by giving the first example (the two orientations of the triangle) of a graph where the Sperner capacity depends on the orientations of the edges. Sperner capacity seems to be achieved by nonlinear codes, whereas Shannon capacity seems to be attainable by linear codes. In particular, linear codes do not achieve Sperner capacity for the cyclic triangle. We use Fourier analysis or linear programming to obtain the best upper bounds for linear codes. The bound for unrestricted codes are obtained from rank arguments, eigenvalue interlacing inequalities and polynomial algebra. The statement of the cyclic q-gon problem is very simple: what is the maximum size Nq(n) of a subset Sn of {0, 1, ..., q - 1}n with the property that for every pair of distinct vectors x = (xi), y = (yi) member of Sn, we have xj - yj ≡ 1(mod q) for some j? For q = 3 (the cyclic triangle), we show N3(n) ≅ 2n. If however Sn is a subgroup, then we give a simple proof that |Sn| ≤ √3n.}, Key = {fds235813} } @article{fds235814, Author = {Pottie, GJ and Calderbank, AR}, Title = {Further asymptotic upper bounds on the minimum distance of trellis codes}, Journal = {IEEE Transactions on Information Theory}, Volume = {39}, Number = {4}, Pages = {1428-1434}, Year = {1993}, url = {http://dx.doi.org/10.1109/18.243464}, Abstract = {Asymptotic upper bounds on the minimum distance of trellis codes are derived. A universal bound and bounds specific to PSK and QAM signal sets are obtained.}, Doi = {10.1109/18.243464}, Key = {fds235814} } @article{fds235815, Author = {Calderbank, AR and Seshadri, N}, Title = {Multilevel codes for unequal error protection}, Journal = {IEEE Transactions on Information Theory}, Volume = {39}, Number = {4}, Pages = {1234-1248}, Year = {1993}, url = {http://dx.doi.org/10.1109/18.243441}, Abstract = {In many speech and image coding schemes, some of the coded bits are extremely sensitive to channel errors while some others exhibit very little sensitivity. In order to make the best use of channel redundancy, unequal error protection (UEP) codes are needed. In a bandlimited environment, such coding and the modulation should be integrated. Two combined UEP coding and modulation schemes are proposed. The first method multiplexes different coded signal constellations, with each coded constellation providing a different level of error protection. The novelty here is that a codeword specifies the multiplexing rule and the choice of the codeword from a fixed codebook is used to convey additional important information. The decoder determines the multiplexing rule before decoding the rest of the data. The second method is based on partitioning a signal constellation into disjoint subsets, where the most important data sequence is encoded, using most of the available redundancy, to specify a sequence of subsets. The partitioning and code construction is done to maximize the minimum Euclidean distance between two different valid subset sequences. This leads to novel ways of partitioning the signal constellations into subsets. Finally, the less important data selects a sequence of signal points to be transmitted from the subsets. A side benefit of the proposed set partitioning procedure is a reduction in the number of nearest neighbors, sometimes even over the uncoded signal constellation. Many of the codes designed provided virtually error free transmission (greater than 6-dB coding gain) for some fraction (for example, 25%) of the data while providing a coding gain of 1-2 dB for the remaining data with respect to uncoded transmission. The two methods can also be combined to realize new coded signal constellations for unequal error protection.}, Doi = {10.1109/18.243441}, Key = {fds235815} } @article{fds236034, Author = {Pottie, GJ and Calderbank, AR}, Title = {Channel coding strategies for cellular radio}, Journal = {Proceedings of the 1993 IEEE International Symposium on Information Theory}, Pages = {251-}, Year = {1993}, Abstract = {To improve re-use of time/frequency slots in a cellular radio system, it is desirable for the average interference levels seen by all users to be made approximately equal. We provide constructions based on orthogonal Latin squares that guarantee different sets of users to interfere in successive slots. We illustrate how this may be combined with convolutional coding to provide large performance improvement with low delay in a slow hopped system.}, Key = {fds236034} } @article{fds331058, Author = {Calderbank, AR and Hammons Jr. and AR and Kumar, PV and Sloane, NJA and Sol\'{e, P}, Title = {A Linear Construction for Certain Kerdock \\ and Preparata Codes}, Journal = {Bulletin of the American Mathematical Society}, Volume = {29}, Number = {2}, Pages = {218-223}, Year = {1993}, Month = {January}, url = {http://dx.doi.org/10.1090/S0273-0979-1993-00426-9}, Doi = {10.1090/S0273-0979-1993-00426-9}, Key = {fds331058} } @article{fds331059, Author = {Calderbank, AR and Frankl, P and Graham, RL and Li, WCW and Shepp, LA}, Title = {The Sperner Capacity of Linear and Nonlinear Codes for the Cyclic Triangle}, Journal = {Journal of Algebraic Combinatorics}, Volume = {2}, Number = {1}, Pages = {31-48}, Year = {1993}, Month = {January}, url = {http://dx.doi.org/10.1023/A:1022424630332}, Abstract = {Shannon introduced the concept of zero-error capacity of a discrete memoryless channel. The channel determines an undirected graph on the symbol alphabet, where adjacency means that symbols cannot be confused at the receiver. The zero-error or Shannon capacity is an invariant of this graph. Gargano, Körner, and Vaccaro have recently extended the concept of Shannon capacity to directed graphs. Their generalization of Shannon capacity is called Sperner capacity. We resolve a problem posed by these authors by giving the first example (the two orientations of the triangle) of a graph where the Sperner capacity depends on the orientations of the edges. Sperner capacity seems to be achieved by nonlinear codes, whereas Shannon capacity seems to be attainable by linear codes. In particular, linear codes do not achieve Sperner capacity for the cyclic triangle. We use Fourier analysis or linear programming to obtain the best upper bounds for linear codes. The bounds for unrestricted codes are obtained from rank arguments, eigenvalue interlacing inequalities and polynomial algebra. The statement of the cyclic q-gon problem is very simple: what is the maximum size N q (n) of a subset S n of {0, 1, (Formula presented.), q−1} n with the property that for every pair of distinct vectors x = (x i ), y = (y i ) (Formula presented.)S n , we have x j −y j ≡ 1(mod q) for some j? For q = 3 (the cyclic triangle), we show N 3 (n)≃2 n . If however S n is a subgroup, then we give a simple proof that (Formula presented.). © 1993, Kluwer Academic Publishers. All rights reserved.}, Doi = {10.1023/A:1022424630332}, Key = {fds331059} } @article{fds331056, Author = {Calderbank, AR and Delsarte, P}, Title = {Extending the $t$-design concept}, Journal = {Transactions of the American Mathematical Society}, Volume = {338}, Number = {2}, Pages = {941-952}, Year = {1993}, Month = {February}, url = {http://dx.doi.org/10.1090/S0002-9947-1993-1134756-0}, Doi = {10.1090/S0002-9947-1993-1134756-0}, Key = {fds331056} } @article{fds235816, Author = {Calderbank, AR and Fishburn, PC}, Title = {Normalized second moment of the binary lattice determined by a convolutional code}, Journal = {IEEE Transactions on Information Theory}, Volume = {40}, Number = {1}, Pages = {166-174}, Year = {1994}, url = {http://dx.doi.org/10.1109/18.272475}, Abstract = {We calculate the per-dimension mean squared error μ(S) of the two-state convolutional code C with generator matrix [1,1+D], for the symmetric binary source S = {0,1}, and for the uniform source S = [0,1]. When S = {0,1}, the quantity μ(S) is the second moment of the coset weight distribution, which gives the expected Hamming distance of a random binary sequence from the code. When S = [0,1], the quantity μ(S) is the second moment of the Voronoi region of the modulo 2 binary lattice determined by C. The key observation is that a convolutional code with 2v states gives 2v approximations to a given source sequence, and these approximations do not differ very much. It is possible to calculate the steady state distribution for the differences in these path metrics, and hence, the second moment. In this paper we shall only give details for the convolutional code [1,1+D], but the method applies to arbitrary codes. We also define the covering radius of a convolutional code, and calculate this quantity for the code [1,1+D].}, Doi = {10.1109/18.272475}, Key = {fds235816} } @article{fds235817, Author = {Kumar, PV and Helleseth, T and Calderbank, AR and Jr, ARH}, Title = {Large families of quaternary sequences with low correlation}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Year = {1994}, Abstract = {A nested chain of quaternary-sequence families having low correlation values is presented. The families are suitable for application in CDMA systems employing QPSK modulation.}, Key = {fds235817} } @article{fds235818, Author = {Kumar, PV and Helleseth, T and Calderbank, AR}, Title = {Upper bound for some exponential sums over Galois rings and applications}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Year = {1994}, Abstract = {An upper bound for Weil-type exponential sums over Galois rings is presented together with some examples where the bound is tight. The bound may be regarded as the Galois-ring analogue of the well-known Weil-Carlitz-Uchiyama bound for exponential sums over finite fields. An application of the bound to the design of large families of eight-phase sequences having low correlation is also given.}, Key = {fds235818} } @article{fds235819, Author = {McLaughlin, SW and Calderbank, AR and Laroia, R}, Title = {Modulation codes for multi-amplitude optical recording channels}, Journal = {National Conference Publication - Institution of Engineers, Australia}, Volume = {2}, Number = {94 /9}, Pages = {941-945}, Year = {1994}, Abstract = {We consider the problem of coding for a recording channel. Traditional magnetic or optical channels employ saturation recording, where the input to the channel is a two-level waveform. A new optical recording channel has been developed that supports unsaturated, M-ary (M≥3) signal levels. In this paper we introduce the new channel and discuss modulation codes for it. In particular, we consider the analysis and design of new partial response codes for these channels. Comparisons are made with M-ary runlength limited codes. The partial response codes achieve the largest known storage density with coding gains of 3 - 5.5 dB above M-ary runlength limited codes.}, Key = {fds235819} } @article{fds235820, Author = {Jr, ARH and Kumar, PV and Calderbank, AR and Sloane, NJA and Sole, P}, Title = {Z_{4}-linearity of Kerdock, Preparata, Goethals, and related codes}, Journal = {IEEE Transactions on Information Theory}, Volume = {40}, Number = {2}, Pages = {301-319}, Year = {1994}, url = {http://dx.doi.org/10.1109/18.312154}, Abstract = {Certain notorious nonlinear binary codes contain more codewords than any known linear code. These include the codes constructed by Nordstrom-Robinson, Kerdock, Preparata, Goethals, and Delsarte-Goethals. It is shown here that all these codes can be very simply constructed as binary images under the Gray map of linear codes over Z4, the integers mod 4 (although this requires a slight modification of the Preparata and Goethals codes). The construction implies that all these binary codes are distance invariant. Duality in the Z4 domain implies that the binary images have dual weight distributions. The Kerdock and 'Preparata' codes are duals over Z4 - and the Nordstrom-Robinson code is self-dual - which explains why their weight distributions are dual to each other. The Kerdock and 'Preparata' codes are Z4-analogues of first-order Reed-Muller and extended Hamming codes, respectively. All these codes are extended cyclic codes over Z4, which greatly simplifies encoding and decoding. An algebraic hard-decision decoding algorithm is given for the 'Preparata' code and a Hadamard-transform soft-decision decoding algorithm for the Kerdock code. Binary first-and second-order Reed-Muller codes are also linear over Z4, but extended Hamming codes of length n ≥ 32 and the Golay code are not. Using Z4-linearity, a new family of distance regular graphs are constructed on the cosets of the 'Preparata' code.}, Doi = {10.1109/18.312154}, Key = {fds235820} } @article{fds235821, Author = {Calderbank, AR and Georghiades, CN}, Title = {Synchronizable codes for the optical OPPM channel}, Journal = {IEEE Transactions on Information Theory}, Volume = {40}, Number = {4}, Pages = {1097-1107}, Year = {1994}, url = {http://dx.doi.org/10.1109/18.335965}, Abstract = {Random overlapping pulse-position modulation (OPPM) sequences result in an unrecoverable error floor on both the probability of erroneous synchronization and the probability of symbol error when only chip synchronization is present. It is known, however, that for a given sequence length M, a subset of the set of all possible sequences is synchronizable in the sense that in the absence of noise, the receiver can correctly symbol synchronize by observing M or more symbol intervals. In this paper we design finite-state machines and codes over a J-ary alphabet, which produce sequences with the property that every subsequence of length L is synchronizable. Some of the codes, in addition to being synchronizable, produce a coding gain. For an optical Poisson channel we introduce joint synchronization and detection algorithms that utilize the memory in the encoded sequences to produce joint estimates of timing and sequences. Their performance is analyzed through simulations and analytical results.}, Doi = {10.1109/18.335965}, Key = {fds235821} } @article{fds236035, Author = {Calderbank, AR and Fishburn, PC}, Title = {Maximal three-independent subsets of {0, 1, 2}^{n}}, Journal = {Designs, Codes and Cryptography}, Volume = {4}, Number = {4}, Pages = {203-211}, Year = {1994}, ISSN = {0925-1022}, url = {http://dx.doi.org/10.1007/BF01388452}, Abstract = {We consider a variant of the classical problem of finding the size of the largest cap in the r-dimensional projective geometry PG(r, 3) over the field IF3 with 3 elements. We study the maximum size f(n) of a subset S of IF3n with the property that the only solution to the equation x1+x2+x3=0 is x1=x2=x3. Let cn=f(n)1/n and c=sup{c1, c2, ...}. We prove that c>2.21, improving the previous lower bound of 2.1955 ... © 1994 Kluwer Academic Publishers.}, Doi = {10.1007/BF01388452}, Key = {fds236035} } @article{fds236036, Author = {Betts, W and Calderbank, AR and Laroia, R}, Title = {Performance of nonuniform constellations on the Gaussian channel}, Journal = {IEEE Transactions on Information Theory}, Volume = {40}, Number = {5}, Pages = {1633-1638}, Year = {1994}, url = {http://dx.doi.org/10.1109/18.333880}, Abstract = {Testing of high-speed voiceband modems has revealed a significant increase in distortion for points near the perimeter of a QAM signal constellation. This distortion increases with distance from the center of the constellation and limits performance at data rates above 19.2 kb/s. The perimeter distortion can be reduced by transforming the signal constellation so that points near the center are closer together, and points near the perimeter are further apart. When the channel SNR is high, such a transformation reduces immunity to Gaussian noise because points near the center of the transformed constellation are closer together than in a uniformly spaced constellation with the same average power. This paper demonstrates theoretically that for channel SNR's of practical interest, there is actually a small gain in immunity to Gaussian noise. In fact, an appropriate coded modulation scheme can produce gains of about 0.25 dB.}, Doi = {10.1109/18.333880}, Key = {fds236036} } @article{fds331055, Author = {Calderbank, AR and Hanlon, P and Sundaram, S}, Title = {Representations of the symmetric group in deformations of the free Lie algebra}, Journal = {Transactions of the American Mathematical Society}, Volume = {341}, Number = {1}, Pages = {315-333}, Year = {1994}, Month = {January}, url = {http://dx.doi.org/10.1090/S0002-9947-1994-1153011-7}, Doi = {10.1090/S0002-9947-1994-1153011-7}, Key = {fds331055} } @article{fds235762, Author = {Vijay Kumar and P and Helleseth, T and Calderbank, AR and Hammons, AR}, Title = {Large families of quaternary sequences with low correlation}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Pages = {71-}, Year = {1994}, Month = {December}, ISSN = {2157-8095}, url = {http://dx.doi.org/10.1109/ISIT.1994.394899}, Abstract = {A nested chain of quaternary-sequence families having low correlation values is presented. The families are suitable for application in CDMA systems employing QPSK modulation.}, Doi = {10.1109/ISIT.1994.394899}, Key = {fds235762} } @article{fds235763, Author = {Kumar, PV and Helleseth, T and Calderbank, AR}, Title = {Upper bound for some exponential sums over Galois rings and applications}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Pages = {70-}, Year = {1994}, Month = {December}, ISSN = {2157-8095}, url = {http://dx.doi.org/10.1109/ISIT.1994.394900}, Abstract = {An upper bound for Weil-type exponential sums over Galois rings is presented together with some examples where the bound is tight. The bound may be regarded as the Galois-ring analogue of the well-known Weil-Carlitz-Uchiyama bound for exponential sums over finite fields. An application of the bound to the design of large families of eight-phase sequences having low correlation is also given.}, Doi = {10.1109/ISIT.1994.394900}, Key = {fds235763} } @article{fds236037, Author = {Gelblum, EA and Calderbank, AR}, Title = {Forbidden rate region for generalized cross constellations}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Pages = {149-}, Year = {1995}, Abstract = {An analysis of the Generalized Cross Constellation (GCC) is presented and a new perspective on its coding algorithm is described. We show how the GCC can be used to address generic sets of symbol points in any multidimensional space through an example based on the matched spectral null coding used in magnetic recording devices. We also prove that there is a forbidden rate region of fractional coding rates that are practically unrealizable using the GCC construction. We introduce the idea of a constellation tree and show how its decomposition can be used to design GCC's matching desired parameters. Following this analysis, an algorithm to design the optimal rate GCC from a restriction on the maximum size of its constellation signal set is given, and a formula for determining the size of the GCC achieving a desired coding rate is derived. We finish with an upper bound on the size of the constellation expansion ratio.}, Key = {fds236037} } @article{fds236038, Author = {Seshadri, N and Calderbank, AR and Pottie, G}, Title = {Channel coding for cochannel interference suppression in wireless communication systems}, Journal = {IEEE Vehicular Technology Conference}, Volume = {2}, Pages = {629-633}, Year = {1995}, Abstract = {Cochannel interference is a major impairment in cellular systems. In practice the performance of time and frequency division multiple access (TDMA and FDMA) systems is limited by a few dominant cochannel interferers. Conventional channel coding techniques treat this interference as noise to mitigate its effect. In this work it is shown that cochannel interference can be totally suppressed by using a adaptive non-linear decoder. We illustrate our ideas using codes in real (complex) field as well as codes in finite field. The decoding technique can be combined with antenna diversity to offer increased interference suppression capability.}, Key = {fds236038} } @article{fds236039, Author = {Seshadri, N and Calderbank, AR and Pottie, GJ}, Title = {Channel coding for co-channel interference suppression in wireless communications}, Journal = {IEEE International Conference on Communications}, Volume = {2}, Pages = {884-888}, Year = {1995}, Abstract = {Co-channel interference is a major impairment in wireless systems with channel re-use. In practice the performance of time division multiple access (TDMA) and frequency division multiple access (FDMA) systems is limited by a few dominant co-channel interferers. We present channel codes that are matched to an adaptive linear receiver, so that the combination provides interference suppression. It is shown that a simple one symbol parity check code is capable of suppressing one interferer, a repetition code of length N is capable of suppressing N-1 interferers, and a code of K information symbols and N channel symbols is capable of suppressing N/K interferers. With simple parity check codes and repetition codes, the tap setting of an adaptive combiner can be configured using a 20-40 symbol training sequence. Simulations for multiple cells reveal significant capacity improvement is possible.}, Key = {fds236039} } @article{fds236040, Author = {Bonnecaze, A and Sole, P and Calderbank, AR}, Title = {Quaternary quadratic residue codes and unimodular lattices}, Journal = {IEEE Transactions on Information Theory}, Volume = {41}, Number = {2}, Pages = {366-377}, Year = {1995}, url = {http://dx.doi.org/10.1109/18.370138}, Abstract = {We construct new self-dual and isodual codes over the integers modulo 4. The binary images of these codes under the Gray map are nonlinear, but formally self-dual. The construction involves Hensel lifting of binary cyclic codes. Quaternary quadratic residue codes are obtained by Hensel lifting of the classical binary quadratic residue codes. Repeated Hensel lifting produces a universal code defined over the 2-adic integers. We investigate the connections between this universal code and the codes defined over Z4, the composition of the automorphism group, and the structure of idempotents over Z4. We also derive a square root bound on the minimum Lee weight, and explore the connections with the finite Fourier transform. Certain self-dual codes over Zd are shown to determine even unimodular lattices, including the extended quadratic residue code of length q + 1, where q ≡ -1(mod 8) is a prime power. When q = 23, the quaternary Golay code determines the Leech lattice in this way. This is perhaps the simplest construction for this remarkable lattice that is known.}, Doi = {10.1109/18.370138}, Key = {fds236040} } @article{fds236041, Author = {Best, MR and Burnashev, MV and Levy, Y and Rabinovich, A and Fishburn, PC and Calderbank, AR and Jr, DJC}, Title = {On a technique to calculate the exact performance of a convolutional code}, Journal = {IEEE Transactions on Information Theory}, Volume = {41}, Number = {2}, Pages = {441-447}, Year = {1995}, url = {http://dx.doi.org/10.1109/18.370145}, Abstract = {A Markovian technique is described to calculate the exact performance of the Viterbi algorithm used as either a channel decoder or a source encoder for a convolutional code. The probability of information bit error and the expected Hamming distortion are computed for codes of various rates and constraint lengths. The concept of tie-breaking rules is introduced and its influence on decoder performance is examined. Computer simulation is used to verify the accuracy of the results. Finally, we discuss the issue of when a coded system outperforms an uncoded system in light of the new results.}, Doi = {10.1109/18.370145}, Key = {fds236041} } @article{fds236042, Author = {Kumar, PV and Helleseth, T and Calderbank, AR}, Title = {Upper bound for Weil exponential sums over Galois rings and applications}, Journal = {IEEE Transactions on Information Theory}, Volume = {41}, Number = {2}, Pages = {456-468}, Year = {1995}, url = {http://dx.doi.org/10.1109/18.370147}, Abstract = {We present an analog of the well-known Weil-Carlitz-Uchiyama upper bound for exponential sums over finite fields for exponential sums over Galois rings. Some examples are given where the bound is tight. The bound has immediate application to the design of large families of phase-shift-keying sequences having low correlation and an alphabet of size pe, p prime, e ≥ 2. Some new constructions of eight-phase sequences are provided.}, Doi = {10.1109/18.370147}, Key = {fds236042} } @article{fds236043, Author = {Calderbank, AR and Fishburn, PC and Rabinovich, A}, Title = {Covering properties of convolutional codes and associated lattices}, Journal = {IEEE Transactions on Information Theory}, Volume = {41}, Number = {3}, Pages = {732-746}, Year = {1995}, url = {http://dx.doi.org/10.1109/18.382019}, Abstract = {This study proposes several Markov methods for the analysis of the expected and worst case performance of sequence-based methods of quantization. The quantization algorithm is assumed as a dynamic programming where the current step is dependent on metric functions. The main objective is to obtain a concise representation of these metric functions including the possible trajectories of the dynamic programming algorithm. To demonstrate this, the quantization of equiprobable binary data using a convolutional code is considered. In addition, these methods are also applicable to the quantization of arbitrary symmetric probability distributions using convolutional codes. For certain convolutional codes a formula that depends only on the distribution of differences for a single pair of path metrics is derived for expected use.}, Doi = {10.1109/18.382019}, Key = {fds236043} } @article{fds236044, Author = {Calderbank, AR and McGuire, G}, Title = {Z_{4}-linear codes obtained as projections of Kerdock and Delsarte-Goethals codes}, Journal = {Linear Algebra and its Applications}, Volume = {226-228}, Number = {C}, Pages = {647-665}, Year = {1995}, ISSN = {0024-3795}, url = {http://dx.doi.org/10.1016/0024-3795(95)00239-N}, Abstract = {The Kerdock and Delsarte-Goethals codes can be very simply constructed as binary images under a certain natural map, called the Gray map, of linear codes over Z4, the integers modulo 4. We consider the Gray images of linear codes over Z4 obtained from the Kerdock and Delsarte-Goethals codes by projection on a hyperplane. For m odd, certain Gray images have the same weight distribution as duals of extended binary BCH codes of length 2m, but are not equivalent to these codes. Inequivalence follows from a general theorem identifying binary linear codes that are not Gray images of linear codes over Z4. © 1995.}, Doi = {10.1016/0024-3795(95)00239-N}, Key = {fds236044} } @article{fds236045, Author = {Calderbank, AR and Sloane, NJA}, Title = {Modular and p-adic cyclic codes}, Journal = {Designs, Codes and Cryptography}, Volume = {6}, Number = {1}, Pages = {21-35}, Year = {1995}, ISSN = {0925-1022}, url = {http://dx.doi.org/10.1007/BF01390768}, Abstract = {This paper presents some basic theorems giving the structure of cyclic codes of length n over the ring of integers modulo pa and over the p-adic numbers, where p is a prime not dividing n. An especially interesting example is the 2-adic cyclic code of length 7 with generator polynomial X3+λX2+(λ-1)X-1, where λ satisfies λ2 - λ + 2 = 0. This is the 2-adic generalization of both the binary Hamming code and the quaternary octacode (the latter being equivalent to the Nordstrom-Robinson code). Other examples include the 2-adic Golay code of length 24 and the 3-adic Golay code of length 12. © 1995 Kluwer Academic Publishers.}, Doi = {10.1007/BF01390768}, Key = {fds236045} } @article{fds236046, Author = {McGuire, G and Calderbank, AR}, Title = {Proof of a conjecture of sarwate and pursley regarding pairs of binary m-sequences}, Journal = {IEEE Transactions on Information Theory}, Volume = {41}, Number = {4}, Pages = {1153-1155}, Year = {1995}, url = {http://dx.doi.org/10.1109/18.391260}, Abstract = {Binary m-sequences are maximal length sequences generated by shift registers of length m, that are employed in navigation, radar, and spread-spectrum communications systems, because of their crosscorrelation properties. It is well known that given a pair of distinct m-sequences, the crosscorrelation function must take on at least three values. This correspondence considers crosscorrelation functions that take on exactly three values, and where these values are preferred in that they are small. The main result is a proof of a conjecture made by Sarwate and Pursley in 1980, that if m ≡ 0 (mod 4) then there are no preferred pairs of binary m-sequences. The proof makes essential use of a deep theorem of McEliece that restricts the possible weights that can occur in a binary cyclic code.}, Doi = {10.1109/18.391260}, Key = {fds236046} } @article{fds236047, Author = {Pottie, GJ and Calderbank, AR}, Title = {Channel coding strategies for cellular radio}, Journal = {IEEE Transactions on Vehicular Technology}, Volume = {44}, Number = {4}, Pages = {763-770}, Year = {1995}, url = {http://dx.doi.org/10.1109/25.467960}, Abstract = {To improve re-use of time/frequency slots in a cellular radio system, it is desirable for the average interference levels seen by all users to be made approximately equal. We provide constructions based on orthogonal latin squares that guarantee different sets of users will interfere in successive slots. When signal to interference ratios are independent from successive symbols, channel codes can provide a large diversity gain which is far in excess of the gain against additive noise. Consequently, coding with interleaving fits together very naturally with this construction. We illustrate how to achieve large performance improvement using convolutional codes with low decoding delay in a slow hopped system.}, Doi = {10.1109/25.467960}, Key = {fds236047} } @article{fds236048, Author = {Calderbank, AR and Shor, PW}, Title = {Good quantum error-correcting codes exist}, Journal = {Physical Review A - Atomic, Molecular, and Optical Physics}, Volume = {54}, Number = {2}, Pages = {1098-1105}, Year = {1996}, Abstract = {A quantum error-correcting code is defined to be a unitary mapping (encoding) of k qubits (two-state quantum systems) into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not necessarily independently, the resulting n qubits can be used to faithfully reconstruct the original quantum state of the k encoded qubits. Quantum error-correcting codes are shown to exist with asymptotic rate k/n = 1-2H2(2t/n) where H2(P) is the binary entropy function -plog2p-(1 -p)log2(l - p). Upper bounds on this asymptotic rate are given.}, Key = {fds236048} } @article{fds236049, Author = {Calderbank, AR and McGuire, G and Kumar, PV and Helleseth, T}, Title = {Cyclic codes over ℤ_{4}locator polynomials, and newton's identities}, Journal = {IEEE Transactions on Information Theory}, Volume = {42}, Number = {1}, Pages = {217-226}, Year = {1996}, ISSN = {0018-9448}, url = {http://dx.doi.org/10.1109/18.481791}, Abstract = {Certain nonlinear binary codes contain more code-words than any comparable linear code presently known. These include the Kerdock and Preparata codes that can be very simply constructed as binary images, under the Gray map, of linear codes over ℤ4 that are defined by means of parity checks involving Galois rings. This paper describes how Fourier transforms on Galois rings and elementary symmetric functions can be used to derive lower bounds on the minimum distance of such codes. These methods and techniques from algebraic geometry are applied to find the exact minimum distance of a family of ℤ4-linear codes with length 2m (m, odd) and size 22m+1-5m-2. The Gray image of the code of length 32 is the best (64, 237) code that is presently known. This paper also determines the exact minimum Lee distance of the linear codes over ℤ4 that are obtained from the extended binary two- and three-error-correcting BCH codes by Hensel lifting. The Gray image of the Hensel lift of the three-error-correcting BCH code of length 32 is the best (64, 232) code that is presently known. This code also determines an extremal 32-dimensional even unimodular lattice. © 1996 IEEE.}, Doi = {10.1109/18.481791}, Key = {fds236049} } @article{fds236050, Author = {Calderbank, AR}, Title = {Signal design for co-channel interference suppression with applications to wireless communications}, Journal = {Electro International, Conference Proceedings}, Pages = {47-}, Year = {1996}, Abstract = {Co-channel interference is a major impairment in wireless systems with channel (frequency and/or time) re-use. In practice the performance of Time Division Multiple Access (TDMA) and Frequency Division Multiple Access (FDMA) systems is limited by a few dominant co-channel interferers. These can be removed by means of multiple antennas but it is difficult to demand this at the mobile because of technology limitations. The standard solution is to treat co-channel interference as Gaussian noise and to employ powerful channel codes. However, this solution is far from optimal since the decoder is using an inappropriate metric for decoding. In this paper it is shown that a more effective use of system redundancy is to design channel codes that are matched to an adaptive linear receiver, so that the combination provides interference suppression. It is shown that a simple one symbol parity check code is capable of suppressing one interferer, a repetition code of length N is capable of suppressing N - 1 interferers, and a code of K information symbols and N channel symbols is capable of suppressing N/K interferers.}, Key = {fds236050} } @article{fds236051, Author = {Kumar, PV and Helleseth, T and Calderbank, AR and Jr, ARH}, Title = {Large families of quaternary sequences with low correlation}, Journal = {IEEE Transactions on Information Theory}, Volume = {42}, Number = {2}, Pages = {579-592}, Year = {1996}, ISSN = {0018-9448}, url = {http://dx.doi.org/10.1109/18.485726}, Abstract = {A family of quaternary (Z4-alphabet) sequences of length L = T -1, size M > L2 +3X+2, and maximum nontrivial correlation parameter Cmax < 2√L + 1 + 1 is presented. The sequence family always contains the four-phase family A. When r is odd, it includes the family of binary Gold sequences. The sequence family is easily generated using two shift registers, one binary, the other quaternary. The distribution of correlation values is provided. The construction can be extended to produce a chain of sequence families, with each family in the chain containing the preceding family. This gives the design flexibility with respect to the number of intermittent users that can be supported, in a code-division multiple-access cellular radio system. When r is odd, the sequence families in the chain correspond to shortened Z4 -linear versions of the Delsarte-Goethals codes. Index Terms-. © 1996 IEEE.}, Doi = {10.1109/18.485726}, Key = {fds236051} } @article{fds236052, Author = {Calderbank, AR and Sloane, NJA}, Title = {The ternary golay code, the integers mod 9, and the coxeter-todd lattice}, Journal = {IEEE Transactions on Information Theory}, Volume = {42}, Number = {2}, Pages = {636-637}, Year = {1996}, ISSN = {0018-9448}, url = {http://dx.doi.org/10.1109/18.485733}, Abstract = {The 12-dimensinnal Coxeter-Todd lattice can be obtained by lifting the ternary Golay code to a code over the integers mod 9 and applying Construction A. © 1996 IEEE.}, Doi = {10.1109/18.485733}, Key = {fds236052} } @article{fds236053, Author = {Calderbank, AR and McGuire, G and Poonen, B and Rubinstein, M}, Title = {On a conjecture of Helleseth regarding pairs of binary m-sequences}, Journal = {IEEE Transactions on Information Theory}, Volume = {42}, Number = {3}, Pages = {988-990}, Year = {1996}, ISSN = {0018-9448}, url = {http://dx.doi.org/10.1109/18.490561}, Abstract = {Binary m-sequences are maximal-length sequences generated by shift registers of length m, that are employed in navigation, radar, and spread-spectrum communication. It is well known that given a pair of distinct /«-sequences, the crosscorrelation function must take on at least three values. This correspondence addresses a conjecture made by Helleseth in 1976, that if rn is a power of 2, then there are no pairs of binary m-sequences with a 3-valued crosscorrelation function. This conjecture is proved under the assumption that the three correlation values are symmetric about -1. © 1996 IEEE.}, Doi = {10.1109/18.490561}, Key = {fds236053} } @article{fds235822, Author = {Calderbank, AR and Mcguire, G}, Title = {Construction of a (64,2^{37},12) Code via Galois Rings}, Journal = {Designs, Codes, and Cryptography}, Volume = {10}, Number = {2}, Pages = {157-165}, Year = {1997}, Abstract = {Certain nonlinear binary codes contain more codewords than any comparable linear code presently known. These include the Kerdock and Preparata codes, which exist for all lengths 4m ≥ 16. At length 16 they coincide to give the Nordstrom-Robinson code. This paper constructs a nonlinear (64, 237, 12) code as the binary image, under the Gray map, of an extended cyclic code defined over the integers modulo 4 using Galois rings. The Nordstrom-Robinson code is defined in this same way, and like the Nordstrom-Robinson code, the new code is better than any linear code that is presently known.}, Key = {fds235822} } @article{fds235823, Author = {Calderbank, AR and Rains, EM and Shor, PW and Sloane, NJA}, Title = {Quantum error correction and orthogonal geometry}, Journal = {Physical Review Letters}, Volume = {78}, Number = {3}, Pages = {405-408}, Year = {1997}, Abstract = {A group theoretic framework is introduced that simplifies the description of known quantum error-correcting codes and greatly facilitates the construction of new examples. Codes are given which map 3 qubits to 8 qubits correcting 1 error, 4 to 10 qubits correcting 1 error, 1 to 13 qubits correcting 2 errors, and 1 to 29 qubits correcting 5 errors.}, Key = {fds235823} } @article{fds235824, Author = {Seshadri, N and Tarokh, V and Calderbank, AR}, Title = {Space-time codes for wireless communication: Code construction}, Journal = {IEEE Vehicular Technology Conference}, Volume = {2}, Pages = {637-641}, Year = {1997}, Abstract = {We consider the design of channel codes for improving the data rate and/or the reliability of communications over fading channels using multiple transmit antennas. Here, data is encoded by a channel code and the encoded data is split into n streams that are simultaneously transmitted using n transmit antennas. The received signal at each receive antenna is a linear superposition of the n transmitted signals. We review the performance criteria for designing such codes under the assumption that the fading is slow and frequency non-selective established in [3]. Performance is determined by diversity gain quantified by ranks and coding gain quantified by determinants of certain matrices that are constructed from the code sequences. The performance criterion is then used to design trellis codes for high data rate wireless communication. These codes are easy to encode and decode. They provide the best trade-off between data rate, diversity gain, constellation size and trellis complexity. Simulation results are provided for 4 and 8 PSK signal sets with data rates of 2 and 3 bits/symbol, demonstrating excellent performance that is within 2-3 dB of the outage capacity for these channels.}, Key = {fds235824} } @article{fds235825, Author = {Tarokh, V and Naguib, AF and Seshadri, N and Calderbank, AR}, Title = {Space-time codes for high data rate wireless communication: Mismatch analysis}, Journal = {IEEE International Conference on Communications}, Volume = {1}, Pages = {309-313}, Year = {1997}, Abstract = {We revisit Space-Time Codes for a mobile communication system that employs multiple antennas at the base and optional antenna diversity at the mobile station. The realistic case when the channel state is not completely known is considered. It is assumed that the channel estimator extracts the fade coefficients using orthogonal pilot tones. Mismatch analysis is then carried out. It is proved that in the absence of ideal channel state information the design criteria for space-time codes developed in [11] is still valid for equal energy constellation case. Using our derivation, it is observed that channel estimation techniques commonly used over rapidly fading channels can be used in conjunction with space-time codes provided that the number of transmit antennas is small.}, Key = {fds235825} } @article{fds235826, Author = {Calderbank, AR and Seshadri, N and Tarokh, V}, Title = {Space-time codes for wireless communication}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Pages = {146-}, Year = {1997}, Abstract = {The design of channel codes for improvement the data rate and/or the reliability of communications over fading channels using multiple transmit antennas is considered. A design criterion is provided and is then used to design space-time codes for high data rate wireless communication. These codes are trellis codes that are easy to encode and decode and have remarkable performance.}, Key = {fds235826} } @article{fds235827, Author = {Tarokh, V and Seshadri, N and Calderbank, AR}, Title = {Space-time codes for high data rate wireless communication: Performance criteria}, Journal = {IEEE International Conference on Communications}, Volume = {1}, Pages = {299-303}, Year = {1997}, Abstract = {We consider the design of channel codes for improving the data rate and/or the reliability of communications over fading channels using multiple transmit antennas. Here, data is encoded by a channel code and the encoded data is split into n streams that are simultaneously transmitted using n transmit antennas. The received signal at each receive antenna is a linear superposition of the n transmitted signals. We derive performance criteria for designing channel codes under the assumption that the fading is slow and frequency non-selective. Performance is shown to be determined by diversity gain quantified by ranks and coding gain quantified by determinants of certain matrices that are constructed from the code sequences.}, Key = {fds235827} } @article{fds235828, Author = {Calderbank, AR and Daubechies, I and Sweldens, W and Yeo, B-L}, Title = {Lossless image compression using integer to integer wavelet transforms}, Journal = {IEEE International Conference on Image Processing}, Volume = {1}, Pages = {596-599}, Year = {1997}, Abstract = {Invertible wavelet transforms that map integers to integers are important for lossless representations. In this paper, we present an approach to build integer to integer wavelet transforms based upon the idea of factoring wavelet transforms into lifting steps. This allows the construction of an integer version of every wavelet transform. We demonstrate the use of these transforms in lossless image compression.}, Key = {fds235828} } @article{fds236054, Author = {Calderbank, AR and Rains, EM and Shor, PW and Sloane, NJA}, Title = {Quantum error correction via codes over GF(4)}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Pages = {292-}, Year = {1997}, Abstract = {The unreasonable effectiveness of quantum computing is founded on coherent quantum superposition or entanglement which allows a large number of calculations to be performed simultaneously. This coherence is lost as a quantum system interacts with its environment. In the present paper the problem of finding quantum-error-correcting codes is transformed into one of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product. Many new codes and new bounds are presented, as well as a table of upper and lower bounds on such codes of length up to 30 qubits.}, Key = {fds236054} } @article{fds236055, Author = {Gelblum, EA and Calderbank, AR}, Title = {A forbidden rate region for generalized cross constellations}, Journal = {IEEE Transactions on Information Theory}, Volume = {43}, Number = {1}, Pages = {335-341}, Year = {1997}, ISSN = {0018-9448}, url = {http://dx.doi.org/10.1109/18.567754}, Abstract = {An analysis of the Generalized Cross Constellation (GCC) is presented and a new perspective on its coding algorithm is described. We show how the GCC can be used to address generic sets of symbol points in any multidimensional space through an example based on the matched spectral null coding used in magnetic recording devices. We also prove that there is a forbidden rate region of fractional coding rates that are practically unrealizable using the GCC construction. We introduce the idea of a constellation tree and show how its decomposition can be used to design GCC's matching desired parameters. Following this analysis, an algorithm to design the optimal rate GCC from a restriction on the maximum size of its constellation signal set is given, and a formula for determining the size of the GCC achieving a desired coding rate is derived. We finish with an upper bound on the size of the constellation expansion ratio. © 1997 IEEE.}, Doi = {10.1109/18.567754}, Key = {fds236055} } @article{fds236056, Author = {Calderbank, AR and Li, W-CW and Poonen, B}, Title = {A 2-adic approach to the analysis of cyclic codes}, Journal = {IEEE Transactions on Information Theory}, Volume = {43}, Number = {3}, Pages = {977-986}, Year = {1997}, ISSN = {0018-9448}, url = {http://dx.doi.org/10.1109/18.568706}, Abstract = {This paper describes how 2-adic numbers can be used to analyze the structure of binary cyclic codes and of cyclic codes defined over ℤ 2a, a ≥ 2, the ring of integers modulo 2 a. It provides a 2-adic proof of a theorem of McEliece that characterizes the possible Hamming weights that can appear in a binary cyclic code. A generalization of this theorem is derived that applies to cyclic codes over ℤ 2a that are obtained from binary cyclic codes by a sequence of Hensel lifts. This generalization characterizes the number of times a residue modulo 2 a appears as a component of an arbitrary codeword in the cyclic code. The limit of the sequence of Hensel lifts is a universal code defined over the 2-adic integers. This code was first introduced by Calderbank and Sloane (1995), and is the main subject of this paper. Binary cyclic codes and cyclic codes over ℤ 2aare obtained from these universal codes by reduction modulo some power of 2. A special case of particular interest is cyclic codes over ℤ 4 that are obtained from binary cyclic codes by means of a single Hensel lift. The binary images of such codes under the Gray isometry include the Kerdock, Preparata, and Delsarte-Goethals codes. These are nonlinear binary codes that contain more codewords than any linear code presently known. Fundamental understanding of the composition of codewords in cyclic codes over ℤ 4 is central to the search for more families of optimal codes. This paper also constructs even unimodular lattices from the Hensel lift of extended binary cyclic codes that are self-dual with all Hamming weights divisible by 4. The Leech lattice arises in this way as do extremal lattices in dimensions 32 through 48. © 1997 IEEE.}, Doi = {10.1109/18.568706}, Key = {fds236056} } @article{fds236057, Author = {Tarokh, V and Naguib, A and Seshadri, N and Calderbank, AR}, Title = {Low-rate multi-dimensional space-time codes for both slow and rapid fading channels}, Journal = {IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, PIMRC}, Volume = {3}, Pages = {1206-1210}, Year = {1997}, Abstract = {We consider the design of channel codes for improving the data rate and/or the reliability of communications using multiple transmit antennas over a fading channel. It is assumed that the transmitter does not know the channel but seeks to choose a codebook that guarantees a diversity gain of r1 when there is no mobility and a diversity gain of r2≥r1 when the channel is fast fading. A solution to this problem is unveiled in this paper. Here, the encoded data is split into n streams that are simultaneously transmitted using n transmit antennas. The signal received at each receive antenna is a superposition of the faded versions of the n transmitted signals. We derive performance criteria for designing codes having the aforementioned properties. Performance is shown to be determined by diversity advantage quantified by a rank/distance and coding advantage quantified by a determinant/product criterion. The criteria is used to design codes for both slow and rapid fading channels. The constructed codes have remarkable performance in low signal to noise ratios and are suitable for improving the frequency reuse factor under a variety of mobility conditions.}, Key = {fds236057} } @article{fds236058, Author = {Calderbank, AR and Cameron, PJ and Kantor, WM and Seidel, JJ}, Title = {ℤ_{4}-kerdock codes, orthogonal spreads, and extremal euclidean line-sets}, Journal = {Proceedings of the London Mathematical Society}, Volume = {75}, Number = {2}, Pages = {436-480}, Year = {1997}, ISSN = {0024-6115}, url = {http://dx.doi.org/10.1112/S0024611597000403}, Doi = {10.1112/S0024611597000403}, Key = {fds236058} } @article{fds236059, Author = {Calderbank, AR and Sloane, NJA}, Title = {Double Circulant Codes over ℤ_{4}and even Unimodular Lattices}, Journal = {Journal of Algebraic Combinatorics}, Volume = {6}, Number = {2}, Pages = {119-131}, Year = {1997}, Abstract = {With the help of some new results about weight enumerators of self-dual codes over ℤ4 we investigate a class of double circulant codes over ℤ4, one of which leads to an extremal even unimodular 40-dimensional lattice. It is conjectured that there should be "Nine more constructions of the Leech lattice".}, Key = {fds236059} } @article{fds235829, Author = {Calderbank, AR and Daubechies, I and Sweldens, W and Yeo, B-L}, Title = {Wavelet Transforms That Map Integers to Integers}, Journal = {Applied and Computational Harmonic Analysis}, Volume = {5}, Number = {3}, Pages = {332-369}, Year = {1998}, Abstract = {Invertible wavelet transforms that map integers to integers have important applications in lossless coding. In this paper we present two approaches to build integer to integer wavelet transforms. The first approach is to adapt the precoder of Laroia et al., which is used in information transmission; we combine it with expansion factors for the high and low pass band in subband filtering. The second approach builds upon the idea of factoring wavelet transforms into socalled lifting steps. This allows the construction of an integer version of every wavelet transform. Finally, we use these approaches in a lossless image coder and compare the results to those given in the literature. © 1998 Academic Press.}, Key = {fds235829} } @article{fds236060, Author = {Fan, JL and Calderbank, AR}, Title = {A modified concatenated coding scheme, with applications to magnetic data storage}, Journal = {IEEE Transactions on Information Theory}, Volume = {44}, Number = {4}, Pages = {1565-1574}, Year = {1998}, ISSN = {0018-9448}, url = {http://dx.doi.org/10.1109/18.681333}, Abstract = {When a block modulation code is concatenated with an errorcorrection code (ECC) in the standard way, the use of a modulation code with long blocklengths results in error propagation. This correspondence analyzes the performance of modified concatenation, which involves reversing the order of modulation and ECC. This modified scheme reduces error propagation, provides greater flexibility in the choice of parameters, and facilitates soft-decision decoding, with little or no loss in transmission rate. In particular, examples are presented which show how this technique can allow fewer interleaves per sector in hard disk drives, and permit the use of more sophisticated block modulation codes which are better suited to the channel. © 1998 IEEE.}, Doi = {10.1109/18.681333}, Key = {fds236060} } @article{fds236061, Author = {Tarokh, V and Seshadri, N and Calderbank, AR}, Title = {Space-time codes for high data rate wireless communication: Performance criterion and code construction}, Journal = {IEEE Transactions on Information Theory}, Volume = {44}, Number = {2}, Pages = {744-765}, Year = {1998}, ISSN = {0018-9448}, url = {http://dx.doi.org/10.1109/18.661517}, Abstract = {We consider the design of channel codes for improving the data rate and/or the reliability of communications over fading channels using multiple transmit antennas. Data is encoded by a channel code and the encoded data is split into n streams that are simultaneously transmitted using n transmit antennas. The received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise. We derive performance criteria for designing such codes under the assumption that the fading is slow and frequency nonselective. Performance is shown to be determined by matrices constructed from pairs of distinct code sequences. The minimum rank among these matrices quantifies the diversity gain, while the minimum determinant of these matrices quantifies the coding gain. The results are then extended to fast fading channels. The design criteria are used to design trellis codes for high data rate wireless communication. The encoding/decoding complexity of these codes is comparable to trellis codes employed in practice over Gaussian channels. The codes constructed here provide the best tradeoff between data rate, diversity advantage, and trellis complexity. Simulation results are provided for 4 and 8 PSK signal sets with data rates of 2 and 3 bits/symbol, demonstrating excellent performance that is within 2-3 dB of the outage capacity for these channels using only 64 state encoders. © 1998 IEEE.}, Doi = {10.1109/18.661517}, Key = {fds236061} } @article{fds236062, Author = {Calderbank, AR}, Title = {The art of signaling: fifty years of coding theory}, Journal = {IEEE Transactions on Information Theory}, Volume = {44}, Number = {6}, Pages = {2561-2595}, Year = {1998}, ISSN = {0018-9448}, url = {http://dx.doi.org/10.1109/18.720549}, Abstract = {In 1948 Shannon developed fundamental limits on the efficiency of communication over noisy channels. The coding theorem asserts that there are block codes with code rates arbitrarily close to channel capacity and probabilities of error arbitrarily close to zero. Fifty years later, codes for the Gaussian channel have been discovered that come close to these fundamental limits. There is now a substantial algebraic theory of error-correcting codes with as many connections to mathematics as to engineering practice, and the last 20 years have seen the construction of algebraic-geometry codes that can be encoded and decoded in polynomial time, and that beat the Gilbert-Varshamov bound. Given the size of coding theory as a subject, this review is of necessity a personal perspective, and the focus is reliable communication, and not source coding or cryptography. The emphasis is on connecting coding theories for Hamming and Euclidean space and on future challenges, specifically in data networking, wireless communication, and quantum information theory. © 1998 IEEE.}, Doi = {10.1109/18.720549}, Key = {fds236062} } @article{fds236063, Author = {Naguib, AF and Seshadri, N and Calderbank, AR}, Title = {Applications of space-time block codes and interference suppression for high capacity and high data rate wireless systems}, Journal = {Conference Record of the Asilomar Conference on Signals, Systems and Computers}, Volume = {2}, Pages = {1803-1810}, Year = {1998}, Abstract = {This paper presents a combined interference suppression and ML decoding scheme for space-time block codes that can effectively suppress interference from other co-channel users while providing each user with a diversity benefit. We consider a multiuser environment with K synchronous co-channel users, each is equipped with N transmit antennas and uses the space-time block coding. By exploiting the temporal and spatial structure of these codes, we develop a minimum mean-squared error (MMSE) interference suppression technique. Assuming that the receiver uses M≥K receive antennas, these technique will perfectly suppress the interference from the K-1 co-channel space-time users and provide a diversity order of N×(M-K+1) to each of the K users. Moreover, this MMSE solution tends itself to an adaptive implementation and does not require any explicit knowledge about the interference. In conjunction with this interference suppression technique, we show how space-time block codes can be used to increasing the capacity and/or data rate of wireless communication systems.}, Key = {fds236063} } @article{fds236064, Author = {Naguib, AF and Tarokh, V and Seshadri, N and Calderbank, AR}, Title = {A space-time coding modem for high-data-rate wireless communications}, Journal = {IEEE Journal on Selected Areas in Communications}, Volume = {16}, Number = {8}, Pages = {1459-1477}, Year = {1998}, ISSN = {0733-8716}, url = {http://dx.doi.org/10.1109/49.730454}, Abstract = {This paper presents the theory and practice of a new advanced modem technology suitable for high-data-rate wireless communications and presents its performance over a frequency-flat Rayleigh fading channel. The new technology is based on space-time coded modulation (STCM) [1]-[5] with multiple transmit and/or multiple receive antennas and orthogonal pilot sequence insertion (O-PSI). In this approach, data is encoded by a space-time (ST) channel encoder and the output of the encoder is split into N streams to be simultaneously transmitted using N transmit antennas. The transmitter inserts periodic orthogonal pilot sequences in each of the simultaneously transmitted bursts. The receiver uses those pilot sequences to estimate the fading channel. When combined with an appropriately designed interpolation filter, accurate channel state information (CSI) can be estimated for the decoding process. Simulation results of the proposed modem, as applied to the IS-136 cellular standard, are presented. We present the frame error rate (FER) performance results as a function of the signal-to-noise ratio (SNR) and the maximum Doppler frequency, in the presence of timing and frequency offset errors. Simulation results show that for 10% FER, a 32-state eight-phase-shift keyed (8-PSK) ST code with two transmit and two receive antennas can support data rates up to 55.8 kb/s on a 30-kHz channel, at an SNR of 11.7 dB and a maximum Doppler frequency of 180 Hz. Simulation results for other codes and other channel conditions are also provided. We also compare the performance of the proposed STCM scheme with delay-diversity schemes and conclude that STCM can provide significant SNR improvement over simple delay diversity.}, Doi = {10.1109/49.730454}, Key = {fds236064} } @article{fds235757, Author = {Vaishampayan, VA and Calderbank, AR and Batllo, JC}, Title = {On reducing granular distortion in multiple description quantization}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Pages = {98}, Year = {1998}, Month = {December}, ISSN = {2157-8095}, url = {http://dx.doi.org/10.1109/ISIT.1998.708685}, Abstract = {There is a gap of 3.07 dB between the distortion product of a multiple description quantizer and the multiple description rate distortion bound. In this paper we seek to close this gap through the design of a quantizer with smaller granular distortion. © 1998 IEEE.}, Doi = {10.1109/ISIT.1998.708685}, Key = {fds235757} } @article{fds235758, Author = {Calderbank, AB and Forney, GD and Vardy, A}, Title = {Minimal tail-biting trellises: The Golay code and more}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Pages = {255}, Year = {1998}, Month = {December}, ISSN = {2157-8095}, url = {http://dx.doi.org/10.1109/ISIT.1998.708860}, Abstract = {A 16-state tail-biting trellis for the binary (24,12,8) Golay code C 24 is exhibited. This tail-biting trellis is minimal. It has many other nice properties, and may be simpler to decode than the minimal conventional trellis for C 24 . Unwrapping this tail-biting trellis produces a periodically-time-varying 16-state rate-1/2 convolutional code. This «Golay convolutional code» is the first known example of a self-dual doubly-even binary linear convolutional code. It has greater minimum distance than any 16-state time-invariant convolutional code of rate 1/2. Demonstrably minimal tail-biting trellises are given for several other binary and nonbinary self-dual codes. For some nonbinary codes, tail-biting trellises based on code generators over a group are simpler than any tail-biting trellis based on linear generators over a field. © 1998 IEEE.}, Doi = {10.1109/ISIT.1998.708860}, Key = {fds235758} } @article{fds235771, Author = {Tarokh, V and Naguib, A and Seshadri, N and Calderbank, AR}, Title = {Recent progress in space-time block and trellis coding}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Pages = {314}, Year = {1998}, Month = {December}, ISSN = {2157-8095}, url = {http://dx.doi.org/10.1109/ISIT.1998.708919}, Abstract = {Techniques for transmission and reception over wireless channels using multiple transmit antennas are presented. © 1998 IEEE.}, Doi = {10.1109/ISIT.1998.708919}, Key = {fds235771} } @article{fds236065, Author = {Tarokh, V and Jafarkhani, H and Calderbank, AR}, Title = {Space-time block codes from orthogonal designs}, Journal = {IEEE Transactions on Information Theory}, Volume = {45}, Number = {5}, Pages = {1456-1467}, Year = {1999}, ISSN = {0018-9448}, url = {http://dx.doi.org/10.1109/18.771146}, Abstract = {The theory of space-time block coding is presented as a simple and elegant method for transmission using multiple transmit antennas in a wireless Rayleigh/Rician environment. These codes have a very simple maximum-likelihood decoding algorithm which is only based on linear processing. Designs that correspond to combined coding and linear processing at the transmitter are also considered.}, Doi = {10.1109/18.771146}, Key = {fds236065} } @article{fds236066, Author = {Calderbank, AR and Harbin, RH and Rains, EM and Shor, PW and Sloane, NJA}, Title = {A Group-Theoretic Framework for the Construction of Packings in Grassmannian Spaces}, Journal = {Journal of Algebraic Combinatorics}, Volume = {9}, Number = {2}, Pages = {129-140}, Year = {1999}, Abstract = {By using totally isotropic subspaces in an orthogonal space Ω+(2i, 2), several infinite families of packings of 2k-dimensional subspaces of real 2i -dimensional space are constructed, some of which are shown to be optimal packings. A certain Clifford group underlies the construction and links this problem with Barnes-Wall lattices, Kerdock sets and quantum-error-correcting codes.}, Key = {fds236066} } @article{fds236067, Author = {Calderbank, AR and Jr, GDF and Vardy, A}, Title = {Minimal tail-biting trellises: the Golay code and more}, Journal = {IEEE Transactions on Information Theory}, Volume = {45}, Number = {5}, Pages = {1435-1455}, Year = {1999}, ISSN = {0018-9448}, url = {http://dx.doi.org/10.1109/18.771145}, Abstract = {Tail-biting trellis representations of block codes are investigated. We develop some elementary theory, and present several intriguing examples, which we hope will stimulate further developments in this field. In particular, we construct a 16-state 12-section structurally invariant tail-biting trellis for the (24, 12, 8) binary Golay code. This tail-biting trellis representation is minimal: it simultaneously minimizes all conceivable measures of state complexity. Moreover, it compares favorably with the minimal conventional 12-section trellis for the Golay code, which has 256 states at its midpoint, or with the best quasi-cyclic representation of this code, which leads to a 64-state tail-biting trellis. Unwrapping this tail-biting trellis produces a periodically time-varying 16-state rate- 1/2 'convolutional Golay code' with d = 8, which has attractive performance/complexity properties. We furthermore show that the (6, 3, 4) quarternary hexacode has a minimal 8-state group tail-biting trellis, even though it has no such linear trellis over F 4. Minimal tail-biting trellises are also constructed for the (8, 4, 4) binary Hamming code, the (4, 2, 3) ternary tetracode, the (4, 2, 3) code over F 4, and the Z 4-linear (8, 4, 4) octacode.}, Doi = {10.1109/18.771145}, Key = {fds236067} } @article{fds236068, Author = {Calderbank, AR and Duel-Hallen, A and Fishburn, PC and Rabinovich, A}, Title = {Interpolation by convolutional codes, overload distortion, and the erasure channel}, Journal = {IEEE Transactions on Information Theory}, Volume = {45}, Number = {1}, Pages = {94-105}, Year = {1999}, ISSN = {0018-9448}, url = {http://dx.doi.org/10.1109/18.746774}, Abstract = {This paper investigates how closely randomly generated binary source sequences can be matched by convolutional code codewords. What distinguishes it from prior work is that a randomly chosen subsequence with density A is to be matched as closely as possible. The so-called marked bits of the subsequence could indicate overload quantization points for a source sample generated from the tails of a probability distribution. They might also indicate bits where the initial estimate is considered reliable, as might happen in iterated decoding. The capacity of a convolutional code to interpolate the marked subsequence might be viewed as a measure of its ability to handle overload distortion. We analyze this capacity using a Markov chain whose states are sets of subsets of trellis vertices of the convolutional code. We investigate the effect of memory on the probability of perfect interpolation and calculate the residual rate on the unmarked bits of the binary source sequence. We relate our interpolation methodology to sequence-based methods of quantization and use it to analyze the performance of convolutional codes on the pure erasure channel. © 1999 IEEE.}, Doi = {10.1109/18.746774}, Key = {fds236068} } @article{fds236069, Author = {Tarokh, V and Jafarkhani, H and Calderbank, AR}, Title = {Space-time block coding for wireless communications: Performance results}, Journal = {IEEE Journal on Selected Areas in Communications}, Volume = {17}, Number = {3}, Pages = {451-460}, Year = {1999}, url = {http://dx.doi.org/10.1109/49.753730}, Abstract = {We document the performance of space-time block codes [13], [14], which provide a new paradigm for transmission over Rayleigh fading channels using multiple transmit antennas. Data is encoded using a space-time block code, and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas. The received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise. Maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection. This uses the orthogonal structure of the space-time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver. We review the encoding and decoding algorithms for various codes and provide simulation results demonstrating their performance. It is shown that using multiple transmit antennas and space-time block coding provides remarkable performance at the expense of almost no extra processing.}, Doi = {10.1109/49.753730}, Key = {fds236069} } @article{fds235830, Author = {Naguib, AF and Seshádri, N and Calderbank, AR}, Title = {Increasing data rate over wireless channels: Space time coding and signal processing for high data rate wireless communications}, Journal = {IEEE Signal Processing Magazine}, Volume = {17}, Number = {3}, Pages = {76-92}, Year = {2000}, ISSN = {1053-5888}, url = {http://dx.doi.org/10.1109/79.841731}, Doi = {10.1109/79.841731}, Key = {fds235830} } @article{fds235831, Author = {Jana, R and Al-Dhahir, N and Calderbank, R}, Title = {Distance spectrum computation for equalized MIMO multipath fading channels}, Journal = {2000 IEEE Wireless Communications and Networking Conference}, Pages = {293-297}, Year = {2000}, Abstract = {In this paper we estimate bit error probability bounds for finite-length delay-optimised multi-input multi-output (MIMO) equalizers. These equalizers shorten the impulse response memory of frequency-selective MIMO channels by minimizing the average energy of the error sequence between the equalized MIMO channel impulse response and the target impulse response. We answer an important question in this paper namely, how much asymptotic loss in SNR do we expect as a result of this shortening? A partial distance spectrum for a 2 × 2 MIMO channel is evaluated with or without channel shortening equalizers. The union bound is then used to upper bound the bit error probability. Similarly, the lower bound is computed from the squared minimum Euclidean distance. Numerical results show that the expected loss is in the order of 2.5 dB for realistic wireless channel environments.}, Key = {fds235831} } @article{fds235833, Author = {Calderbank, AR and Pottie, G and Seshadri, N}, Title = {Cochannel interference suppression through time/space diversity}, Journal = {IEEE Transactions on Information Theory}, Volume = {46}, Number = {3}, Pages = {922-932}, Year = {2000}, ISSN = {0018-9448}, url = {http://dx.doi.org/10.1109/18.841171}, Abstract = {Wireless systems are subject to a time-varying and unknown a priori combination of cochannel interference, fading, and Gaussian noise. It is well known that multiple antennas can provide diversity in space that allows system tradeoffs between interference suppression and mitigation of fading. This paper describes how to achieve these same tradeoffs through diversity in time provided by channel coding. The mathematical description of time diversity is identical to that of space diversity, and what emerges is a unified framework for signal processing. Decoding algorithms are provided for repetition codes, rate 1/n convolutional codes, first-order Reed-Muller codes, and a new class of linear combination codes that provide cochannel interference suppression. In all cases it is possible to trade performance for complexity by choosing between joint estimation and a novel low-complexity linear canceler structure that treats interference as noise. This means that a single code can be used in a variety of system environments just by changing the processing in the receiver.}, Doi = {10.1109/18.841171}, Key = {fds235833} } @article{fds326906, Author = {Calderbank, R}, Title = {Abuse and disabled people: vulnerability or social indifference?}, Journal = {Disability and Society}, Volume = {15}, Number = {3}, Pages = {521-534}, Year = {2000}, Month = {May}, url = {http://dx.doi.org/10.1080/713661966}, Doi = {10.1080/713661966}, Key = {fds326906} } @article{fds235832, Author = {Naguib, AF and Calderbank, R}, Title = {Space - Time coding and signal processing for high data rate wireless communications}, Journal = {Wireless Communications & Mobile Computing}, Volume = {1}, Number = {1}, Pages = {13-34}, Year = {2001}, ISSN = {1530-8669}, url = {http://dx.doi.org/10.1002/1530-8677(200101/03)1:1<13::AID-WCM2>3.0.CO;2-J}, Abstract = {The information capacity of wireless communication systems can be increased dramatically by employing multiple transmit and receive antennas [Foschini GJ, Gans MJ. On limits of wireless communications in a fading environment when using multiple antennas. Wireless Communications Magazine 1998; 6 311-335. Telatar E. Capacity of Multi-Antenna Gaussian Channels, Technical Memorandum, AT&T Bell Laboratories, 1995.] An effective approach to increasing data rate over wireless channels is to employ coding techniques appropriate to multiple transmit antennas, that is space-time coding. Space-time codes introduce temporal and spatial correlation into signals transmitted from different antennas, in order to provide diversity at the receiver, and coding gain over an uncoded system. The spatial-temporal structure of these codes can be exploited to further increase the capacity of wireless systems with a relatively simple receiver structure. This paper provides an overview of space-time coding techniques and the associated signal processing framework. Copyright © 2001 John Wiley & Sons, Ltd.}, Doi = {10.1002/1530-8677(200101/03)1:1<13::AID-WCM2>3.0.CO;2-J}, Key = {fds235832} } @article{fds235834, Author = {Stamoulis, A and Al-Dhahir, N and Calderbank, AR}, Title = {Further results on interference cancellation and space-time block codes}, Journal = {Conference Record of the Asilomar Conference on Signals, Systems and Computers}, Volume = {1}, Pages = {257-261}, Year = {2001}, Abstract = {Space-Time Blocks Codes (STBC) make use of a rich algebraic structure to provide diversity gains with small decoding complexity. In this work, we show that the rich algebraic structure of STBC reduces the hardware and software complexity of interference cancellation (IC) techniques. Additionally, after the IC stage, transmitted symbols can still be recovered with space-time diversity gains. We present three illustrative examples of IC in wireless networks where co-channel users employ STBC. First, we show that any STBC that is based on an orthogonal design allows IC of two co-channel users with simple linear processing. Second, we show that for the Alamouti STBC, K > 2 users can be detected with simple linear processing, while still ensuring space-time diversity gains. Third, capitalizing on recent work on single-carrier frequency-domain STBC, we study how the aforementioned IC schemes can be modified for frequency-selective channels.}, Key = {fds235834} } @article{fds235835, Author = {Al-Dhahir, N and Naguib, AF and Calderbank, AR}, Title = {Finite-length MIMO decision feedback equalization for space-time block-coded signals over multipath-fading channels}, Journal = {IEEE Transactions on Vehicular Technology}, Volume = {50}, Number = {4}, Pages = {1176-1182}, Year = {2001}, ISSN = {0018-9545}, url = {http://dx.doi.org/10.1109/25.938592}, Abstract = {A finite-length optimized-delay multi-input-multi-output (MIMO) mean-square-error decision-feedback equalizer for space-time block-coded transmissions over multipath-fadingchannels is presented. Alamouti's space-time block code with two transmit and two receive antennas on a typical urban EDGE channel is taken as a case study. We propose a combined equalization and decoding scheme under the constraint of linear processing complexity (no trellis search) at the receiver. Performance comparisons are made with the single-transmit/single-receive antenna case and the case of MIMO feedforward linear equalization only with no decision feedback.}, Doi = {10.1109/25.938592}, Key = {fds235835} } @article{fds326905, Author = {Calderbank, R and Sloane, NJ}, Title = {Obituary. Claude Shannon (1916-2001).}, Journal = {Nature}, Volume = {410}, Number = {6830}, Pages = {768}, Year = {2001}, Month = {April}, url = {http://dx.doi.org/10.1038/35071223}, Doi = {10.1038/35071223}, Key = {fds326905} } @article{fds235836, Author = {Diggavi, SN and Al-Dhahir, N and Stamoulis, A and Calderbank, AR}, Title = {Differential space-time coding for frequency-selective channels}, Journal = {IEEE Communications Letters}, Volume = {6}, Number = {6}, Pages = {253-255}, Year = {2002}, ISSN = {1089-7798}, url = {http://dx.doi.org/10.1109/LCOMM.2002.1010872}, Abstract = {In this letter we introduce two space-time transmission schemes which allow full-rate and full-diversity noncoherent communications using two transmit antennas over fading frequency-selective channels. The first scheme operates in the frequency domain where it combines differential Alamouti space-time block-coding (STBC) with OFDM. The second scheme operates in the time domain and employs differential time-reversal STBC to guarantee blind channel identifiability without the need for temporal oversampling or multiple receive antennas.}, Doi = {10.1109/LCOMM.2002.1010872}, Key = {fds235836} } @article{fds235837, Author = {Al-Dhahir, N and Fragouli, C and Stamoulis, A and Younis, W and Calderbank, R}, Title = {Space-time processing for broadband wireless access}, Journal = {IEEE Communications Magazine}, Volume = {40}, Number = {9}, Pages = {136-142}, Year = {2002}, ISSN = {0163-6804}, url = {http://dx.doi.org/10.1109/MCOM.2002.1031840}, Abstract = {We present an overview of research activities on space-time coding for broadband wireless transmission performed at AT&T Shannon Laboratory over the past two years. The emphasis is on physical layer modem algorithms such as channel estimation, equalization, and interference cancellation. However, we also discuss the impact of space-time coding gains at the physical layer on throughput at or above the networking layer. Furthermore, we describe a flexible graphical user interface attached to our physical layer simulation engine in order to explore the performance of space-time codes under a variety of practical transmission scenarios. Simulation results for the EDGE cellular system and the 802.11 wireless LAN environment are presented.}, Doi = {10.1109/MCOM.2002.1031840}, Key = {fds235837} } @article{fds235838, Author = {Calderbank, AR and Daubechies, I}, Title = {The pros and cons of democracy}, Journal = {IEEE Transactions on Information Theory}, Volume = {48}, Number = {6}, Pages = {1721-1725}, Year = {2002}, ISSN = {0018-9448}, url = {http://dx.doi.org/10.1109/TIT.2002.1003852}, Abstract = {The concept of democracy was introduced in which the individual bits in a coarsely quantized representation of a signal were given equal weight in the approximation to the original signal. It was proved that such democratic representations could not achieve the same accuracy as optimal nondemocratic schemes. Convolutional decoding was found to be convenient in digital to analog conversion.}, Doi = {10.1109/TIT.2002.1003852}, Key = {fds235838} } @article{fds235839, Author = {Diggavi, SN and Al-Dhahir, N and Calderbank, AR}, Title = {On interference cancellation and high-rate space-time codes}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Pages = {238-}, Year = {2003}, Abstract = {We study the design and decoding of high-rate space-time codes in two contexts. The first part of the paper examines the multiple-access channel (MAC) where users employ space-time block codes (STBC). The problem is formulated in the context of an inter-symbol interference (ISI) channel which occurs for transmission over frequency-selective channels. We show that a diversity order of 2Mτ (v + 1) is achievable at full transmission rate for each user, when we have Mτ receive antennas, channel memory of v and an optimal multiuser maximum-likelihood (ML) decoder is used. In the second part, we examine high-rate space-time codes that have a high-diversity code embedded within them. This can also be viewed as unequal error protection codes designed for unequal diversity order, which is the metric suitable for fading channels.}, Key = {fds235839} } @article{fds235840, Author = {Diggavi, SN and Al-Dhahir, N and Calderbank, AR}, Title = {Multiuser joint equalization and decoding of space-time codes}, Journal = {IEEE International Conference on Communications}, Volume = {4}, Pages = {2643-2647}, Year = {2003}, Abstract = {In this paper we study the multiple-access channel where users employ space-time block codes (STBC). The problem is formulated in the context of an inter-symbol interference (ISI) multiple-access channel. The algebraic structure of the STBC is utilized to design joint interference suppression, equalization, and decoding schemes. Each user transmits using 2 transmit antennas and a time-reversed space-time block code suitable for frequency-selective channels. We first show that a diversity order of 2Mτ(ν+1) is achievable at full transmission rate for each user, when we have Mτ receive antennas, channel memory of ν and an optimal multiuser maximum-likelihood (ML) decoder is used. Due to the decoding complexity of the ML detector we study the algebraic structure of linear multiuser detectors which utilize the properties of the STBC. We do this both in the transform domain (D-domain formulation) and when we impose finite block length constraints (matrix formulation). The receiver is designed to utilize the algebraic structure of the codes in order to preserve the block quaternionic structure of the equivalent channel for each user.}, Key = {fds235840} } @article{fds235841, Author = {Diggavi, SN and Al-Dhahir, N and Calderbank, AR}, Title = {Diversity-Embedded Space-Time Codes}, Journal = {Conference Record / IEEE Global Telecommunications Conference}, Volume = {4}, Pages = {1909-1914}, Year = {2003}, Abstract = {Rate and diversity impose a fundamental trade-off in space-time coding. High-rate space-time codes come at a cost of lower diversity, and high reliability (diversity) implies a lower rate. In this paper we explore a different point of view where we design high-rate space-time codes that have a high-diversity code embedded within them. This allows a form of communication where the high-rate code opportunistically takes advantage of good channel realizations whereas the embedded high-diversity code ensures that at least part of the information is received reliably. We explore this point of view with design issues, along with some preliminary progress on code constructions and some information-theoretic considerations.}, Key = {fds235841} } @article{fds235842, Author = {Diggavi, SN and Al-Dhahir, N and Calderbank, AR}, Title = {Algebraic properties of space-time block codes in intersymbol interference multiple-access channels}, Journal = {IEEE Transactions on Information Theory}, Volume = {49}, Number = {10}, Pages = {2403-2414}, Year = {2003}, url = {http://dx.doi.org/10.1109/TIT.2003.817833}, Abstract = {In this paper, we study the multiple-access channel where users employ space-time block codes (STBC). The problem is formulated in the context of an intersymbol interference (ISI) multiple-access channel which occurs for transmission over frequency-selective channels. The algebraic structure of the STBC is utilized to design joint interference suppression, equalization, and decoding schemes. Each of the K users transmits using Mt = 2 transmit antennas and a time-reversed STBC suitable for frequency-selective channels. We first show that a diversity order of 2Mr (v + 1) is achievable at full transmission rate for each user, when we have Mr receive antennas, channel memory of v, and an optimal multiuser maximum-likelihood (ML) decoder is used. Due to the decoding complexity of the ML detector we study the algebraic structure of linear multiuser detectors which utilize the properties of the STBC. We do this both in the transform (D-domain) formulation and when we impose finite block-length constraints (matrix formulation). The receiver is designed to utilize the algebraic structure of the codes in order to preserve the block quaternionic structure of the equivalent channel for each user. We also explore some algebraic properties of D-domain quaternionic matrices and of quaternionic circulant block matrices that arise in this study.}, Doi = {10.1109/TIT.2003.817833}, Key = {fds235842} } @article{fds235843, Author = {Tarokh, V and Naguib, A and Seshadri, N and Calderbank, AR}, Title = {Erratum: Space-time codes for high data rate wireless communications: Performance criteria in the presence of channel estimation errors, mobility, and multiple paths (IEEE Trans. Commun. (1999) 47, (199-207))}, Journal = {IEEE Transactions on Communications}, Volume = {51}, Number = {12}, Pages = {2141-}, Year = {2003}, url = {http://dx.doi.org/10.1109/TCOMM.2003.822179}, Doi = {10.1109/TCOMM.2003.822179}, Key = {fds235843} } @article{fds235844, Author = {Calderbank, AR and Diggavi, SN and Al-Dhahir, N}, Title = {Space-time signaling based on Kerdock and Delsarte-Goethals codes}, Journal = {IEEE International Conference on Communications}, Volume = {1}, Pages = {483-487}, Year = {2004}, Abstract = {This paper designs space-time codes for standard PSK and QAM signal constellations that have flexible rate, diversity and require no constellation expansion. Central to this construction are binary partitions of the PSK and QAM constellations that appear in codes designed for the Gaussian channel. The space-time codes presented here are designed by separately specifying the different levels of the binary partition in the space-time array. The individual levels are addressed by either the binary symmetric matrices associated with codewords in a Kerdock code or other families of binary matrices. Binary properties of these sets are sufficient to verify the diversity property of the codewords in the complex domain. Larger sets of binary symmetric matrices (such as the set used in Delsarte-Goethals codes) are used to trade diversity protection for increased rate.}, Key = {fds235844} } @article{fds235845, Author = {Calderbank, AR and Diggavi, S and Das, S and Al-Dhahir, N}, Title = {Construction and analysis of a new 4 × 4 orthogonal space-time block code}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Pages = {310-}, Year = {2004}, Abstract = {The construction and the analysis of a nonlinear 4×4 full rate, full-diversity orthogonal space-time block codes was discussed. The main aspect was the design, analysis and low complexity decoding of a full rate full diversity orthogonal STBC for four transmit antennas that was constructed by means of 2×2 arrays over the quaternions. It was observed that the structure of the code was a generalization of the 2×2 Alamouti code and were reduced if the quaternions in the code were replaced by complex numbers. The results show that the PSK signalling code has full diversity while QPSK signalling code had no constellation expansion.}, Key = {fds235845} } @article{fds235846, Author = {Diggavi, SN and Al-Dhahir, N and Stamoulis, A and Calderbank, AR}, Title = {Great expectations: The value of spatial diversity in wireless networks}, Journal = {Proceedings of the IEEE}, Volume = {92}, Number = {2}, Pages = {219-270}, Year = {2004}, url = {http://dx.doi.org/10.1109/JPROC.2003.821914}, Abstract = {In this paper, the effect of spatial diversity on the throughput and reliability of wireless networks is examined. Spatial diversity is realized through multiple independently fading transmit/receive antenna paths in single-user communication and through independently fading links in multiuser communication. Adopting spatial diversity as a central theme, we start by studying its information-theoretic foundations, then we illustrate its benefits across the physical (signal transmission/coding and receiver signal processing) and networking (resource allocation, routing, and applications) layers. Throughout the paper, we discuss engineering intuition and tradeoffs, emphasizing the strong interactions between the various network functionalities. © 2004 IEEE.}, Doi = {10.1109/JPROC.2003.821914}, Key = {fds235846} } @article{fds235847, Author = {Oggier, FE and Sloane, NJA and Diggavi, SN and Calderbank, R}, Title = {Nonintersecting subspaces based on finite alphabets}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Pages = {455-}, Year = {2004}, Abstract = {Codewords were constructed subject to the constraint that the elements of the codewords use symbols from a fixed, small constellation. The subspaces constructed remain nonintersecting when lifted to the complex field. The construction shows that the codewords are nonintersecting over the finite field. The construction gives full diversity order when the elements of the codewords are restricted to come from a finite field.}, Key = {fds235847} } @article{fds235848, Author = {Calderbank, AR and Gilbert, A and Levchenko, K and Muthukrishnan, S and Strauss, M}, Title = {Improved range-summable random variable construction algorithms}, Journal = {Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms}, Pages = {840-849}, Year = {2005}, Abstract = {Range-summable universal hash functions, also known as range-summable random variables, are binary-valued hash functions which can efficiently hash single values as well as ranges of values from the domain. They have found several applications in the area of data stream processing where they are used to construct sketches - small-space summaries of the input sequence. We present two new constructions of range-summable universal hash functions on n-bit strings, one based on Reed-Muller codes which gives k-universal hashing using O(n log k) space arid time for point operations and O(n 2 1og k) for range operations, and another based on a new subcode of the second-order Reed-Muller code, which gives 5-universal hashing using O(n) space, O(n log 3 n) time for point operations, and O(n 3) time for range operations. We also present a new sketch data structure using the new hash functions which improves several previous results.}, Key = {fds235848} } @article{fds235849, Author = {Howard, SD and Moran, W and Calderbank, AR and Schmitt, HA and Savage, CO}, Title = {Relationships between radar ambiguity and coding theory}, Journal = {IEEE International Conference on Acoustics Speech and Signal Processing}, Volume = {V}, Pages = {V897-V900}, Year = {2005}, ISSN = {1520-6149}, url = {http://dx.doi.org/10.1109/ICASSP.2005.1416449}, Abstract = {We investigate the theory of the finite discrete Heisenberg-Weyl group in relation to the development of adaptive radar. We contend that this group can form the basis for the representation of the radar environment in terms of operators on the space of waveforms. We also demonstrate, following recent developments in the theory of error correcting codes, that the finite discrete Heisenberg-Weyl group provides a unified basis for the construction of useful waveforms/sequences for radar, communications and the theory of error correcting codes. © 2005 IEEE.}, Doi = {10.1109/ICASSP.2005.1416449}, Key = {fds235849} } @article{fds235850, Author = {Lee, J-W and Chiang, M and Calderbank, AR}, Title = {Distributed algorithms for optimal rate-reliability tradeoff in networks}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Volume = {2005}, Pages = {2246-2250}, Year = {2005}, url = {http://dx.doi.org/10.1109/ISIT.2005.1523747}, Abstract = {The current framework of network utility maximization for distributed rate allocation assumes fixed channel code rates. However, by adapting the physical layer channel coding, different rate-reliability tradeoffs can be achieved on each link and for each end user. Consider a network where each user has a utility function that depends on both signal quality and data rate, and each link may provide a 'fatter' ('thinner') information 'pipe' by allowing a higher (lower) decoding error probability. We propose two distributed, pricing-based algorithms to attain optimal rate-reliability tradeoff, with an interpretation that each user provides its willingness to pay for reliability to the network and the network feeds back congestion prices to users. The proposed algorithms converge to a tradeoff point between rate and reliability, which is proved to be globally optimal for codes with sufficiently large codeword lengths and user utilities with sufficiently negative curvatures.}, Doi = {10.1109/ISIT.2005.1523747}, Key = {fds235850} } @article{fds235851, Author = {Ashikhmin, A and Calderbank, AR}, Title = {Space-time reed-muller codes for noncoherent MIMO transmission}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Volume = {2005}, Pages = {1952-1956}, Year = {2005}, url = {http://dx.doi.org/10.1109/ISIT.2005.1523686}, Abstract = {We present a family of Space-Time codes for the noncoherent MIMO channel. The codes are constructed via functions that can be considered as a generalization of boolean functions to commuting projection operators which arise in the theory of quantum stabilizer codes. These space-time codes are strongly related to standard binary Reed-Muller codes. In particular, they can be decoded by adapting a decoding algorithm for Reed-Muller codes. We show that the first subclass of codes from this family, which we view as the first order space-time Reed-Muller codes, allow transmission with rates close to the MIMO noncoherent channel capacity in the low signal to noise ratio (SNR) regime.}, Doi = {10.1109/ISIT.2005.1523686}, Key = {fds235851} } @article{fds235852, Author = {Das, S and Al-Dhahir, N and Calderbank, AR}, Title = {Exploiting algebraic structure in cross-layer design}, Journal = {2005 International Conference on Wireless Networks, Communications and Mobile Computing}, Volume = {2}, Pages = {1466-1471}, Year = {2005}, url = {http://dx.doi.org/10.1109/WIRLES.2005.1549629}, Abstract = {We demonstrate the value of algebraic structure to cross-layer design of multiple-antenna wireless communication systems. At the network layer we will develop techniques for multiple access (many to one) and broadcast (one to many) communication where algebraic structure enables very simple implementation. At the physical layer, we emphasize enabling mobility and integrating receive chain functionality (for example, channel estimation, joint decoding and equalization) at a level of complexity that is comparable to single-antenna systems. Algebraic structure will make it possible to integrate these different functions very efficiently. Another important theme in this work is the emphasis on measuring the value of innovation at the physical layer in terms of networking throughput or coverage area of broadband wireless systems such as WiFi and WiMAX. © 2005 IEEE.}, Doi = {10.1109/WIRLES.2005.1549629}, Key = {fds235852} } @article{fds235853, Author = {Thangaraj, A and Dihidar, S and Calderbank, AR and McLaughlin, SW and Merolla, J-M}, Title = {On achieving capacity on the wire tap channel using LDPC codes}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Volume = {2005}, Pages = {1498-1502}, Year = {2005}, url = {http://dx.doi.org/10.1109/ISIT.2005.1523593}, Abstract = {We investigate the use of capacity and near-capacity achieving LPDC codes on the wire tap channel, where the dual conditions of reliable communications and security are required. We show that good codes for conventional channels (like BSC and BEC) also have interesting and useful security properties. In this paper we show the connection between the decoding threshold of the code and its security against eavesdropping. We also give practical code constructions for some special cases of the wire tap channel and show that security (in the Shannon sense) is a function of the decoding threshold. Some of these constructions achieve the secrecy capacity as denned by Wyner. These codes provide secure communications without conventional key distribution and provide a physical-layer approach for either secure communications or key distribution.}, Doi = {10.1109/ISIT.2005.1523593}, Key = {fds235853} } @article{fds235854, Author = {Oggier, FE and Sloane, NJA and Diggavi, SN and Calderbank, AR}, Title = {Nonintersecting subspaces based on finite alphabets}, Journal = {IEEE Transactions on Information Theory}, Volume = {51}, Number = {12}, Pages = {4320-4325}, Year = {2005}, ISSN = {0018-9448}, url = {http://dx.doi.org/10.1109/TIT.2005.858946}, Abstract = {Two subspaces of a vector space are here called "nonintersecting" if they meet only in the zero vector. Motivated by the design of noncoherent multiple-antenna communications systems, we consider the following question. How many pairwise nonintersecting Mt-dimensional subspaces of an m-dimensional vector space V over a field F can be found, if the generator matrices for the subspaces may contain only symbols from a given finite alphabet A ⊆ F? The most important case is when F is the field of complex numbers C; then Mt is the number of antennas. If A = F = GF(q) it is shown that the number of nonintersecting subspaces is at most (qm - 1)/(qMt - 1), and that this bound can be attained if and only if m is divisible by Mt. Furthermore, these subspaces remain nonintersecting when "lifted" to the complex field. It follows that the finite field case is essentially completely solved. In the case when F = C only the case Mt = 2 is considered. It is shown that if A is a PSK-configuration, consisting of the 2r complex roots of unity, the number of nonintersecting planes is at least 2r(m-2) and at most 2r(m-1)-1 (the lower bound may in fact be the best that can be achieved. © 2005 IEEE.}, Doi = {10.1109/TIT.2005.858946}, Key = {fds235854} } @article{fds235772, Author = {Tang, A and Lee, J-W and Huang, J and Chiang, M and Calderbank, AR}, Title = {Reverse engineering MAC}, Journal = {2006 4th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks, WiOpt 2006}, Year = {2006}, url = {http://dx.doi.org/10.1109/WIOPT.2006.1666466}, Abstract = {This paper reverse engineers backoff-based random-access MAC protocols in ad-hoc networks. We show that contention resolution algorithm in such protocols is implicitly participating in a non-cooperative game. Each link attempts to maximize a selfish local utility function, whose exact shape is reverse engineered from protocol description, through a stochastic subgradient method in which link updates its persistence probability based on its transmission success or failure. We prove that existence of a Nash equilibrium is guaranteed in general. minimum amount of backoff aggressiveness needed for uniqueness of Nash equilibrium and convergence of best response strategy are established as a function of user density. Convergence properties and connection with best response strategy are also proved for variants of stochastic-subgradient-based dynamics of game. Together with known results in reverse engineering TCP and BGP, this paper completes recent efforts in reverse engineering main protocols in layers 2-4. © 2006 IEEE.}, Doi = {10.1109/WIOPT.2006.1666466}, Key = {fds235772} } @article{fds235855, Author = {Howard, S and Calderbank, A and Moran, W}, Title = {The finite Heisenberg-Weyl groups in radar and communications}, Journal = {Eurasip Journal on Advances in Signal Processing}, Volume = {2006}, Year = {2006}, ISSN = {1110-8657}, url = {http://dx.doi.org/10.1155/ASP/2006/85685}, Abstract = {We investigate the theory of the finite Heisenberg-Weylgroup in relation to the development of adaptive radar and to theconstruction of spreading sequences and error-correcting codes incommunications. We contend that this group can form the basis forthe representation of the radar environment in terms of operatorson the space of waveforms. We also demonstrate, following recentdevelopments in the theory of error-correcting codes, that thefinite Heisenberg-Weyl groups provide a unified basis for theconstruction of useful waveforms/sequences for radar,communications, and the theory of error-correcting codes.}, Doi = {10.1155/ASP/2006/85685}, Key = {fds235855} } @article{fds235856, Author = {Lee, J-W and Chiang, M and Calderbank, AR}, Title = {Jointly optimal congestion and medium access control in ad hoc wireless networks}, Journal = {IEEE VTS ... Vehicular Technology Conference : VTC : [proceedings]}, Volume = {1}, Pages = {284-288}, Year = {2006}, ISSN = {1550-2252}, url = {http://dx.doi.org/10.1109/VETECS.2004.1387959}, Abstract = {We study joint end-to-end congestion control and per-link medium access control (MAC) in ad-hoc wireless networks. We use a network utility maximization formulation, in which by adjusting the types of utility functions, we can accommodate multi-class services as well as exploit the tradeoff between efficiency and fairness of resource allocation. Despite the inherent difficulties of non-convexity and non-separability of the optimization problem, we show that, under readily-verifiable sufficient conditions, we can develop a distributed algorithm that converges to the globally and jointly optimal rate allocation and persistence probabilities. A key contribution is that our results can accommodate general concave utility function rather than just the logarithmic utility function in existing results. © 2006 IEEE.}, Doi = {10.1109/VETECS.2004.1387959}, Key = {fds235856} } @article{fds235857, Author = {Lee, J-W and Chiang, M and Calderbank, AR}, Title = {Utility-optimal medium access control: Reverse and forward engineering}, Journal = {Proceedings - IEEE INFOCOM}, Year = {2006}, ISSN = {0743-166X}, url = {http://dx.doi.org/10.1109/INFOCOM.2006.252}, Abstract = {This paper analyzes and designs medium access control (MAC) protocols for wireless ad-hoc networks through the network utility maximization (NUM) framework. We first reverse-engineer the current exponential backoff (EB) type of MAC protocols such as the BEB (binary exponential backoff) in the IEEE 802.11 standard through a non-cooperative gametheoretic model. This MAC protocol is shown to be implicitly maximizing, using a stochastic subgradient, a selfish local utility at each link in the form of expected net reward for successful transmission. While the existence of a Nash equilibrium can be established, neither convergence nor social welfare optimality is guaranteed due to the inadequate feedback mechanism in the EB protocol. This motivates the forward-engineering part of the paper, where a network-wide utility maximization problem is formulated, using a collision and persistence probability model and aligning selfish utility with total social welfare. By adjusting the parameters in the utility objective functions of the NUM problem, we can also control the tradeoff between efficiency and fairness of radio resource allocation through a rigorous and systematic design. We develop two distributed algorithms to solve the MAC design NUM problem, which lead to random access protocols that have slightly more message passing overhead than the current EB protocol, but significant potential for efficiency and fairness improvement. We provide readily-verifiable sufficient conditions under which convergence of the proposed algorithms to a global optimality of network utility can be guaranteed, and through numerical examples illustrate the value of the NUM approach to the complexity-performance tradeoff in MAC design. © 2006 IEEE.}, Doi = {10.1109/INFOCOM.2006.252}, Key = {fds235857} } @article{fds235858, Author = {Chiang, M and Low, SH and Calderbank, AR and Doyle, JC}, Title = {Layering as optimization decomposition: Framework and examples}, Journal = {2006 IEEE Information Theory Workshop, ITW 2006}, Pages = {52-56}, Year = {2006}, Abstract = {Network protocols in layered architectures have historically been obtained primarily on an ad-hoc basis. Recent research has shown that network protocols may instead be holistically analyzed and systematically designed as distributed solutions to some global optimization problems in the form of Network Utility Maximization (NUM), providing insight into what they optimize and structures of the network protocol stack. This paper presents a short survey of the recent efforts towards a systematic understanding of 'layering' as 'optimization decomposition', where the overall communication network is modeled by a generalized NUM problem, each layer corresponds to a decomposed subproblem, and the interfaces among layers are quantified as functions of the optimization variables coordinating the subproblems. Different decompositions lead to alternative layering architectures. We summarize several examples of horizontal decomposition into distributed computation and vertical decomposition into functional modules such as congestion control, routing, scheduling, random access, power control, and coding. © 2006 IEEE.}, Key = {fds235858} } @article{fds235859, Author = {Lee, J-W and Chiang, M and Calderbank, AR}, Title = {Network utility maximization and price-based distributed algorithms for rate-reliability tradeoff}, Journal = {Proceedings - IEEE INFOCOM}, Year = {2006}, ISSN = {0743-166X}, url = {http://dx.doi.org/10.1109/INFOCOM.2006.110}, Abstract = {The current framework of network utility maximization for rate allocation and its price-based algorithms assumes that each link provides a fixed-size transmission 'pipe' and each user's utility is a function of transmission rate only. These assumptions break down in many practical systems, where, by adapting the physical layer channel coding or transmission diversity, different tradeoffs between rate and reliability can be achieved. In network utility maximization problems formulated in this paper, the utility for each user depends on both transmission rate and signal quality, with an intrinsic tradeoff between the two. Each link may also provide a higher (lower) rate on the transmission 'pipes' by allowing a higher (lower) decoding error probability. Despite non-separability and nonconvexity of these optimization problems, we propose new pricebased distributed algorithms and prove their convergence to the globally optimal rate-reliability tradeoff under readily-verifiable sufficient conditions. We first consider networks in which the rate-reliability tradeoff is controlled by adapting channel code rates in each link's physical layer error correction codes, and propose two distributed algorithms based on pricing, which respectively implement the 'integrated' and 'differentiated' policies of dynamic ratereliability adjustment. In contrast to the classical price-based rate control algorithms, in our algorithms each user provides an offered price for its own reliability to the network while the network provides congestion prices to users. The proposed algorithms converge to a tradeoff point between rate and reliability, which we prove to be a globally optimal one for channel codes with sufficiently large coding length and utilities whose curvatures are sufficiently negative. Under these conditions, the proposed algorithms can thus generate the Pareto optimal tradeoff curves between rate and reliability for all the users. The distributed algorithms and convergence proofs are extended for wireless MIMO multi-hop networks, in which diversity and multiplexing gains of each link are controlled to achieve the optimal ratereliability tradeoff. © 2006 IEEE.}, Doi = {10.1109/INFOCOM.2006.110}, Key = {fds235859} } @article{fds235860, Author = {Liu, J and Calderbank, AR}, Title = {The icosian code and the e_{8}lattice: A new 4 × 4 space-time code with non-vanishing determinant}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Pages = {1006-1010}, Year = {2006}, url = {http://dx.doi.org/10.1109/ISIT.2006.261879}, Abstract = {This paper introduces a new full-rate, full-diversity space-time code for 4 transmit antennas. The 4 × 4 codeword matrix consists of four 2 × 2 Alamouti blocks with entries from Q(i, √5), and these blocks can be viewed as quaternions which in turn represent rotations in R3. The Alamouti blocks that appear in a codeword are drawn from the icosian ring consisting of all linear combinations of 120 basic rotations corresponding to symmetries of the icosahedron. This algebraic structure is different from the Golden code, but the complex entries are taken from a similar underlying field. The minimum determinant is bounded below by a constant that is independent of the signal constellation, and the new code admits a simple decoding scheme that makes use of a geometric correspondence between the icosian ring and the E 8 lattice. © 2006 IEEE.}, Doi = {10.1109/ISIT.2006.261879}, Key = {fds235860} } @article{fds235861, Author = {Minn, H and Li, Y and Al-Dhahir, N and Calderbank, R}, Title = {Pilot designs for consistent frequency offset estimation in OFDM systems}, Journal = {Conference Record - International Conference on Communications}, Volume = {10}, Pages = {4566-4571}, Year = {2006}, ISSN = {0536-1486}, url = {http://dx.doi.org/10.1109/ICC.2006.255359}, Abstract = {This paper presents pilot designs for consistent frequency offset estimation of OFDM systems in frequencyselective fading channels. We describe two design approaches, namely consistency in the probabilistic sense and absolute consistency. Existing preambles and pilot designs in the literature do not guarantee the absolute consistency. We derive general criteria for both approaches, present sufficient conditions on the pilot structures, and derive simple pilot designs satisfying these conditions. Absolute consistency should not be compromised in emergency-related or other critical communication scenarios and our proposed consistent pilot designs address this need. © 2006 IEEE.}, Doi = {10.1109/ICC.2006.255359}, Key = {fds235861} } @article{fds235862, Author = {Chul, J and Calderbank, AR}, Title = {Effective coding gain for space-time codes}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Pages = {252-256}, Year = {2006}, url = {http://dx.doi.org/10.1109/ISIT.2006.261844}, Abstract = {The performance of space-time codes is evaluated in terms of diversity gain and coding gain, two measures which describe the worst-case pairwise error probability between codewords at high signal-to-noise ratio (SNR). We introduce the concept of effective coding gain to provide an estimate on the bit error rate (BER) at low-to-moderate SNR. This concept connects the number of nearest neighbours with degradation in error performance. We demonstrate the value of the new concept through analysis of space-time block codes for the quasi-static Rayleigh fading channel. © 2006 IEEE.}, Doi = {10.1109/ISIT.2006.261844}, Key = {fds235862} } @article{fds235863, Author = {Das, S and Al-Dhahir, N and Calderbank, R and Chui, J}, Title = {New full-diversity high-rate space-time block codes based on selective power scaling}, Journal = {European Signal Processing Conference}, Year = {2006}, ISSN = {2219-5491}, Abstract = {We design a new rate-5/4 full-diversity orthogonal STBC for QPSK and 2 transmit antennas by enlarging the signalling set from the set of quaternions used in the Alamouti [1] code. Selective power scaling of information symbols is used to guarantee full-diversity while maximizing the coding gain and minimizing the transmitted signal peak-to-minimum power ratio. The optimum power scaling factor is derived using two equivalent criteria and shown to outperform schemes based on only constellation rotation while still enjoying a lowcomplexity ML decoding algorithm. Extensions to the case of 4 transmit antennas are reported in [4].}, Key = {fds235863} } @article{fds235864, Author = {Calderbank, AR and Howard, SD and Moran, W and Pezeshki, A and Zoltowski, M}, Title = {Instantaneous radar polarimetry with multiple dually-polarized antennas}, Journal = {Conference Record of the Asilomar Conference on Signals, Systems and Computers}, Pages = {757-761}, Year = {2006}, ISSN = {1058-6393}, url = {http://dx.doi.org/10.1109/ACSSC.2006.354850}, Abstract = {Fully Polarimetric radar systems are capable of simultaneously transmitting and receiving in two orthogonal polarizations. Instantaneous radar polarimetry exploits both polarization modes of a dually-polarized radar transmitter and receiver on a pulse by pulse basis, and can improve the radar detection performance and suppress range sidelobes. In this paper, we extend the use of instantaneous radar polarimetry for radar systems with multiple dually-polarized transmit and receive antennas. Alamouti signal processing is used to coordinate transmission of Golay pairs of phase codes waveforms across polarizations and multiple antennas. The integration of multi-antenna signal processing with instantaneous radar polarimetry can further improve the detection performance, at a computational cost comparable to single channel matched filtering.}, Doi = {10.1109/ACSSC.2006.354850}, Key = {fds235864} } @article{fds235865, Author = {Das, S and Al-Dhahir, N and Calderbank, R}, Title = {Novel full-diversity high-rate STBC for 2 and 4 transmit antennas}, Journal = {IEEE Communications Letters}, Volume = {10}, Number = {3}, Pages = {171-173}, Year = {2006}, ISSN = {1089-7798}, url = {http://dx.doi.org/10.1109/LCOMM.2006.1603374}, Abstract = {We design a new rate-5/4 full-diversity orthogonal space-time block code (STBC) for QPSK and 2 transmit antennas (TX) by enlarging the signalling set from the set of quaternions used in the Alamouti [1] code. Selective power scaling of information symbols is used to guarantee full-diversity while maximizing the coding gain (CG) and minimizing the transmitted signal peak-to-minimum power ratio (PMPR). The optimum power scaling factor is derived analytically and shown to outperform schemes based only on constellation rotation while still enjoying a low-complexity maximum likelihood (ML) decoding algorithm. Finally, we extend our designs to the case of 4 TX by enlarging the set of Quasi-Orthogonal STBC with power scaling. Extensions to general M-PSK constellations are straightforward. © 2006 IEEE.}, Doi = {10.1109/LCOMM.2006.1603374}, Key = {fds235865} } @article{fds235866, Author = {Lee, J-W and Chiang, M and Calderbank, AR}, Title = {Jointly optimal congestion and contention control based on network utility maximization}, Journal = {IEEE Communications Letters}, Volume = {10}, Number = {3}, Pages = {216-218}, Year = {2006}, ISSN = {1089-7798}, url = {http://dx.doi.org/10.1109/LCOMM.2006.1603389}, Abstract = {We study joint end-to-end congestion control and per-link medium access control (MAC) in ad-hoc networks. We use a network utility maximization formulation, in which by adjusting the types of utility functions, we can accommodate multi-class services as well as exploit the tradeoff between efficiency and fairness of resource allocation. Despite the inherent difficulties of non-convexity and non-separability of the optimization problem, we show that, with readily-verifiable sufficient conditions, we can develop a distributed algorithm that converges to the globally and jointly optimal rate allocation and persistence probabilities. © 2006 IEEE.}, Doi = {10.1109/LCOMM.2006.1603389}, Key = {fds235866} } @article{fds235867, Author = {Lee, J-W and Chiang, M and Calderbank, AR}, Title = {Price-based distributed algorithms for rate-reliability tradeoff in network utility maximization}, Journal = {IEEE Journal on Selected Areas in Communications}, Volume = {24}, Number = {5}, Pages = {962-976}, Year = {2006}, ISSN = {0733-8716}, url = {http://dx.doi.org/10.1109/JSAC.2006.872877}, Abstract = {The current framework of network utility maximization for rate allocation and its price-based algorithms assumes that each link provides a fixed-size transmission "pipe" and each user's utility is a function of transmission rate only. These assumptions break down in many practical systems, where, by adapting the physical layer channel coding or transmission diversity, different tradeoffs between rate and reliability can be achieved. In network utility maximization problems formulated in this paper, the utility for each user depends on both transmission rate and signal quality, with an intrinsic tradeoff between the two. Each link may also provide a higher (or lower) rate on the transmission "pipes" by allowing a higher (or lower) decoding error probability. Despite non-separability and nonconvexity of these optimization problems, we propose new price-based distributed algorithms and prove their convergence to the globally optimal rate-reliability tradeoff under readily-verifiable sufficient conditions. We first consider networks in which the rate-reliability tradeoff is controlled by adapting channel code rates in each link's physical-layer error correction codes, and propose two distributed algorithms based on pricing, which respectively implement the "integrated" and "differentiated" policies of dynamic rate-reliability adjustment. In contrast to the classical price-based rate control algorithms, in our algorithms, each user provides an offered price for its own reliability to the network, while the network provides congestion prices to users. The proposed algorithms converge to a tradeoff point between rate and reliability, which we prove to be a globally optimal one for channel codes with sufficiently large coding length and utilities whose curvatures are sufficiently negative. Under these conditions, the proposed algorithms can thus generate the Pareto optimal tradeoff curves between rate and reliability for all the users. In addition, the distributed algorithms and convergence proofs are extended for wireless multiple-inpit-multiple-output multihop networks, in which diversity and multiplexing gains of each link are controlled to achieve the optimal rate-reliability tradeoff. Numerical examples confirm that there can be significant enhancement of the network utility by distributively trading-off rate and reliability, even when only some of the links can implement dynamic reliability. © 2006 IEEE.}, Doi = {10.1109/JSAC.2006.872877}, Key = {fds235867} } @article{fds235741, Author = {Calderbank, AR and Naguib, AF}, Title = {Introduction to space-time codes}, Volume = {9780521851053}, Pages = {133-153}, Year = {2006}, Month = {January}, url = {http://dx.doi.org/10.1017/CBO9780511616815.008}, Abstract = {© Cambridge University Press 2006. Introduction Information-theoretic analysis by Foschini (1996) and by Telatar (1999) shows that multiple antennas at the transmitter and receiver enable very high rate wireless communication. Space-time codes, introduced by Tarokh. (1998), improve the reliability of communication over fading channels by correlating signals across different transmit antennas. Design criteria developed for the high-SNR regime in Tarokh. (1998) and Guey. (1999) are presented in Section 7.3 from the perspective of typical error events (following the exposition by Tse and Viswanath (2005)). Techniques for multiple access and broadcast communication are described very briefly in Sections 7.9 and 7.10, where algebraic structure enables simple implementation. The emphasis throughout is on low cost, low complexity mobile receivers. Section 7.2 provides a description of set partitioning, which was developed by Ungerboeck (1982) as the basis of code design for the additive white Gaussian noise (AWGN) channel. The importance of set partitioning to code design for the AWGN channel is that it provides a lower bound on squared Euclidean distance between signals that depends only on the binary sum of signal labels. Section 7.9 describes the importance of set partitioning to code design for wireless channels, where it provides a mechanism for translating constraints in the binary domain into lower bounds on diversity protection in the complex domain. Section 7.4 describes space-time trellis codes, starting from simple delay diversity, and then using intuition about the product distance to realize additional coding gain.}, Doi = {10.1017/CBO9780511616815.008}, Key = {fds235741} } @article{fds235742, Author = {Naguib, AF and Calderbank, AR}, Title = {Diversity in wireless systems}, Volume = {9780521851053}, Pages = {44-65}, Year = {2006}, Month = {January}, url = {http://dx.doi.org/10.1017/CBO9780511616815.004}, Abstract = {© Cambridge University Press 2006. Introduction The main impairment in wireless channels is fading or random fluctuation of the signal level. This signal fluctuation happens across time, frequency, and space. Diversity techniques provide the receiver with multiple independent looks at the signal to improve reception. Each one of those independent looks is considered a diversity branch. The probability that all diversity branches will fade at the same time goes down as the number of branches increases. Hence, with a high probability, there will be at least one branch or link with a good signal such that the transmitted data can be detected reliably. Wireless channels are, in general, characterized by frequency-selective multipath propagation, Doppler-induced time-selective fading, and spaceselective fading. An emitted signal propagating through the wireless channel is reflected and scattered from a large number of scatterers, thereby arriving at the receiver through different paths and hence arriving at different times. This results in the time dispersion of the transmitted signal. A measure of this dispersion is called the channel delay spread Tmax. The coherence bandwidth of the channel Bc ≈ l/Tmax measures the frequency bandwidth over which the propagation channel remains correlated. Therefore, a propagation channel with a small delay spread will have a large coherence bandwidth, i.e., the channel frequency response will remain correlated over a large bandwidth, and vice versa. In addition, transmitter and receiver mobility as well as changes in the propagation medium induce time variations in the propagation channel.}, Doi = {10.1017/CBO9780511616815.004}, Key = {fds235742} } @article{fds235769, Author = {Calderbank, R}, Title = {Technology as driver of change in telecommunications}, Pages = {69-86}, Year = {2006}, Month = {January}, url = {http://dx.doi.org/10.1007/3-540-32556-5_4}, Doi = {10.1007/3-540-32556-5_4}, Key = {fds235769} } @article{fds235868, Author = {Sira, SP and Cochran, D and Papandreou-Suppappola, A and Morrell, D and Moran, B and Howards, S and Calderbank, R}, Title = {Improving detection in sea clutter using waveform scheduling}, Journal = {IEEE International Conference on Acoustics Speech and Signal Processing}, Volume = {3}, Pages = {III1241-III1244}, Year = {2007}, ISSN = {1520-6149}, url = {http://dx.doi.org/10.1109/ICASSP.2007.367068}, Abstract = {In this paper, we propose a method to exploit waveform agility in modern radars to improve performance in the challenging task of detecting small targets on the ocean surface in heavy clutter. The approach exploits the compound-Gaussian model for sea clutter returns to achieve clutter suppression by forming an orthogonal projection of the received signal into the clutter subspace. Waveform scheduling is then performed by incorporating the information about the clutter into the design of the next transmitted waveform. A simulation study demonstrates the effectiveness of our approach. © 2007 IEEE.}, Doi = {10.1109/ICASSP.2007.367068}, Key = {fds235868} } @article{fds235869, Author = {Li, Y and Chiang, M and Calderbank, AR and Diggavi, SN}, Title = {Optimal rate-reliability-delay tradeoff in networks with composite links}, Journal = {Proceedings - IEEE INFOCOM}, Pages = {526-534}, Year = {2007}, ISSN = {0743-166X}, url = {http://dx.doi.org/10.1109/INFCOM.2007.68}, Abstract = {Networks need to accommodate diverse applications with different Quality-of-Service (QoS) requirements. New ideas at the physical layer are being developed for this purpose, such as diversity embedded coding, which is a technique that combines high rates with high reliability. We address the problem of how to fully utilize different rate-reliability characteristics at the physical layer to support different types of traffic over a network and to jointly maximize their utilities. We set up a new framework based on utility maximization for networks with composite links, meaning that each link consists of sub-links that can attain different rate-reliability characteristics simultaneously. We incorporate delay, in addition to rate and reliability, into the utility functions. To accommodate different types of traffic, we propose distributed algorithms for the optimal rate-reliability-delay tradeoff based on capacity division and priority queueing. Numerical results show that compared with traditional codes, the new codes can provide higher network utilities for all traffic types simultaneously. The results also show that priority queueing achieves higher network utility than capacity division. © 2007 IEEE.}, Doi = {10.1109/INFCOM.2007.68}, Key = {fds235869} } @article{fds235870, Author = {Xu, D and Li, Y and Chiang, M and Calderbank, AR}, Title = {Optimal provisioning of elastic service availability}, Journal = {Proceedings - IEEE INFOCOM}, Pages = {1505-1513}, Year = {2007}, ISSN = {0743-166X}, url = {http://dx.doi.org/10.1109/INFCOM.2007.177}, Abstract = {Service availability is one of the most closely scrutinized metrics in offering network services. The network vendor can earn more revenue from the customers by guaranteeing higher service availability at the cost of higher operational expense. It is important to cost-effectively provision a managed and differentiated network with various service availability guarantees under a unified platform. In this paper, we establish the framework of provisioning elastic service availability through network utility maximization, and propose an optimal and distributed solution using differentiated failure recovery schemes. First, we develop a utility function with configurable parameters to represent the satisfaction perceived by a user upon service availability as well as its allowed source rate. Second, adopting Quality of Protection [1] and shared path protection, we transform optimal provisioning of elastic service availability into a convex optimization problem. The desirable service availability and source rate for each user can be achieved using a price-based distributed algorithm. Finally, we numerically show the tradeoff between the throughput and the service availability obtained by users in various network topologies. Several quantitative observations are made from this investigation. For example, indiscriminately provisioning service availabilities for different kinds of users within one network leads to noteworthy sub-optimality in total network utility. The profile of bandwidth usage also illustrates that provisioning high service availability exclusively for critical applications leads to significant waste in bandwidth resource. © 2007 IEEE.}, Doi = {10.1109/INFCOM.2007.177}, Key = {fds235870} } @article{fds235871, Author = {Chiang, M and Low, SH and Calderbank, AR and Doyle, JC}, Title = {Layering as optimization decomposition: Questions and answers}, Journal = {Proceedings - IEEE Military Communications Conference MILCOM}, Year = {2007}, url = {http://dx.doi.org/10.1109/MILCOM.2006.302293}, Abstract = {Network protocols in layered architectures have historically been obtained on an ad-hoc basis, and much of the recent cross-layer designs are conducted through piecemeal approaches. Network protocols may instead be holistically analyzed and systematically designed as distributed solutions to some global optimization problems in the form of generalized Network Utility Maximization (NUM), providing insight on what they optimize and on the structures of network protocol stacks. In the form of 10 Questions and Answers, this paper presents a short survey of the recent efforts towards a systematic understanding of "layering" as "optimization decomposition". The overall communication network is modeled by a generalized NUM problem, each layer corresponds to a decomposed subproblem, and the interfaces among layers are quantified as functions of the optimization variables coordinating the subproblems. Furthermore, there are many alternative decompositions, each leading to a different layering architecture. Industry adoption of this unifying framework has also started. Here we summarize the current status of horizontal decomposition into distributed computation and vertical decomposition into functional modules such as congestion control, routing, scheduling, random access, power control, and coding. We also discuss under-explored future research directions in this area. More importantly than proposing any particular crosslayer design, this framework is working towards a mathematical foundation of network architectures and the design process of modularization.}, Doi = {10.1109/MILCOM.2006.302293}, Key = {fds235871} } @article{fds235872, Author = {Li, Y and Minn, H and Al-Dhahir, N and Calderbank, R}, Title = {Robust pilot design for consistent carrier frequency offset estimation}, Journal = {Proceedings - IEEE Military Communications Conference MILCOM}, Year = {2007}, url = {http://dx.doi.org/10.1109/MILCOM.2006.302204}, Abstract = {Consistent pilot designs [6] for carrier frequency offset (CFO) estimation eliminate ambiguity in the noise-free estimation metric trajectory regardless of the channel impulse response. Their importance is more pronounced in emergency and disaster situations since an inconsistent CFO estimate will result in a link failure. The CFO estimation performances of distinct consistent pilot designs can be quite different at moderate or low SNR due to different statistics of outlier which also yields a link failure. In this paper, we develop novel pilot designs that provide both consistency and robustness against outliers. We also propose new generalized pilot designs that yield consistency over any arbitrary but fixed CFO estimation range and that include our previous consistent pilot designs in [6] as a special case which provides consistency over the maximum CFO estimation range (half of the sampling rate). Our new consistent pilot designs facilitate more flexible and economical implementation while our robust pilot designs enable wireless links with less outage and better resilience.}, Doi = {10.1109/MILCOM.2006.302204}, Key = {fds235872} } @article{fds235873, Author = {Chiang, M and Low, SH and Calderbank, AR and Doyle, JC}, Title = {Layering as optimization decomposition: Current status and open issues}, Journal = {2006 IEEE Conference on Information Sciences and Systems, CISS 2006 - Proceedings}, Pages = {355-362}, Year = {2007}, url = {http://dx.doi.org/10.1109/CISS.2006.286492}, Abstract = {Network protocols in layered architectures have historically been obtained on an ad-hoc basis, and much of the recent cross-layer designs are conducted through piecemeal approaches. Network protocols may instead be holistically analyzed and systematically designed as distributed solutions to some global optimization problems in the form of generalized Network Utility Maximization (NUM), providing insight on what they optimize and structures of the network protocol stack. This paper presents a short survey of the recent efforts towards a systematic understanding of "layering" as "optimization decomposition", where the overall communication network is modeled by a generalized NUM problem, each layer corresponds to a decomposed subproblem, and the interfaces among layers are quantified as functions of the optimization variables coordinating the subproblems. Furthermore, there are many alternative decompositions, each leading to a different layering architecture. Industry adoption of this unifying framework has also started. Here we summarize the current status of horizontal decomposition into distributed computation and vertical decomposition into functional modules such as congestion control, routing, scheduling, random access, power control, and coding. Key messages and methodologies arising out of many recent work are listed. Then we present a list of challenging open issues in this area and the initial progress made on some of them. © 2006 IEEE.}, Doi = {10.1109/CISS.2006.286492}, Key = {fds235873} } @article{fds235874, Author = {Li, Y and Chiang, M and Calderbank, AR}, Title = {Congestion control in networks with delay sensitive traffic}, Journal = {GLOBECOM - IEEE Global Telecommunications Conference}, Pages = {2746-2751}, Year = {2007}, url = {http://dx.doi.org/10.1109/GLOCOM.2007.520}, Abstract = {We study the congestion control in a network where the users may have different types of traffic, such as the traffic with fixed/variable rate, delay sensitive/insensitive, etc. To reflect the different requirements on delay by different applications, explicit terms of delay are added to the utility function. We analyze the essential dynamics for the network utility maximization (NUM) with the new utility functions. Compared with the basic NUM where the utility function is only a function of rate, the dynamics for link price is now related to the delay term added in the utility function. The analysis is applied to the system with voice and data traffic, and distributed algorithms are proposed to allocate the resource such that the utility of voice and data is jointly optimized. The numerical results show that by the new price dynamics, we can accomplish optimal congestion control for users with delay sensitive/insensitive traffic in a network. In particular, in a network with data and voice traffic with priority queueing, the algorithm can lead the network to achieve higher quality of voice traffic and higher throughput of data traffic, with the sacrifice of the packet delay of data traffic. © 2007 IEEE.}, Doi = {10.1109/GLOCOM.2007.520}, Key = {fds235874} } @article{fds235875, Author = {Howard, SD and Sirianunpiboon, S and Calderbank, AR}, Title = {Fast decoding of the golden code by diophantine approximation}, Journal = {2007 IEEE Information Theory Workshop, ITW 2007, Proceedings}, Pages = {590-594}, Year = {2007}, url = {http://dx.doi.org/10.1109/ITW.2007.4313140}, Abstract = {The Golden Code is incorporated in the IEEE 802.16 standard and is representative of a large class of space-time codes where performance is determined by the difficulty of solving an associated Diophantine approximation problem. This paper develops a new approach to coherent decoding where channel state information is used to select from a plurality of zero-forcing decoders. The selection is made to maximize effective signal to noise ratio and the underlying Diophantine geometry guarantees that at least one of the available choices is good. The approach is described in detail for the important special case of the Golden code but it applies to a larger class of space-time codes where it provides a means of avoiding the uncertainties and implementation complexity associated with sphere decoding. In particular it extends battery life at the mobile terminal by eliminating the need for a second receive antenna. Simulation results for the Golden Code show performance within 2 dB of full maximum-likelihood decoding with worst case complexity that is quadratic in the size of the QAM signal constellation. © 2007 IEEE.}, Doi = {10.1109/ITW.2007.4313140}, Key = {fds235875} } @article{fds235876, Author = {Calderbank, R and Kobayashi, H}, Title = {Greetings}, Journal = {2006 IEEE Conference on Information Sciences and Systems, CISS 2006 - Proceedings}, Pages = {iii}, Year = {2007}, url = {http://dx.doi.org/10.1109/CISS.2006.286417}, Doi = {10.1109/CISS.2006.286417}, Key = {fds235876} } @article{fds235877, Author = {Dusad, S and Diggavi, SN and Calderbank, AR}, Title = {Cross layer utility of diversity embedded codes}, Journal = {2006 IEEE Conference on Information Sciences and Systems, CISS 2006 - Proceedings}, Pages = {795-800}, Year = {2007}, url = {http://dx.doi.org/10.1109/CISS.2006.286575}, Abstract = {Diversity embedded codes are opportunistic codes designed for the wireless fading channel. They are high-rate space-time codes which have embedded within them a high-diversity (low rate) code. In this paper, we focus on the application of diversity embedded code to transmission of images over wireless channels. We match the diversity embedded code with a hierarchical (layered) source coder and quantify the image quality as compared to a single-layer space-time code. These preliminary results suggest that diversity embedded codes might be the right physical layer functionality required for wireless multimedia transmission. © 2006 IEEE.}, Doi = {10.1109/CISS.2006.286575}, Key = {fds235877} } @article{fds235878, Author = {Aggarwal, V and Bennatan, A and Calderbank, AR}, Title = {On maximizing coverage in Gaussian relay networks}, Journal = {Proceedings of the 2007 IEEE Information Theory Workshop on Information Theory for Wireless Networks, ITW}, Pages = {37-41}, Year = {2007}, url = {http://dx.doi.org/10.1109/ITWITWN.2007.4318027}, Abstract = {Results for Gaussian relay channels typically focus on maximizing transmission rates for given locations of the source, relay and destination. We consider an alternative approach, focusing on maximizing coverage for a given rate. This novel perspective enables treatment of the relay location as a design parameter, producing an extra degree of freedom that may be optimized. Focusing on coverage, we evaluate existing approaches, like decode and forward (DF), compress and forward (CF) and compare them with upper bounds. In the process, we obtain some surprising insights on the performance of these approaches. ©2007 IEEE.}, Doi = {10.1109/ITWITWN.2007.4318027}, Key = {fds235878} } @article{fds235879, Author = {Sirianunpiboon, S and Howard, SD and Calderbank, AR}, Title = {Diversity gains across line of sight and rich scattering environments from space-polarization-time codes}, Journal = {Proceedings of the 2007 IEEE Information Theory Workshop on Information Theory for Wireless Networks, ITW}, Pages = {1-5}, Year = {2007}, url = {http://dx.doi.org/10.1109/ITWITWN.2007.4318020}, Abstract = {Space-time codes built out of Alamouti components have been adopted in wireless standards such as UMTS, IEEE 802.11n and IEEE 802.16 where they facilitate higher data rates through multiplexing of parallel data streams and the addition of two or more antennas at the receiver that perform interference cancellation. This paper provides new theoretical insight into an algorithm for interference cancellation through a Bayesian analysis that expresses performance as a function of SNR in terms of the "angles" between different space-time coded data streams. Our approach provides insights into the coupling of channel coding to spatial and polarization degrees of freedom. ©2007 IEEE.}, Doi = {10.1109/ITWITWN.2007.4318020}, Key = {fds235879} } @article{fds235880, Author = {Pezeshki, A and Calderbank, R and Howard, SD and Moran, W}, Title = {Doppler resilient golay complementary pairs for radar}, Journal = {IEEE Workshop on Statistical Signal Processing Proceedings}, Pages = {483-487}, Year = {2007}, url = {http://dx.doi.org/10.1109/SSP.2007.4301305}, Abstract = {We present a systematic way of constructing a Doppler resilient sequence of Golay complementary waveforms for radar, for which the composite ambiguity function maintains ideal shape at small Doppler shifts. The idea is to determine a sequence of Golay pairs that annihilates the low-order terms of the Taylor expansion of the composite ambiguity function. The Prouhet-Thue-Morse sequence plays a key role in the construction of Doppler resilient sequences of Golay pairs. We extend this construction to multiple dimensions. In particular, we consider radar polarimetry, where the dimensions are realized by two orthogonal polarizations. We determine a sequence of two-by-two Alamouti matrices, where the entries involve Golay pairs and for which the matrix-valued composite ambiguity function vanishes at small Doppler shifts. ©2007 IEEE.}, Doi = {10.1109/SSP.2007.4301305}, Key = {fds235880} } @article{fds235881, Author = {Suvorova, S and Howard, S and Moran, B and Calderbank, R and Pezeshki, A}, Title = {Doppler resilience, reed-müller codes and complementary waveforms}, Journal = {Conference Record of the Asilomar Conference on Signals, Systems and Computers}, Pages = {1839-1843}, Year = {2007}, ISSN = {1058-6393}, url = {http://dx.doi.org/10.1109/ACSSC.2007.4487553}, Abstract = {While the use of complementary waveforms has been considered as a technique for providing essentially perfect range sidelobe performance in radar systems, its lack of resilience to Doppler is often cited as a reason not to deploy it. This work describes and examines techniques both for providing Doppler resilience as well as tailoring Doppler performance to specific aims. The Doppler performance can be varied by suitably changing the order of transmission of multiple sets of complementary waveforms. We propose a method which improves Doppler performance significantly in specific Doppler ranges by arranging the transmission of multiple copies of complementary waveforms according to a suitable choice from the first order Reed-Müller codes. We provide both a theoretical analysis and computer simulations of the Doppler response of waveform sequences constructed in this way. © 2007 IEEE.}, Doi = {10.1109/ACSSC.2007.4487553}, Key = {fds235881} } @article{fds235882, Author = {Dusad, S and Diggavi, SN and Calderbank, AR}, Title = {Rank distance codes for ISI channels}, Journal = {Proceedings of the 2007 IEEE Information Theory Workshop on Information Theory for Wireless Networks, ITW}, Pages = {32-36}, Year = {2007}, url = {http://dx.doi.org/10.1109/ITWITWN.2007.4318026}, Abstract = {Designs for transmit alphabet constrained space-time codes naturally lead to questions about the design of rank distance codes. Recently, diversity embedded multi-level space-time codes for flat fading channels have been designed by using sets of binary matrices with rank distance guarantees over the binary field and mapping them onto QAM and PSK constellations. In this paper we give the design of diversity embedded space-time codes for fading Inter-Symbol Interference (ISI) channels with provable rank distance guarantees. In the process of doing so we also get a (asymptotic) characterization of the rate-diversity trade-off for multiple antenna fading ISI channels when there is a fixed transmit alphabet constraint. The key idea is to construct and analyze properties of binary matrices with the particular structure induced by ISI channels. ©2007 IEEE.}, Doi = {10.1109/ITWITWN.2007.4318026}, Key = {fds235882} } @article{fds235883, Author = {Chiang, M and Low, SH and Calderbank, AR and Doyle, JC}, Title = {Layering as optimization decomposition: A mathematical theory of network architectures}, Journal = {Proceedings of the Institute of Electrical and Electronics Engineers (IEEE)}, Volume = {95}, Number = {1}, Pages = {255-312}, Year = {2007}, ISSN = {0018-9219}, url = {http://dx.doi.org/10.1109/JPROC.2006.887322}, Abstract = {Network protocols in layered architectures have historically been obtained on an ad hoc basis, and many of the recent cross-layer designs are also conducted through piecemeal approaches. Network protocol stacks may instead be holistically analyzed and systematically designed as distributed solutions to some global optimization problems. This paper presents a survey of the recent efforts towards a systematic understanding of layering as optimization decomposition, where the overall communication network is modeled by a generalized network utility maximization problem, each layer corresponds to a decomposed subproblem, and the interfaces among layers are quantified as functions of the optimization variables coordinating the subproblems. There can be many alternative decompositions, leading to a choice of different layering architectures. This paper surveys the current status of horizontal decomposition into distributed computation, and vertical decomposition into functional modules such as congestion control, routing, scheduling, random access, power control, and channel coding. Key messages and methods arising from many recent works are summarized, and open issues discussed. Through case studies, it is illustrated how layering as Optimization Decomposition provides a common language to think about modularization in the face of complex, networked interactions, a unifying, top-down approach to design protocol stacks, and a mathematical theory of network architectures © 2006 IEEE.}, Doi = {10.1109/JPROC.2006.887322}, Key = {fds235883} } @article{fds235884, Author = {Aggarwal, V and Calderbank, AR}, Title = {Boolean functions, projection operators and quantum error correcting codes}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Pages = {2091-2095}, Year = {2007}, url = {http://dx.doi.org/10.1109/ISIT.2007.4557529}, Abstract = {This paper describes a common mathematical framework for the design of additive and non-additive Quantum Error Correcting Codes. It is based on a correspondence between boolean functions and projection operators. The new framework extends to operator quantum error correcting codes. ©2007 IEEE.}, Doi = {10.1109/ISIT.2007.4557529}, Key = {fds235884} } @article{fds235885, Author = {Howard, SD and Calderbank, AR and Moran, W}, Title = {A simple signal processing architecture for instantaneous radar polarimetry}, Journal = {IEEE Transactions on Information Theory}, Volume = {53}, Number = {4}, Pages = {1282-1289}, Year = {2007}, ISSN = {0018-9448}, url = {http://dx.doi.org/10.1109/TIT.2007.892809}, Abstract = {This paper describes a new radar primitive that enables instantaneous radar polarimetry at essentially no increase in signal processing complexity. This primitive coordinates transmission of distinct waveforms on orthogonal polarizations and applies a unitary matched filter bank on receive. This avoids the information loss inherent in single-channel matched filters. A further advantage of this scheme is the elimination of range sidelobes. © 2007 IEEE.}, Doi = {10.1109/TIT.2007.892809}, Key = {fds235885} } @article{fds235886, Author = {Li, Y and Minn, H and Al-Dhahir, N and Calderbank, AR}, Title = {Pilot designs for consistent frequency-offset estimation in OFDM systems}, Journal = {IEEE Transactions on Communications}, Volume = {55}, Number = {5}, Pages = {864-877}, Year = {2007}, ISSN = {0090-6778}, url = {http://dx.doi.org/10.1109/TCOMM.2007.896105}, Abstract = {This paper presents pilot designs for consistent frequency-offset estimation of orthogonal frequency-division multiplexing systems in frequency-selective fading channels. We describe two design approaches, namely, consistency in the probabilistic sense and absolute consistency. Existing preambles and pilot designs in the literature do not guarantee the absolute consistency. We derive general criteria for both approaches, present sufficient conditions on the pilot structures over the maximum carrier frequency offset (CFO) estimation range (half of the sampling rate), and derive simple pilot designs satisfying these conditions. We also extend the sufficient conditions to any arbitrary but fixed CFO estimation range, and present some generalized design patterns. Furthermore, the CFO estimation performances of distinct consistent pilot designs can be quite different at moderate or low signal-to-noise ratio (SNR) due to different statistics of outliers which also yields a link failure. We develop efficient pilot-design criteria that provide both consistency and robustness against outliers at moderate-to-low SNR. Our consistent pilot designs facilitate flexible and economical implementation, while our robust pilot designs enable wireless links with less outage and better resilience. © 2007 IEEE.}, Doi = {10.1109/TCOMM.2007.896105}, Key = {fds235886} } @article{fds235887, Author = {Sira, SP and Cochran, D and Papandreou-Suppappola, A and Morrell, D and Moran, W and Howard, SD and Calderbank, R}, Title = {Adaptive waveform design for improved detection of low-RCS targets in heavy sea clutter}, Journal = {IEEE Journal of Selected Topics in Signal Processing}, Volume = {1}, Number = {1}, Pages = {56-66}, Year = {2007}, ISSN = {1932-4553}, url = {http://dx.doi.org/10.1109/JSTSP.2007.897048}, Abstract = {The dynamic adaptation of waveforms for transmission by active radar has been facilitated by the availability of waveform-agile sensors. In this paper, we propose a method to employ waveform agility to improve the detection of low radar-cross section (RCS) targets on the ocean surface that present low signal-to-clutter ratios due to high sea states and low grazing angles. Employing the expectation-maximization algorithm to estimate the time-varying parameters for compound-Gaussian sea clutter, we develop a generalized likelihood ratio test (GLRT) detector and identify a range bin of interest. The clutter estimates are then used to dynamically design a phase-modulated waveform that minimizes the out-of-bin clutter contributions to this range bin. A simulation based on parameters derived from real sea clutter data demonstrates that our approach provides around 10 dB improvement in detection performance over a nonadaptive system. © 2007 IEEE.}, Doi = {10.1109/JSTSP.2007.897048}, Key = {fds235887} } @article{fds235888, Author = {Lee, J-W and Chiang, M and Calderbank, AR}, Title = {Utility-optimal random-access control}, Journal = {IEEE Transactions on Wireless Communications}, Volume = {6}, Number = {7}, Pages = {2741-2750}, Year = {2007}, ISSN = {1536-1276}, url = {http://dx.doi.org/10.1109/TWC.2007.05991}, Abstract = {This paper designs medium access control (MAC) protocols for wireless networks through the network utility maximization (NUM) framework. A network-wide utility maximization problem is formulated, using a collision/persistenceprobabilistic model and aligning selfish utility with total social welfare. By adjusting the parameters in the utility objective functions of the NUM problem, we can also control the tradeoff between efficiency and fairness of radio resource allocation. We develop two distributed algorithms to solve the utility-optimal random-access control problem, which lead to random access protocols that have slightly more message passing overhead than the current exponential-backoff protocols, but significant potential for efficiency and fairness improvement. We provide readily-verifiable sufficient conditions under which convergence of the proposed algorithms to a global optimality of network utility can be guaranteed, and numerical experiments that illustrate the value of the NUM approach to the complexity-performance tradeoff in MAC design. © 2007 IEEE.}, Doi = {10.1109/TWC.2007.05991}, Key = {fds235888} } @article{fds235889, Author = {Lee, J-W and Tang, A and Huang, J and Chiang, M and Calderbank, AR}, Title = {Reverse-engineering MAC: A non-cooperative game model}, Journal = {IEEE Journal on Selected Areas in Communications}, Volume = {25}, Number = {6}, Pages = {1135-1147}, Year = {2007}, ISSN = {0733-8716}, url = {http://dx.doi.org/10.1109/JSAC.2007.070808}, Abstract = {This paper reverse-engineers backoff-based random-access MAC protocols in ad-hoc networks. We show that the contention resolution algorithm in such protocols is implicitly participating in a non-cooperative game. Each link attempts to maximize a selfish local utility function, whose exact shape is reverse-engineered from the protocol description, through a stochastic subgradient method in which the link updates its persistence probability based on its transmission success or failure. We prove that existence of a Nash equilibrium is guaranteed in general. Then we establish the minimum amount of backoff aggressiveness needed, as a function of density of active users, for uniqueness of Nash equilibrium and convergence of the best response strategy. Convergence properties and connection with the best response strategy are also proved for variants of the stochastic-subgradient-based dynamics of the game. Together with known results in reverse-engineering TCP and BGP, this paper further advances the recent efforts in reverse-engineering layers 2-4 protocols. In contrast to the TCP reverse-engineering results in earlier literature, MAC reverse-engineering highlights the non-cooperative nature of random access. © 2007 IEEE.}, Doi = {10.1109/JSAC.2007.070808}, Key = {fds235889} } @article{fds235890, Author = {Thangaraj, A and Dihidar, S and Calderbank, AR and McLaughlin, SW and Merolla, J-M}, Title = {Applications of LDPC codes to the wiretap channel}, Journal = {IEEE Transactions on Information Theory}, Volume = {53}, Number = {8}, Pages = {2933-2945}, Year = {2007}, ISSN = {0018-9448}, url = {http://dx.doi.org/10.1109/TIT.2007.901143}, Abstract = {With the advent of quantum key distribution (QKD) systems, perfect (i.e., information-theoretic) security can now be achieved for distribution of a cryptographic key. QKD systems and similar protocols use classical error-correcting codes for both error correction (for the honest parties to correct errors) and privacy amplification (to make an eavesdropper fully ignorant). From a coding perspective, a good model that corresponds to such a setting is the wire tap channel introduced by Wyner in 1975. In this correspondence, we study fundamental limits and coding methods for wire tap channels. We provide an alternative view of the proof for secrecy capacity of wire tap channels and show how capacity achieving codes can be used to achieve the secrecy capacity for any wiretap channel. We also consider binary erasure channel and binary symmetric channel special cases for the wiretap channel and propose specific practical codes. In some cases our designs achieve the secrecy capacity and in others the codes provide security at rates below secrecy capacity. For the special case of a noiseless main channel and binary erasure channel, we consider encoder and decoder design for codes achieving secrecy on the wiretap channel; we show that it is possible to construct linear-time decodable secrecy codes based on low-density parity-check (LDPC) codes that achieve secrecy. © 2007 IEEE.}, Doi = {10.1109/TIT.2007.901143}, Key = {fds235890} } @article{fds235743, Author = {Biglieri, E and Calderbank, R and Constantinides, A and Goldsmith, A and Paulraj, A and Poor, HV}, Title = {MIMO wireless communications}, Journal = {MIMO Wireless Communications}, Volume = {9780521873284}, Pages = {1-323}, Year = {2007}, Month = {January}, url = {http://dx.doi.org/10.1017/CBO9780511618420}, Abstract = {© Cambridge University Press 2007 and Cambridge University Press, 2010. Multiple-input multiple-output (MIMO) technology constitutes a breakthrough in the design of wireless communications systems, and is already at the core of several wireless standards. Exploiting multipath scattering, MIMO techniques deliver significant performance enhancements in terms of data transmission rate and interference reduction. This book is a detailed introduction to the analysis and design of MIMO wireless systems. Beginning with an overview of MIMO technology, the authors then examine the fundamental capacity limits of MIMO systems. Transmitter design, including precoding and space-time coding, is then treated in depth, and the book closes with two chapters devoted to receiver design. Written by a team of leading experts, the book blends theoretical analysis with physical insights, and highlights a range of key design challenges. It can be used as a textbook for advanced courses on wireless communications, and will also appeal to researchers and practitioners working on MIMO wireless systems.}, Doi = {10.1017/CBO9780511618420}, Key = {fds235743} } @article{fds235891, Author = {Diggavi, SN and Calderbank, AR and Dusad, S and Al-Dhahir, N}, Title = {Diversity embedded space-time codes}, Journal = {IEEE Transactions on Information Theory}, Volume = {54}, Number = {1}, Pages = {33-50}, Year = {2008}, ISSN = {0018-9448}, url = {http://dx.doi.org/10.1109/TIT.2007.911280}, Abstract = {Rate and diversity impose a fundamental tradeoff in wireless communication. High-rate space-time codes come at a cost of lower reliability (diversity), and high reliability (diversity) implies a lower rate. However, wireless networks need to support applications with very different quality-of-service (QoS) requirements, and it is natural to ask what characteristics should be built into the physical layer link in order to accommodate them. In this paper, we design high-rate space-time codes that have a high-diversity code embedded within them. This allows a form of communication where the high-rate code opportunistically takes advantage of good channel realizations while the embedded high-diversity code provides guarantees that at least part of the information is received reliably.We provide constructions of linear and nonlinear codes for a fixed transmit alphabet constraint. The nonlinear constructions are a natural generalization to wireless channels of multilevel codes developed for the additive white Gaussian noise (AWGN) channel that are matched to binary partitions of quadrature amplitude modulation (QAM) and phase-shift keying (PSK) constellations. The importance of set-partitioning to code design for the wireless channel is that it provides a mechanism for translating constraints in the binary domain into lower bounds on diversity protection in the complex domain. We investigate the systems implications of embedded diversity codes by examining value to unequal error protection, rate opportunism, and packet delay optimization. These applications demonstrate that diversity-embedded codes have the potential to outperform traditional single-layer codes in moderate signal-to-noise (SNR) regimes. © 2008 IEEE.}, Doi = {10.1109/TIT.2007.911280}, Key = {fds235891} } @article{fds235892, Author = {Pezeshki, A and Calderbank, AR and Moran, W and Howard, SD}, Title = {Doppler resilient Golay complementary waveforms}, Journal = {IEEE Transactions on Information Theory}, Volume = {54}, Number = {9}, Pages = {4254-4266}, Year = {2008}, ISSN = {0018-9448}, url = {http://dx.doi.org/10.1109/TIT.2008.928292}, Abstract = {We describe a method of constructing a sequence (pulse train) of phase-coded waveforms, for which the ambiguity function is free of range sidelobes along modest Doppler shifts. The constituent waveforms are Golay complementary waveforms which have ideal ambiguity along the zero Doppler axis but are sensitive to nonzero Doppler shifts. We extend this construction to multiple dimensions, in particular to radar polarimetry, where the two dimensions are realized by orthogonal polarizations. Here we determine a sequence of two-by-two Alamouti matrices where the entries involve Golay pairs and for which the range sidelobes associated with a matrix-valued ambiguity function vanish at modest Doppler shifts. The Prouhet-Thue-Morse sequence plays a key role in the construction of Doppler resilient sequences of Golay complementary waveforms. © 2008 IEEE.}, Doi = {10.1109/TIT.2008.928292}, Key = {fds235892} } @article{fds235893, Author = {Li, Y and Li, Z and Chiang, M and Calderbank, AR}, Title = {Video transmission scheduling for Peer-to-Peer live streaming systems}, Journal = {2008 IEEE International Conference on Multimedia and Expo, ICME 2008 - Proceedings}, Pages = {653-656}, Year = {2008}, url = {http://dx.doi.org/10.1109/ICME.2008.4607519}, Abstract = {For Internet based video broadcasting applications such as IPTV, the Peer-to-Peer (P2P) streaming scheme has been found to be an effective solution. An important issue in live broadcasting is to avoid playback buffer underflow. How to utilize the playback buffer and upload bandwidth of peers to minimize the freeze-ups in playback, is the problem we try to solve. In this work, we propose a successive water-filling (SWaF) algorithm for the video transmission scheduling in P2P live streaming system, to minimize the playback freeze-ups among peers. SWaF algorithm only needs each peer to optimally transmit (within its uploading bandwidth) part of its available video segments in the buffer to other peers requiring the content and pass small amount message to some other peers. Moreover, SWaF has low complexity and provable optimality. Numerical results demonstrated the effectiveness of the proposed algorithm. © 2008 IEEE.}, Doi = {10.1109/ICME.2008.4607519}, Key = {fds235893} } @article{fds235894, Author = {Sirianunpiboon, S and Calderbank, AR and Howard, SD}, Title = {Bayesian analysis of interference cancellation for Alamouti multiplexing}, Journal = {IEEE Transactions on Information Theory}, Volume = {54}, Number = {10}, Pages = {4755-4761}, Year = {2008}, ISSN = {0018-9448}, url = {http://dx.doi.org/10.1109/TIT.2008.929012}, Abstract = {Space-time codes built out of Alamouti components have been adopted in wireless standards such as UMTS, IEEE 802.11n, and IEEE 802.16, where they facilitate higher data rates through multiplexing of parallel data streams and the addition of two or more antennas at the receiver that perform interference cancellation. This correspondence provides new theoretical insight into different algorithms for interference cancellation through a Bayesian analysis that expresses performance as a function of signal-to-noise ratio (SNR) in terms of the "angles" between different space-time coded data streams. © 2008 IEEE.}, Doi = {10.1109/TIT.2008.929012}, Key = {fds235894} } @article{fds235895, Author = {Dusad, S and Diggavi, SN and Calderbank, AR}, Title = {Embedded rank distance codes for ISI channels}, Journal = {IEEE Transactions on Information Theory}, Volume = {54}, Number = {11}, Pages = {4866-4886}, Year = {2008}, ISSN = {0018-9448}, url = {http://dx.doi.org/10.1109/TIT.2008.929960}, Abstract = {Designs for transmit alphabet constrained space-time codes naturally lead to questions about the design of rank distance codes. Recently, diversity embedded multilevel space-time codes for flat-fading channels have been designed from sets of binary matrices with rank distance guarantees over the binary field by mapping them onto quadrature amplitude modulation (QAM) and phase-shift keying (PSK) constellations. In this paper, we demonstrate that diversity embedded space-time codes for fading intersymbol interference (ISI) channels can be designed with provable rank distance guarantees. As a corollary, we obtain an asymptotic characterization of the fixed transmit alphabet rate-diversity tradeoff for multiple antenna fading ISI channels. The key idea is to construct and analyze properties of binary matrices with a particular structure (Toeplitz structure) induced by ISI channels. © 2008 IEEE.}, Doi = {10.1109/TIT.2008.929960}, Key = {fds235895} } @article{fds235896, Author = {Bennatan, A and Calderbank, AR and Shamai, S}, Title = {Bounds on the MMSE of "bad" LDPC codes at rates above capacity}, Journal = {46th Annual Allerton Conference on Communication, Control, and Computing}, Pages = {1065-1072}, Year = {2008}, url = {http://dx.doi.org/10.1109/ALLERTON.2008.4797677}, Abstract = {We present bounds on the minimum mean square error (MMSE) of LDPC codes at rates above capacity. One potential application for MMSE estimation involves cooperative communication. A relay following a compress-and-forward (CF) strategy could first compute an estimate of the transmitted codeword, to reduce the level of noise in the retransmitted signal. Our first bound is based on an analysis of the LDPC belief-propagation decoder. A second bound relies on the relationship between the mutual information and the MMSE, which was discovered by Guo et al.. We compute our bounds for "bad" LDPC codes (requiring SNRs that are far above the Shannon limit, for reliable communications to be possible) and show that such codes substantially outperform "good" codes. This advantage of "bad" codes implies an interesting degree of freedom in the design of codes for cooperative communications. © 2008 IEEE.}, Doi = {10.1109/ALLERTON.2008.4797677}, Key = {fds235896} } @article{fds235897, Author = {Chandrashekhar, TPS and Bennatan, A and Zhang, J and Calderbank, R and Cochran, D}, Title = {Rate-achievability strategies for two-hop interference flows}, Journal = {46th Annual Allerton Conference on Communication, Control, and Computing}, Pages = {1432-1439}, Year = {2008}, url = {http://dx.doi.org/10.1109/ALLERTON.2008.4797731}, Abstract = {We consider a basic model for two-hop transmissions of two information flows which interfere with each other. In this model, two sources simultaneously transmit to two relays (in the first hop), which then simultaneously transmit to two destinations (in the second hop). While the transmission during the first hop is essentially the transmission over a classical interference channel, the transmission in the second hop enjoys an interesting advantage. Specifically, as a by-product of the Han-Kobayashi transmission scheme applied to the first hop, each of the relays (in the second hop) has access to some of the data that is intended to the other destination, in addition to its own data. As recently observed by Simeone et al., this opens the door to cooperation between the relays. In this paper, we observe that the cooperation can take the form of distributed MIMO broadcast, thus greatly enhancing its effectiveness at high SNR. However, since each relay is only aware of part of the data beyond its own, full cooperation is not possible. We propose several approaches that combine MIMO broadcast strategies (including "dirty paper") with standard non-cooperative strategies for the interference channel. Numerical results are provided, which indicate that our approaches provide substantial benefits at high SNR. © 2008 IEEE.}, Doi = {10.1109/ALLERTON.2008.4797731}, Key = {fds235897} } @article{fds235898, Author = {Zoltowski, MD and Qureshi, TR and Calderbank, R}, Title = {Complementary codes based channel estimation for MIMO-OFDM systems}, Journal = {46th Annual Allerton Conference on Communication, Control, and Computing}, Pages = {133-138}, Year = {2008}, url = {http://dx.doi.org/10.1109/ALLERTON.2008.4797546}, Abstract = {We present a pilot-assisted method for estimating the frequency selective channel in a MIMO-OFDM (Multiple Input Multiple Output - Orthogonal Frequency Division Multiplexing) system. The pilot sequence is designed using the DFT (Discrete Fourier Transform) of the Golay complementary sequences. Novel exploitation of the perfect autocorrelation property of the Golay codes, in conjunction with OSTBC (Orthogonal Space-Time Block Code) based pilot waveform scheduling across multiple OFDM frames, facilitates simple separation of the channel mixtures at the receive antennas. The DFT length used to transform the complementary sequence into the frequency domain is shown to be a key critical parameter for correctly estimating the channel. NMSE (Normalized Mean Squared Error) between the actual and the estimated channel is used to characterize the estimation performance. © 2008 IEEE.}, Doi = {10.1109/ALLERTON.2008.4797546}, Key = {fds235898} } @article{fds235899, Author = {Dusad, S and Diggavi, SN and Al-Dhahir, N and Calderbank, AR}, Title = {Diversity embedded codes: Theory and practice}, Journal = {IEEE Journal of Selected Topics in Signal Processing}, Volume = {2}, Number = {2}, Pages = {202-219}, Year = {2008}, ISSN = {1932-4553}, url = {http://dx.doi.org/10.1109/JSTSP.2008.923817}, Abstract = {Diversity embedded codes are high-rate space-time codes that have a high-diversity code embedded within them. They allow a form of communication where the high-rate code opportunistically takes advantage of good channel realizations while the embedded high-diversity code provides guarantees that at least part of the information is received reliably. Over the past few years, code designs and fundamental limits of performance for such codes have been developed. In this paper, we review these ideas by giving the developments in a unified framework. In particular, we present both the coding technique as well as information-theoretic bounds in the context of Intersymbol Interference (ISI) channels. We investigate the systems implications of diversity embedded codes by examining value to network utility maximization, unequal error protection for wireless transmission, rate opportunism and packet delay optimization. © 2008 IEEE.}, Doi = {10.1109/JSTSP.2008.923817}, Key = {fds235899} } @article{fds235900, Author = {Li, Y and Li, Z and Chiang, M and Calderbank, AR}, Title = {Content-aware distortion-fair video streaming in networks}, Journal = {GLOBECOM - IEEE Global Telecommunications Conference}, Pages = {1768-1773}, Year = {2008}, url = {http://dx.doi.org/10.1109/GLOCOM.2008.ECP.342}, Abstract = {Internet is experiencing an explosive growth of video traffic. Given the limited network bandwidth resources, how to provide Internet users with good video playback quality is a key problem. For video clips competing bandwidth, we propose an approach of Content-Aware distortion-Fair (CAF) video delivery scheme, which is assumed to be aware of the characteristics of video frames and ensures max-min distortion fair sharing among video flows. Different from bandwidth fair sharing, CAF targets video playback quality fairness for the reason that users care about video quality rather than bandwidth. The proposed CAF approach does not need an analytical rate-distortion function which is difficult to estimate, but instead, it uses the explicit distortion of every frame which is induced by frame drop. Our CAF approach is fast and practical with content-aware cooperation. Experimental results show that the proposed approach yields better quality of service when the network is congested compared with the approach not rate-distortion optimized, and it makes competing video clips help each other to get fair playback quality. © 2008 IEEE.}, Doi = {10.1109/GLOCOM.2008.ECP.342}, Key = {fds235900} } @article{fds235901, Author = {Lee, J-W and Chiang, M and Calderbank, AR}, Title = {On the achievable efficiency-fairness tradeoff in utility-optimal MAC protocols}, Journal = {IEICE Transactions on Communications}, Volume = {E91-B}, Number = {4}, Pages = {1231-1234}, Year = {2008}, ISSN = {0916-8516}, url = {http://dx.doi.org/10.1093/ietcom/e91-b.4.1231}, Abstract = {We use the network utility maximization (NUM) framework to create an efficient and fair medium access control (MAC) protocol for wireless networks. By adjusting the parameters in the utility objective functions of NUM problems, we control the tradeoff between efficiency and fairness of radio resource allocation through a rigorous and systematic design. In this paper, we propose a scheduling-based MAC protocol. Since it provides an upper-bound on the achievable performance, it establishes the optimality benchmarks for comparison with other algorithms in related work. Copyright © 2008 The Institute of Electronics, Information and Communication Engineers.}, Doi = {10.1093/ietcom/e91-b.4.1231}, Key = {fds235901} } @article{fds235902, Author = {Li, Y and Tian, C and Diggavi, S and Chiang, M and Calderbank, AR}, Title = {Network resource allocation for competing multiple description transmissions}, Journal = {GLOBECOM - IEEE Global Telecommunications Conference}, Pages = {2366-2371}, Year = {2008}, url = {http://dx.doi.org/10.1109/GLOCOM.2008.ECP.455}, Abstract = {To provide real-time multimedia services over a network is challenging due to the stringent delay requirements in the presence of complex network dynamics. Yet such services are beginning to be deployed over best effort networks. Multiple description (MD) coding is one approach to transmit the media over diverse (multiple) paths to reduce the detrimental effects caused by path failures or delay. The novelty of this work is to investigate the resource allocation in a network, where there are several competing MD coded streams. This is done by considering a framework that chooses the operating points for asymmetric MD coding to maximize total quality of the users, while these streams are sent over multiple routing paths. We study the joint optimization of multimedia (source) coding and congestion control in wired networks. These ideas are extended to joint source coding and channel coding in wireless networks. In both situations, we propose distributed algorithms for optimal resource allocation. In the presence of path loss and competing users, the service quality to any particular MD stream could be uncertain. In such circumstances it might be tempting to expect that greater redundancy in the MD streams is needed to protect against such failures. However, one surprising aspect of our study reveals that for large number of users competing for the same resources, the overall system could benefit through opportunistic (hierarchical) strategies. In general networks, our studies indicate that the user composition varies from conservative to opportunistic operating points, depending on the number of users and their network vantage points. © 2008 IEEE.}, Doi = {10.1109/GLOCOM.2008.ECP.455}, Key = {fds235902} } @article{fds235903, Author = {Sirianunpiboon, S and Calderbank, AR and Howard, SD}, Title = {Cognitive decoding and the Golden code}, Journal = {European Signal Processing Conference}, Year = {2008}, ISSN = {2219-5491}, Abstract = {Space time signal processing starts with a system of linear equations where signals are multiplied by channel gains, and the standard criteria for the design of space time codes focus on differences between codewords at the transmitter. The value of algebraic constructions is to transfer structure (correlation) at the transmitter to structure at the receiver, and the focus of this paper is the induced channel at the receiver. We use the Golden code to explore the idea of introducing structure at the transmitter to enable low complexity decoding at the receiver. This is an important special case, since the Golden code is incorporated in the IEEE 802.16 standard, but the value of our approach is not limited to this example. We describe a cognitive decoder for the Golden code with complexity O(N 2) that comes within 3dB of full MAP/ML decoding. The decoder is cognitive in that it uses channel state information to choose between two algorithms in a way that is independent of the signal-to-noise ratio. The primary algorithm is interference cancellation which fails to perform well on a proportion of channels. We identify the channel conditions for which inteference cancellation fails and show that for these channels the decoding problem effectively reduces to a single receive antenna decoding problem for which we have developed an efficient zero forcing algorithm. Previous hybrid approaches based on sphere decoding have cubic worst case complexity and employ decision rules based on condition number of the posterior covariance matrix. Interference cancellation is different in that orientation of the covariance matters. The cognitive decoder for the Golden code provides a uniform solution to different wireless environments (Rayleigh/Rician) that combine rich scattering and line of sight components. The gap between cognitive and full MAP/ML decoding reduces to essentially ML performance as the line of sight component becomes more dominant. copyright by EURASIP.}, Key = {fds235903} } @article{fds235904, Author = {Zoltowski, MD and Qureshi, TR and Calderbank, R and Moran, W}, Title = {Unitary design of radar waveform diversity sets}, Journal = {Conference Record of the Asilomar Conference on Signals, Systems and Computers}, Pages = {26-30}, Year = {2008}, ISSN = {1058-6393}, url = {http://dx.doi.org/10.1109/ACSSC.2008.5074353}, Abstract = {In this work, multiple radar waveforms are simultaneously transmitted, emitted from different "virtual" antennas. The goal is to process the returns in such a way that the overall ambiguity function is a sum of ambiguity functions better approximating the desired thumbtack shape. A 4×4 example involves two spatially separated antennas with each able to transmit and receive simultaneously on two different polarizations. The 4×4 unitary design dictates the scheduling of the waveforms over the four virtual antennas over four PRIs (Pulse Repetition Intervals), and how the matched filtering of the returns over four PRIs is combined in to achieve both perfect separation (of the superimposed returns) and perfect reconstruction. Perfect reconstruction means the sum of the time-autocorrelations associated with each of the four waveforms is a delta function. Conditions for both perfect separation and perfect reconstruction are developed, and a variety of waveform sets satisfying both are presented. © 2008 IEEE.}, Doi = {10.1109/ACSSC.2008.5074353}, Key = {fds235904} } @article{fds235905, Author = {Liu, J and Calderbank, AR}, Title = {The Icosian code and the E_{8}lattice: A new 4 × 4 space-time code with nonvanishing determinant}, Journal = {IEEE Transactions on Information Theory}, Volume = {54}, Number = {8}, Pages = {3782-3789}, Year = {2008}, ISSN = {0018-9448}, url = {http://dx.doi.org/10.1109/TIT.2008.926352}, Abstract = {This paper introduces a new rate-2, full-diversity space-time code for four transmit antennas and one receive antenna. The 4 × 4 codeword matrix consists of four 2 × 2 Alamouti blocks with entries from Q(i,√5), and these blocks can be viewed as quaternions which in turn represent rotations in R3. The Alamouti blocks that appear in a codeword are drawn from the icosian ring consisting of all linear combinations of 120 basic rotations corresponding to symmetries of the icosahedron. This algebraic structure is different from the Golden code, but the complex entries are taken from a common underlying field. The minimum determinant is bounded below by a constant that is independent of the signal constellation, and the new code admits a simple decoding scheme that makes use of a geometric correspondence between the icosian ring and the E8 lattice. © 2008 IEEE.}, Doi = {10.1109/TIT.2008.926352}, Key = {fds235905} } @article{fds235906, Author = {Aggarwal, V and Calderbank, AR}, Title = {Boolean functions, projection operators, and quantum error correcting codes}, Journal = {IEEE Transactions on Information Theory}, Volume = {54}, Number = {4}, Pages = {1700-1707}, Year = {2008}, ISSN = {0018-9448}, url = {http://dx.doi.org/10.1109/TIT.2008.917720}, Abstract = {This paper describes a fundamental correspondence between Boolean functions and projection operators in Hilbert space. The correspondence is widely applicable, and it is used in this paper to provide a common mathematical framework for the design of both additive and nonadditive quantum error correcting codes. The new framework leads to the construction of a variety of codes including an infinite class of codes that extend the original ((5, 6, 2)) code found by Rains et al It also extends to operator quantum error correcting codes. © 2008 IEEE.}, Doi = {10.1109/TIT.2008.917720}, Key = {fds235906} } @article{fds236070, Author = {Pezeshki, A and Kutyniok, G and Calderbank, R}, Title = {Fusion frames and robust dimension reduction}, Journal = {CISS 2008, The 42nd Annual Conference on Information Sciences and Systems}, Pages = {264-268}, Year = {2008}, url = {http://dx.doi.org/10.1109/CISS.2008.4558533}, Abstract = {We consider the linear minimum meansquared error (LMMSE) estimation of a random vector of interest from its fusion frame measurements in presence noise and subspace erasures. Each fusion frame measurement is a low-dimensional vector whose elements are inner products of an orthogonal basis for a fusion frame subspace and the random vector of interest. We derive bounds on the mean-squared error (MSE) and show that the MSE will achieve its lower bound if the fusion frame is tight. We prove that tight fusion frames consisting of equidimensional subspaces have maximum robustness with respect to erasures of one subspace, and that the optimal dimension depends on SNR. We also show that tight fusion frames consisting of equi-dimensional subspaces with equal pairwise chordal distances are most robust with respect to two and more subspace erasures, and refer to such fusion frames as equi-distance tight fusion frames. Finally, we show that the squared chordal distance between the subspaces in such fusion frames meets the so-called simplex bound, and thereby establish a connection between equidistance tight fusion frames and optimal Grassmannian packings. © 2008 IEEE.}, Doi = {10.1109/CISS.2008.4558533}, Key = {fds236070} } @article{fds236071, Author = {Calderbank, R and Dickinson, B}, Title = {CISS 2008, The 42nd Annual Conference on Information Sciences and Systems: Welcome}, Journal = {CISS 2008, The 42nd Annual Conference on Information Sciences and Systems}, Pages = {i-ii}, Year = {2008}, url = {http://dx.doi.org/10.1109/CISS.2008.4558477}, Doi = {10.1109/CISS.2008.4558477}, Key = {fds236071} } @article{fds236072, Author = {Suvorova, S and Moron, B and Howard, S and Calderbank, R}, Title = {Application of Doppler resilient complementary waveforms to target tracking}, Journal = {IEEE International Conference on Acoustics Speech and Signal Processing}, Pages = {1497-1500}, Year = {2008}, ISSN = {1520-6149}, url = {http://dx.doi.org/10.1109/ICASSP.2008.4517905}, Abstract = {The use of complementary codes as a means of reducing radar range sidelobes is well-known, but lack of resilience to Doppler is often cited as a reason not to deploy them. This work describes techniques for providing Doppler resilience with an emphasis on tailoring Doppler performance to the specific aim of target tracking. The Doppler performance can be varied by suitably changing the order of transmission of multiple sets of complementary waveforms. We have developed a method that improves Doppler performance significantly by arranging the transmission of multiple copies of complementary waveforms according to the first order Reed-Müller codes. Here we demonstrate significant tracking gains in the context of accelerating targets by the use of adaptively chosen waveform sequences of this kind, compared to both a fixed sequence of similar waveforms, and an LFM waveform. ©2008 IEEE.}, Doi = {10.1109/ICASSP.2008.4517905}, Key = {fds236072} } @article{fds236073, Author = {Howard, SD and Calderbank, AR and Searle, SJ}, Title = {A fast reconstruction algorithm for deterministic compressive sensing using second order reed-muller codes}, Journal = {CISS 2008, The 42nd Annual Conference on Information Sciences and Systems}, Pages = {11-15}, Year = {2008}, url = {http://dx.doi.org/10.1109/CISS.2008.4558486}, Abstract = {This paper proposes a deterministic compressed sensing matrix that comes by design with a very fast reconstruction algorithm, in the sense that its complexity depends only on the number of measurements n and not on the signal dimension N. The matrix construction is based on the second order Reed-Muller codes and associated functions. This matrix does not have RIP uniformly with respect to all k-sparse vectors, but it acts as a near isometry on k-sparse vectors with very high probability. © 2008 IEEE.}, Doi = {10.1109/CISS.2008.4558486}, Key = {fds236073} } @article{fds236074, Author = {Wu, Y and Calderbank, R}, Title = {Code diversity in multiple antenna wireless communication}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Pages = {1078-1082}, Year = {2008}, url = {http://dx.doi.org/10.1109/ISIT.2008.4595153}, Abstract = {The standard approach to the design of individual space-time codes is based on optimizing diversity and coding gain. This geometric approach leads to remarkable examples, such as the Golden Code, for which the complexity of Maximum Likelihood (ML) decoding is considerable. Code diversity is an alternative approach where a small number of feedback bits are used to select from a family of space-time codes. Feedback can be combined with sub-optimal low complexity decoding of the component codes to match ML decoding performance of any individual code in the family. It can also be combined with ML decoding of the component codes to improve performance beyond ML decoding performance of any individual code. One method of implementing code diversity is the use of feedback to adapt the phase of a transmitted signal. Phase adaptation with the 4 × 4 Quasi-Orthogonal Space-Time Code (QOSTBC) is shown to be almost information lossless; that is, this form of space-time coding does not reduce the capacity of the underlying multiple antenna wireless channel. Code diversity can also be used to improve performance of multi-user detection by reducing interference between users. Phase adaptation with two Alamouti users makes it possible for the Zero Forcing (ZF) or decorrelating detector to match the performance of ML joint detection. © 2008 IEEE.}, Doi = {10.1109/ISIT.2008.4595153}, Key = {fds236074} } @article{fds236075, Author = {Chui, J and Calderbank, AR}, Title = {Multilevel diversity-embedded space-time codes for video broadcasting over WiMAX}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Pages = {1068-1072}, Year = {2008}, url = {http://dx.doi.org/10.1109/ISIT.2008.4595151}, Abstract = {Advances in wireless technologies, such as WiMAX [1], allow high data rates and high reliability through the use of MIMO-OFDM. However, they are not optimally designed for broadcasting. The nature of the wireless medium may cause an entire frame to be in outage with little chance of recovery. One strategy to overcome this deficit is to employ diversity embedding, which protect different bits with different diversity orders. Such codes exhibit the property that even if the entire frame is in outage, a subset of the frame may still be reliably recovered. In this paper, we present space-time codes designed for MIMO-OFDM systems which achieve diversity embedding. We demonstrate how these codes can increase PSNR for video broadcasting in WiMAX © 2008 IEEE.}, Doi = {10.1109/ISIT.2008.4595151}, Key = {fds236075} } @article{fds236076, Author = {Jafarpour, S and Pezeshki, A and Calderbank, R}, Title = {Experiments with compressively sampled images and a new debluring-denoising algorithm}, Journal = {Proceedings - 10th IEEE International Symposium on Multimedia, ISM 2008}, Pages = {66-73}, Year = {2008}, url = {http://dx.doi.org/10.1109/ISM.2008.119}, Abstract = {In this paper we will examine the effect of different parameters in the quality of real compressively sampled images in the compressed sensing framework. We will select a variety of different real images of different types and test the quality of the recovered images, the recovery time, and required resources when different measurement methods with different parameters are used or when different recovering methods are applied. Then we will propose an algorithm to reduce the noise in the recovered images and sharpen them simultaneously. The algorithm exploits a well-known bilateral filtering in order to increase the confidence in margins and edges, and then uses an adaptive unsharp mask method to sharpen the images. The adaptive unsharp mask method extends the ordinary unsharp mask method and uses machine learning square loss minimization and regression in order to learn the optimal unsharping parameters. We will argue why both bilateral filtering and unsharp mask methods should be used in the algorithm simultaneously. Finally, we will show the results of applying the algorithm on real images that are recovered using the compressed sensing method and we will interpret the experimental results. © 2008 IEEE.}, Doi = {10.1109/ISM.2008.119}, Key = {fds236076} } @article{fds331053, Author = {Dahai Xu, and Ying Li, and Mung Chiang, and Calderbank, A}, Title = {Elastic service availability: utility framework and optimal provisioning}, Journal = {IEEE Journal on Selected Areas in Communications}, Volume = {26}, Number = {6}, Pages = {55-65}, Year = {2008}, Month = {August}, url = {http://dx.doi.org/10.1109/JSACOCN.2008.030607}, Doi = {10.1109/JSACOCN.2008.030607}, Key = {fds331053} } @article{fds235907, Author = {Papandreou-Suppappola, A and Nehorai, A and Calderbank, R}, Title = {Waveform-agile sensing and processing}, Journal = {IEEE Signal Processing Magazine}, Volume = {26}, Number = {1}, Pages = {10-11}, Year = {2009}, ISSN = {1053-5888}, url = {http://dx.doi.org/10.1109/MSP.2008.930413}, Abstract = {The six articles in this special issue focus on waveform-agile sensing and processing. © 2009 IEEE.}, Doi = {10.1109/MSP.2008.930413}, Key = {fds235907} } @article{fds235908, Author = {Kutyniok, G and Pezeshki, A and Calderbank, R and Liu, T}, Title = {Robust dimension reduction, fusion frames, and Grassmannian packings}, Journal = {Applied and Computational Harmonic Analysis}, Volume = {26}, Number = {1}, Pages = {64-76}, Year = {2009}, ISSN = {1063-5203}, url = {http://dx.doi.org/10.1016/j.acha.2008.03.001}, Abstract = {We consider estimating a random vector from its measurements in a fusion frame, in presence of noise and subspace erasures. A fusion frame is a collection of subspaces, for which the sum of the projection operators onto the subspaces is bounded below and above by constant multiples of the identity operator. We first consider the linear minimum mean-squared error (LMMSE) estimation of the random vector of interest from its fusion frame measurements in the presence of additive white noise. Each fusion frame measurement is a vector whose elements are inner products of an orthogonal basis for a fusion frame subspace and the random vector of interest. We derive bounds on the mean-squared error (MSE) and show that the MSE will achieve its lower bound if the fusion frame is tight. We then analyze the robustness of the constructed LMMSE estimator to erasures of the fusion frame subspaces. We limit our erasure analysis to the class of tight fusion frames and assume that all erasures are equally important. Under these assumptions, we prove that tight fusion frames consisting of equi-dimensional subspaces have maximum robustness (in the MSE sense) with respect to erasures of one subspace among all tight fusion frames, and that the optimal subspace dimension depends on signal-to-noise ratio (SNR). We also prove that tight fusion frames consisting of equi-dimensional subspaces with equal pairwise chordal distances are most robust with respect to two and more subspace erasures, among the class of equi-dimensional tight fusion frames. We call such fusion frames equi-distance tight fusion frames. We prove that the squared chordal distance between the subspaces in such fusion frames meets the so-called simplex bound, and thereby establish connections between equi-distance tight fusion frames and optimal Grassmannian packings. Finally, we present several examples for the construction of equi-distance tight fusion frames. © 2008 Elsevier Inc. All rights reserved.}, Doi = {10.1016/j.acha.2008.03.001}, Key = {fds235908} } @article{fds235909, Author = {Calderbank, R and Howard, SD and Moran, B}, Title = {Waveform diversity in radar signal processing: A focus on the use and control of degrees of freedom}, Journal = {IEEE Signal Processing Magazine}, Volume = {26}, Number = {1}, Pages = {32-41}, Year = {2009}, ISSN = {1053-5888}, url = {http://dx.doi.org/10.1109/MSP.2008.930414}, Abstract = {Complementary waveforms developed by Golay are conceived to improve the sensitivity of far infrared spectrometry, which is similar to those developed by Tseng and Liu to analyze acoustic surface wave phenomena. In such a matrix, phase coded waveforms indexed by array element and by the pulse-repetition intervals are the basis of radar illumination. Their polarization of constituent waveforms also may vary. This thus make it possible to segregate and calibrate methods of controlling individual degrees of freedom before examining them in combination.}, Doi = {10.1109/MSP.2008.930414}, Key = {fds235909} } @article{fds235910, Author = {Li, Z and Li, Y and Chiang, M and Calderbank, R and Chen, YC}, Title = {Optimal transmission scheduling for scalable wireless video broadcast with rateless erasure correction code}, Journal = {2009 6th IEEE Consumer Communications and Networking Conference, CCNC 2009}, Year = {2009}, url = {http://dx.doi.org/10.1109/CCNC.2009.4784712}, Abstract = {With the advances in wireless technology and explosive growth of mobile devices and wireless networks, mobile TV is becoming a popular application. The main technical challenge to wireless video broadcast is to provide the best quality of service possible under the radio resource constraints. In this paper we propose an application layer middleware solution that utilizes the scalability in video coding with rateless erasure correction codes to achieve a balance in the quality of service (QoS) and radio resource efficiency. Simulation results demonstrate the effectiveness of the solution. ©2009 IEEE.}, Doi = {10.1109/CCNC.2009.4784712}, Key = {fds235910} } @article{fds235911, Author = {Li, Y and Li, Z and Chiang, M and Calderbank, AR}, Title = {Energy-efficient video transmission scheduling for wireless peer-to-peer live streaming}, Journal = {2009 6th IEEE Consumer Communications and Networking Conference, CCNC 2009}, Year = {2009}, url = {http://dx.doi.org/10.1109/CCNC.2009.4784766}, Abstract = {The Peer-to-Peer (P2P) streaming has shown as an effective solution for wireline video applications, while for the wireless video streaming applications, the limited radio resource and battery energy are the main constraints on the way of P2P applications. An important issue in live video streaming quality of service is to avoid playback buffer underflow, and a challenge from wireless applications is the desire of energy efficiency. The problem we try to solve is how to utilize P2P schemes in video streaming and schedule the video transmission among peers to minimize the "freeze- ups" in playback caused by buffer underflow. In this work, we propose energy-efficient algorithm for the video transmission scheduling in wireless P2P live streaming system, to minimize the playback freeze-ups among peers. Further the algorithm is extended to two scenarios: peers' reluctance of consuming battery energy and allowing overhearing, with alternative energy-efficient algorithms proposed for the second scenario. Numerical results show the effectiveness of the proposed algorithms. The results also demonstrate that peers' selfishness may reduce the energy efficiency, but allowing overhearing could increase energy efficiency. ©2009 IEEE.}, Doi = {10.1109/CCNC.2009.4784766}, Key = {fds235911} } @article{fds235912, Author = {Qureshi, T and Zoltowski, M and Calderbank, R}, Title = {MIMO-OFDM channel estimation using golay complementary sequences}, Journal = {2009 International Waveform Diversity and Design Conference Proceedings, WDD 2009}, Pages = {253-257}, Year = {2009}, url = {http://dx.doi.org/10.1109/WDDC.2009.4800355}, Abstract = {We present a pilot-assisted method for estimating the frequency selective channel in a MIMO-OFDM (Multiple Input Multiple Output - Orthogonal Frequency Division Multiplexing) system. The pilot sequence is designed using the DFT (Discrete Fourier Transform) of the Golay complementary sequences. Novel exploitation of the perfect autocorrelation property of Golay complementary sequences, in conjunction with OSTBC (Orthogonal Space Time Block Code) based pilot waveform scheduling across multiple OFDM frames, facilitates simple separation of the channel mixtures at the receive antennas. The DFT length used to transform the complementary sequence into the frequency domain is shown to be a key critical parameter for correctly estimating the channel. This channel estimation scheme is then extended to antenna arrays of arbitrary sizes. ©2009 IEEE.}, Doi = {10.1109/WDDC.2009.4800355}, Key = {fds235912} } @article{fds235913, Author = {Chi, Y and Pezeshki, A and Calderbank, R and Howard, S}, Title = {Range sidelobe suppression in a desired Doppler interval}, Journal = {2009 International Waveform Diversity and Design Conference Proceedings, WDD 2009}, Pages = {258-262}, Year = {2009}, url = {http://dx.doi.org/10.1109/WDDC.2009.4800356}, Abstract = {We present a novel method of constructing a Doppler resilient pulse train of Golay complementary waveforms, for which the range sidelobes of the pulse train ambiguity function vanish inside a desired Doppler interval. This is accomplished by coordinating the transmission of a Golay pair of phase coded waveforms in time according to the 1's and -1's in a biphase sequence. The magnitude of the range sidelobes of the pulse train ambiguity function is shown to be proportional to the magnitude spectrum of the biphase sequence. Range sidelobes inside a desired Doppler interval are suppressed by selecting a sequence whose spectrum has a high-order null at a Doppler frequency inside the desired interval. We show that the spectrum of the biphase sequence obtained by oversampling the length-2M Prouhet-Thue-Morse (PTM) sequence by a factor m has an Mth-order null at all rational Doppler shifts Θ0 = 2πl /m, where l ≠ 0 and m≠ 1 are co-prime integers. This spectrum also has an (M - 1)th-order null at zero Doppler and (M - h - 1)th-order nulls at all Doppler shifts Θ0 = 2πl /(2hm), where l ≠ 0 andm ≠ 1 are again co-prime and 1 ≤ h ≤ M - 1. ©2009 IEEE.}, Doi = {10.1109/WDDC.2009.4800356}, Key = {fds235913} } @article{fds235914, Author = {Sirianunpiboon, S and Davis, LM and Calderbank, R}, Title = {Performance of the golden code in the presence of polarization diversity}, Journal = {Proceedings of the 2009 Australian Communications Theory Workshop, AusCTW 2009}, Pages = {23-27}, Year = {2009}, url = {http://dx.doi.org/10.1109/AUSCTW.2009.4805594}, Abstract = {The performance of a multiple-input multipleoutput (MIMO) system depends strongly on the scattering environment and antenna spacing. The use of dual-polarized antennas is a promising alternative both in terms of diversity and effective use of space. In this paper we investigate the performance of the Golden code with polarization diversity; where the two spatially separated antennas are replaced by a single dual polarised antenna. We analyse the performance of the Golden code in terms of an angle between the channels corresponding to the two receivers, which allows us to predict performance without necessarily needing to resort to simulations. Analysis and simulation results show that with the introduction of polarization diversity the performance of the Golden code can be made consistently good across both rich scattering and line of sight (LOS) conditions. © 2009 IEEE.}, Doi = {10.1109/AUSCTW.2009.4805594}, Key = {fds235914} } @article{fds235915, Author = {Li, Y and Chiang, M and Calderbank, AR and Diggavi, SN}, Title = {Optimal rate-reliability-delay tradeoff in networks with composite links}, Journal = {IEEE Transactions on Communications}, Volume = {57}, Number = {5}, Pages = {1390-1401}, Year = {2009}, ISSN = {0090-6778}, url = {http://dx.doi.org/10.1109/TCOMM.2009.05.070198}, Abstract = {Networks need to accommodate diverse applications with different Quality-of-Service (QoS) requirements. New ideas at the physical layer are being developed for this purpose, such as diversity embedded coding, which is a technique that combines high rates with high reliability. We address the problem of how to fully utilize different rate-reliability characteristics at the physical layer to support different types of traffic over a network and to jointly maximize their utilities. We set up a new framework based on utility maximization for networks with composite links, meaning that each link consists of sub-links that can attain different rate-reliability characteristics simultaneously. We incorporate delay, in addition to rate and reliability, into the utility functions. To accommodate different types of traffic, we propose distributed algorithms converging to the optimal rate-reliability-delay tradeoff based on capacity division and priority queueing. Numerical results show that compared with traditional codes, the new codes can provide higher network utilities for all traffic types simultaneously. The results also show that priority queueing achieves higher network utility than capacity division. © 2009 IEEE.}, Doi = {10.1109/TCOMM.2009.05.070198}, Key = {fds235915} } @article{fds235916, Author = {Aggarwal, V and Bennatan, A and Calderbank, AR}, Title = {On maximizing coverage in Gaussian relay channels}, Journal = {IEEE Transactions on Information Theory}, Volume = {55}, Number = {6}, Pages = {2518-2536}, Year = {2009}, ISSN = {0018-9448}, url = {http://dx.doi.org/10.1109/TIT.2009.2018337}, Abstract = {Results for Gaussian relay channels typically focus on maximizing transmission rates for given locations of the source, relay, and destination. We introduce an alternative perspective, where the objective is maximizing coverage for a given rate. The new objective captures the problem of how to deploy relays to provide a given level of service to a particular geographic area, where the relay locations become a design parameter that can be optimized. We evaluate the decode-and-forward (DF) and compress-and-forward (CF) strategies for the relay channel with respect to the new objective of maximizing coverage. When the objective is maximizing rate, different locations of the destination favor different strategies. When the objective is coverage for a given rate, and the relay is able to decode, DF is uniformly superior in that it provides coverage at any point served by CF. When the channel model is modified to include random fading, we show that the monotone ordering of coverage regions is not always maintained. While the coverage provided by DF is sensitive to changes in the location of the relay and the path loss exponent, CF exhibits a more graceful degradation with respect to such changes. The techniques used to approximate coverage regions are new and may be of independent interest. © 2009 IEEE.}, Doi = {10.1109/TIT.2009.2018337}, Key = {fds235916} } @article{fds235917, Author = {Zoltowski, MD and Qureshi, TR and Calderbank, R}, Title = {Channel estimation for MIMO-OFDM using complementary codes}, Journal = {RWS 2009 IEEE Radio and Wireless Symposium, Proceedings}, Pages = {159-162}, Year = {2009}, url = {http://dx.doi.org/10.1109/RWS.2009.4957309}, Abstract = {We present a pilot-assisted method for estimating the frequency selective channel in a MIMO-OFDM (Multiple Input Multiple Output - Orthogonal Frequency Division Multiplexing) system. The pilot sequence is designed using the DFT (Discrete Fourier Transform) of the Golay complementary sequences. Novel exploitation of the perfect autocorrelation property of the Golay codes, in conjunction with OSTBC (Orthogonal Space-Time Block Code) based pilot waveform scheduling across multiple OFDM frames, facilitates simple separation of the channel mixtures at the receive antennas. The DFT length used to transform the complementary sequence into the frequency domain is shown to be a key critical parameter for correctly estimating the channel. NMSE (Normalized Mean Squared Error) between the actual and the estimated channel is used to characterize the estimation performance. ©2009 IEEE.}, Doi = {10.1109/RWS.2009.4957309}, Key = {fds235917} } @article{fds235918, Author = {Islam, KMZ and Rabiei, P and Al-Dhahir, N and Diggavi, SN and Calderbank, AR}, Title = {Linear diversity-embedding STBC: Design issues and applications}, Journal = {IEEE Transactions on Communications}, Volume = {57}, Number = {6}, Pages = {1578-1583}, Year = {2009}, ISSN = {0090-6778}, url = {http://dx.doi.org/10.1109/TCOMM.2009.06.080008}, Abstract = {We design a novel class of space-time codes, called linear diversity-embedding space-time block codes (LDE-STBC) where a high-rate STBC is linearly superimposed on a highdiversity STBC without requiring channel knowledge at the transmitter. In applying this scheme to multimedia wireless communications, each traffic type constitutes a transmission layer that operates at a suitable rate-diversity tradeoff point according to its quality-of-service requirements. This, in turn, provides an unequal-error-protection (UEP) capability to the different information traffic types and allows a form of wireless communications where the high-rate STBC opportunistically takes advantage of good channel realizations while the embedded high-diversity STBC ensures that at least part of the information is decoded reliably. We investigate transceiver design issues specific to LDE-STBC including reduced-complexity coherent decoding and effective schemes to vary the coding gain to further enhance UEP capabilities of the code. Furthermore, we investigate the application of LDE-STBC to wireless multicasting and demonstrate its performance advantage over conventional equal-error-protection STBC. © 2009 IEEE.}, Doi = {10.1109/TCOMM.2009.06.080008}, Key = {fds235918} } @article{fds235919, Author = {Tan, CW and Calderbank, AR}, Title = {Multiuser detection of alamouti signals}, Journal = {IEEE Transactions on Communications}, Volume = {57}, Number = {7}, Pages = {2080-2089}, Year = {2009}, ISSN = {0090-6778}, url = {http://dx.doi.org/10.1109/TCOMM.2009.07.070592}, Abstract = {In a MIMO multiple-access channel where users employ Space-Time Block Codes (STBC), interference cancellation can be used to suppress co-channel interference and recover the desired signal of each user at the receiver. Leveraging the special properties of Alamouti matrices, we first show that spatial multiplexing of Alamouti signals retains the space-time diversity gain of Alamouti signaling using our proposed low-complexity Alamouti BLAST-MMSE (A-BLAST) Algorithm. Next, in contrast to traditional transmit diversity that focuses on STBC construction at the transmitter, this paper looks at transmit diversity from the perspective of the receiver. In other words, the receiver gets to choose the STBC's, which are favourable to the channel assuming a fixed BLAST receive algorithm. In a multiuserMAC setting, we first present a systematic methodology to exploit different decomposition structure in Alamouti matrices, each with different tradeoff between performance and decoding complexity using possibly different MIMO receive algorithms. We then demonstrate that the notion of angles (the inner product of two quaternionic vectors) between multiuser channels determines the performance of MIMO receive algorithms. As an application of the general theory, we transform the decoding problem for several types of Quasi-Orthogonal STBC (QOSTBC) into multiuser detection of virtual Alamouti users. Building upon our A-BLAST Algorithm, we propose new algorithms for decoding single-user and multiuser QOSTBC. In particular, we show that bit error probability is a function of the quaternionic angle between virtual users (for a single user) or multiple users. This angle varies with the type of QOSTBC and leads to a new form of adaptive modulation called code diversity, where feedback instructs the transmitter how to choose from a plurality of codes. © 2009 IEEE.}, Doi = {10.1109/TCOMM.2009.07.070592}, Key = {fds235919} } @article{fds235920, Author = {Aggarwal, V and Sankar, L and Calderbank, AR and Poor, HV}, Title = {Secrecy capacity of a class of orthogonal relay eavesdropper channels}, Journal = {EURASIP Journal on Wireless Communications and Networking}, Volume = {2009}, Year = {2009}, ISSN = {1687-1472}, url = {http://dx.doi.org/10.1155/2009/494696}, Abstract = {The secrecy capacity of relay channels with orthogonal components is studied in the presence of an additional passive eavesdropper node. The relay and destination receive signals from the source on two orthogonal channels such that the destination also receives transmissions from the relay on its channel. The eavesdropper can overhear either one or both of the orthogonal channels. Inner and outer bounds on the secrecy capacity are developed for both the discrete memoryless and the Gaussian channel models. For the discrete memoryless case, the secrecy capacity is shown to be achieved by a partial decode-and-forward (PDF) scheme when the eavesdropper can overhear only one of the two orthogonal channels. Two new outer bounds are presented for the Gaussian model using recent capacity results for a Gaussian multiantenna point-to-point channel with a multiantenna eavesdropper. The outer bounds are shown to be tight for two subclasses of channels. The first subclass is one in which the source and relay are clustered, and the eavesdropper receives signals only on the channel from the source and the relay to the destination, for which the PDF strategy is optimal. The second is a subclass in which the source does not transmit to the relay, for which a noise-forwarding strategy is optimal. Copyright © 2009 Vaneet Aggarwal et al.}, Doi = {10.1155/2009/494696}, Key = {fds235920} } @article{fds235921, Author = {Jafarpour, S and Xu, W and Hassibi, B and Calderbank, R}, Title = {Efficient and robust compressed sensing using optimized expander graphs}, Journal = {IEEE Transactions on Information Theory}, Volume = {55}, Number = {9}, Pages = {4299-4308}, Year = {2009}, ISSN = {0018-9448}, url = {http://dx.doi.org/10.1109/TIT.2009.2025528}, Abstract = {Expander graphs have been recently proposed to construct efficient compressed sensing algorithms. In particular, it has been shown that any n-dimensional vector that is k-sparse can be fully recovered using O(k log n) measurements and only O(k log n) simple recovery iterations. In this paper, we improve upon this result by considering expander graphs with expansion coefficient beyond 3\4 and show that, with the same number of measurements, only O(k) recovery iterations are required, which is a significant improvement when n is large. In fact, full recovery can be accomplished by at most 2 k very simple iterations. The number of iterations can be reduced arbitrarily close to k, and the recovery algorithm can be implemented very efficiently using a simple priority queue with total recovery time O(n log(n/k))). We also show that by tolerating a small penalty on the number of measurements, and not on the number of recovery iterations, one can use the efficient construction of a family of expander graphs to come up with explicit measurement matrices for this method. We compare our result with other recently developed expander-graph-based methods and argue that it compares favorably both in terms of the number of required measurements and in terms of the time complexity and the simplicity of recovery. Finally, we will show how our analysis extends to give a robust algorithm that finds the position and sign of the k significant elements of an almost k-sparse signal and then, using very simple optimization techniques, finds a k-sparse signal which is close to the best k-term approximation of the original signal. © 2009 IEEE.}, Doi = {10.1109/TIT.2009.2025528}, Key = {fds235921} } @article{fds235922, Author = {Gilbert, G and Weinstein, YS and Aggarwal, V and Calderbank, AR}, Title = {Practical quantum fault tolerance}, Journal = {Proceedings of SPIE - The International Society for Optical Engineering}, Volume = {7342}, Year = {2009}, ISSN = {0277-786X}, url = {http://dx.doi.org/10.1117/12.818683}, Abstract = {The standard approach to quantum fault tolerance is to calculate error thresholds on basic gates in the limit of arbitrarily many concatenation levels. In contrast this paper takes the number of qubits and the target implementation accuracy as given, and provides a framework for engineering the constrained quantum system to the required tolerance. The approach requires solving the full dynamics of the quantum system for an arbitrary admixture (biased or unbiased) of Pauli errors. The inaccuracy between ideal and implemented quantum systems is captured by the supremum of the Schatten k-norm of the difference between the ideal and implemented density matrices taken over all density matrices. This is a more complete analysis than the standard approach, where an intricate combination of worst case assumptions and combinatorial analysis is used to analyze the special case of equiprobable errors. Conditions for fault tolerance are now expressed in terms of error regions rather than a single number (the standard error threshold). In the important special case of a stochastic noise model and a single logical qubit, an optimization over all 2×2 density matrices is required to obtain the full dynamics. The complexity of this calculation is greatly simplified through reduction to an optimization over only three projectors. Error regions are calculated for the standard 5- and 7-qubit codes. Knowledge of the full dynamics makes it possible to design sophisticated concatenation strategies that go beyond repeatedly using the same code, and these strategies can achieve target fault tolerance thresholds with fewer qubits. © 2009 SPIE.}, Doi = {10.1117/12.818683}, Key = {fds235922} } @article{fds235923, Author = {Pezeshki, A and Calderbank, R and Scharf, LL}, Title = {Sidelobe suppression in a desired range/Doppler interval}, Journal = {IEEE National Radar Conference - Proceedings}, Year = {2009}, ISSN = {1097-5659}, url = {http://dx.doi.org/10.1109/RADAR.2009.4977144}, Abstract = {We present simple methods for constructing radar waveforms whose ambiguity functions are free of sidelobes inside a desired range or Doppler interval. We exploit the time-frequency duality between pulse amplitude modulation (PAM) and orthogonal frequency division multiplexing (OFDM) to sequence Golay complementary codes across time or frequency and clear out range/Doppler sidelobes. Proper sequencing of complementary codes in time (PAM design) enables the annihilation of range sidelobes along a desired Doppler interval. The dual design, i.e., OFDM signaling of complementary codes, enables the annihilation of Doppler sidelobes along a desired range interval. The two designs can be used sequentially to bring weak targets out of the sidelobes of nearby strong reflectors inside a range-Doppler interval of interest. ©2009 IEEE.}, Doi = {10.1109/RADAR.2009.4977144}, Key = {fds235923} } @article{fds235924, Author = {Qureshi, TR and Zoltowski, MD and Calderbank, R}, Title = {A MIMO-OFDM channel estimation scheme utilizing complementary sequences}, Journal = {IEEE International Conference on Acoustics Speech and Signal Processing}, Pages = {2677-2680}, Year = {2009}, ISSN = {1520-6149}, url = {http://dx.doi.org/10.1109/ICASSP.2009.4960174}, Abstract = {We present a pilot-assisted method for estimating the frequency selective channel in a MIMO-OFDM system. The pilot sequence is designed using the DFT of the Golay complementary sequences. Novel exploitation of the perfect autocorrelation property of Golay complementary sequences, in conjunction with OSTBC based pilot waveform scheduling across multiple OFDM frames, facilitates simple separation of the channel mixtures at the receive antennas. The DFT length used to transform the complementary sequence into the frequency domain is shown to be a key critical parameter for correctly estimating the channel. This channel estimation scheme is then extended to antenna arrays of arbitrary sizes. ©2009 IEEE.}, Doi = {10.1109/ICASSP.2009.4960174}, Key = {fds235924} } @article{fds235925, Author = {Howard, SD and Sirianunpiboon, S and Calderbank, AR}, Title = {Low complexity essentially maximum likelihood decoding of perfect space-time block codes}, Journal = {IEEE International Conference on Acoustics Speech and Signal Processing}, Pages = {2725-2728}, Year = {2009}, ISSN = {1520-6149}, url = {http://dx.doi.org/10.1109/ICASSP.2009.4960186}, Abstract = {Perfect space-time block codes (STBCs) were first introduced by Oggier et al. to have full rate, full diversity and non-vanishing determinant. A maximum likelihood decoder based on the sphere decoder has been used for efficient decoding of perfect STBCs. However the worst-case complexity for the sphere decoder is an exhaustive search. In this paper we present a reduced complexity algorithm for 3 x 3 perfect STBC which gives essentially maximum likelihood (ML) performance and which can be extended to other perfect STBC. The algorithm is based on the conditional maximization of the likelihood function with respect to one of the set of signal points given another. There are a number of choices for which signal points to condition on and the underlying structure of the code guarantees that one of the choices is good with high probability. Furthermore, the approach can be integrated with the sphere decoding algorithm with worst case complexity corresponding exactly to that of our algorithm. ©2009 Australian Crown Copyright.}, Doi = {10.1109/ICASSP.2009.4960186}, Key = {fds235925} } @article{fds235926, Author = {Aggarwal, V and Sankar, L and Calderbank, AR and Poor, HV}, Title = {Secrecy capacity of a class of orthogonal relay eavesdropper channels}, Journal = {Information Theory and Applications Workshop, ITA 2009}, Pages = {295-300}, Year = {2009}, url = {http://dx.doi.org/10.1109/ITA.2009.5044960}, Abstract = {The secrecy capacity is developed for a class of relay channels with orthogonal components and a passive eavesdropper node. The relay and destination receive signals from the source on two orthogonal channels such that the destination also receives transmissions from the relay on its channel. The eavesdropper can overhear either one or both of the orthogonal channels. Inner and outer bounds on the secrecy capacity are developed for both the discrete memoryless and the Gaussian channel models. For the discrete memoryless case, the secrecy capacity is shown to be achieved by a partial decode-and-forward (PDF) scheme when the eavesdropper can overhear only one of the two orthogonal channels. Two new outer bounds are presented for the Gaussian model using recent capacity results for a Gaussian multi-antenna channel with a multi-antenna eavesdropper. The outer bounds are shown to be tight for two sub-classes of channels. The first sub-class is one in which the source and relay are clustered and the eavesdropper overhears on only one of the two channels for which the PDF strategy is optimal. The second is a sub-class in which the source does not transmit to the relay for which a noise-forwarding strategy is optimal. © 2009 IEEE.}, Doi = {10.1109/ITA.2009.5044960}, Key = {fds235926} } @article{fds235927, Author = {Wu, Y and Davis, LM and Calderbank, R}, Title = {On the capacity of the discrete-time channel with uniform output quantization}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Pages = {2194-2198}, Year = {2009}, url = {http://dx.doi.org/10.1109/ISIT.2009.5205826}, Abstract = {This paper provides new insight into the classical problem of determining both the capacity of the discrete-time channel with uniform output quantization and the capacity achieving input distribution. It builds on earlier work by Gallager and Witsenhausen to provide a detailed analysis of two particular quantization schemes. The first is saturation quantization where overflows are mapped to the nearest quantization bin, and the second is modulo quantization where overflows are mapped to the nearest quantization bin after reduction by some modulus. Both the capacity of modulo quantization and the capacity achieving input distribution are determined. When the additive noise is gaussian and relatively small, the capacity of saturation quantization is shown to be bounded below by that of modulo quantization. In the limit of arbitrarily many uniform quantization levels, it is shown that the difference between the upper and lower bounds on capacity given by Ihara is only 0.26 bits. © 2008 IEEE.}, Doi = {10.1109/ISIT.2009.5205826}, Key = {fds235927} } @article{fds235928, Author = {Aggarwal, V and Lai, L and Calderbank, AR and Poor, HV}, Title = {Wiretap channel type II with an active eavesdropper}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Pages = {1944-1948}, Year = {2009}, url = {http://dx.doi.org/10.1109/ISIT.2009.5205631}, Abstract = {The wiretap channel type II with an active eavesdropper is considered in this paper. Compared with the eavesdropper model considered in much of the literature, the eavesdropper considered here can not only overhear but also modify the signal transmitted over the channel. Two modification modelsare considered. In the first model, the eavesdropper erases the bits it observes. In the second model, the eavesdropper modifies the bits it observes. For this channel with memory (introduced bythe activity of the eavesdropper), one should conduct the worst case scenario analysis. Novel concatenated coding schemes that provide perfect security for the communications are developed for both models to give bounds on the achievable secrecy rate. The technique to modify the inner code to maintain the secrecyproperties of the outer code may be of independent interest. © 2009 IEEE.}, Doi = {10.1109/ISIT.2009.5205631}, Key = {fds235928} } @article{fds235929, Author = {Hande, P and Chiang, M and Calderbank, R and Rangan, S}, Title = {Network pricing and rate allocation with content provider participation}, Journal = {Proceedings - IEEE INFOCOM}, Pages = {990-998}, Year = {2009}, ISSN = {0743-166X}, url = {http://dx.doi.org/10.1109/INFCOM.2009.5062010}, Abstract = {Pricing content-providers for connectivity to endusers and setting connection parameters based on the price is an evolving model on the Internet. The implications are heavily debated in telecom policy circles, and some advocates of "Network Neutrality" have opposed price based differentiation in connectivity. However, pricing content providers can possibly subsidize the end-user's cost of connectivity, and the consequent increase in end-user demand can benefit ISPs and content providers. This paper provides a framework to quantify the precise trade-off in the distribution of benefits among ISPs, content-providers, and end-users. The framework generalizes the well-known utility maximization based rate allocation model, which has been extensively studied as an interplay between the ISP and the end-users, to incorporate pricing of content-providers. We derive the resulting equilibrium prices and data rates in two different ISP market conditions: competition and monopoly. Network neutrality based restriction on content-provider pricing is then modeled as a constraint on the maximum price that can be charged to content-providers. We demonstrate that, in addition to gains in total and enduser surplus, content-provider experiences a net surplus from participation in rate allocation under low cost of connectivity. The surplus gains are, however, limited under monopoly conditions in comparison to competition in the ISP market. © 2009 IEEE.}, Doi = {10.1109/INFCOM.2009.5062010}, Key = {fds235929} } @article{fds235930, Author = {Calderbank, R and Casazza, PG and Heinecke, A and Kutyniok, G and Pezeshki, A}, Title = {Constructing fusion frames with desired parameters}, Journal = {Proceedings of SPIE - The International Society for Optical Engineering}, Volume = {7446}, Year = {2009}, ISSN = {0277-786X}, url = {http://dx.doi.org/10.1117/12.825782}, Abstract = {A fusion frame is a frame-like collection of subspaces in a Hilbert space. It generalizes the concept of a frame system for signal representation. In this paper, we study the existence and construction of fusion frames. We first introduce two general methods, namely the spatial complement and the Naimark complement, for constructing a new fusion frame from a given fusion frame. We then establish existence conditions for fusion frames with desired properties. In particular, we address the following question: Given M, N, m ∈ N and {λj}Mj =1, does there exist a fusion frame in RM with N subspaces of dimension m for which {λj} Mj =1are the eigenvalues of the associated fusion frame operator? We address this problem by providing an algorithm which computes such a fusion frame for almost any collection of parameters M, N, m ∈ N and {λj}Mj =1. Moreover, we show how this procedure can be applied, if subspaces are to be added to a given fusion frame to force it to become tight.© 2009 SPIE.}, Doi = {10.1117/12.825782}, Key = {fds235930} } @article{fds235931, Author = {Aggarwal, V and Sankar, L and Calderbank, AR and Poor, HV}, Title = {Information secrecy from multiple eavesdroppers in orthogonal relay channels}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Pages = {2607-2611}, Year = {2009}, url = {http://dx.doi.org/10.1109/ISIT.2009.5205963}, Abstract = {The secrecy capacity of relay channels with orthogonal components is studied in the presence of additional passive eavesdropper nodes. The relay and destination receive signals from the source on two orthogonal channels such that the destination also receives transmissions from the relay on its channel. The eavesdropper(s) can overhear either one or both of the orthogonal channels. For a single eavesdropper node, the secrecy capacity is shown to be achieved by a partial decodeand-forward (PDF) scheme when the eavesdropper can overhear only one of the two orthogonal channels. For the case of two eavesdropper nodes, secrecy capacity is shown to be achieved by PDF for a sub-class of channels. © 2009 IEEE.}, Doi = {10.1109/ISIT.2009.5205963}, Key = {fds235931} } @article{fds235932, Author = {Wu, Y and Calderbank, R}, Title = {Construction of high rate super-orthogonal space-time block codes}, Journal = {Conference Record - International Conference on Communications}, Year = {2009}, ISSN = {0536-1486}, url = {http://dx.doi.org/10.1109/ICC.2009.5198848}, Abstract = {It is standard practice to integrate outer trellis codes with inner space-time block codes to increase coding gain, but the drawback is a decrease in rate. Jafarkhani and Seshadri [1] have introduced an alternative method of combining multiple inner orthogonal space-time codes with outer trellis codes that both preserves rate and increases coding gain. However their work is limited to orthogonal codes, for which the achievable rate is typically low. This paper presents a method of achieving higher transmission rates by integrating higher rate non-orthogonal space with outer trellis codes, and new methods are introduced to avoid catastrophic codes. The method is presented with reference to the particular example of the Silver Code, but it applies to all multiplexed orthogonal designs and to more general codes. ©2009 IEEE.}, Doi = {10.1109/ICC.2009.5198848}, Key = {fds235932} } @article{fds235933, Author = {Aggarwal, V and Calderbank, R and Gilbert, G and Weinstein, YS}, Title = {Engineering fault tolerance for realistic quantum systems via the full error dynamics of quantum codes}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Pages = {958-962}, Year = {2009}, url = {http://dx.doi.org/10.1109/ISIT.2009.5205593}, Abstract = {The standard approach to quantum fault tolerance is to calculate error thresholds on basic gates in the limit of arbitrarily many concatenation levels. In contrast this paper takes the number of qubits and the target implementation accuracy as given, and provides a framework for engineering the constrained quantum system to the required tolerance. The approach requires solving the full dynamics of the quantum system for an arbitrary admixture (biased or unbiased) of Pauli errors. The inaccuracy between ideal and implemented quantum systems is captured by the supremum of the Schatten-k norm of the difference between the ideal and implemented density matrices taken over all density matrices. This is a more complete analysis than the standard approach, where an intricate combination of worst case assumptions and combinatorial analysis is used to analyze the special case of equiprobable errors. Conditions for fault tolerance are now expressed in terms of error regions rather than a single number (the standard error threshold). In the important special case of a stochastic noise model and a single logical qubit, an optimization over all 2 × 2 density matrices is required to obtain the full dynamics. The complexity of this calculation is greatly simplified through reduction to an optimization over only three projectors. Error regions are calculated for the standard 5- and 7-qubit codes. Knowledge of the full dynamics makes it possible to design sophisticated concatenation strategies that go beyond repeatedly using the same code, and these strategies can achieve target fault tolerance thresholds with fewer qubits. © 2009 IEEE.}, Doi = {10.1109/ISIT.2009.5205593}, Key = {fds235933} } @article{fds235934, Author = {Wu, Y and Jia, T and Calderbank, R and Duel-Hallen, A and Hallen, H}, Title = {Integration of code diversity and long-range channel prediction in wireless communication}, Journal = {Proceedings of the 2009 International Conference on Electromagnetics in Advanced Applications, ICEAA '09}, Pages = {241-244}, Year = {2009}, url = {http://dx.doi.org/10.1109/ICEAA.2009.5297458}, Abstract = {Code diversity integrates space-time coding with beamforming by using a small number of feedback bits to select from a family of space-time codes. Different codes lead to different induced channels at the receiver, where Channel State information (CSI) is used to instruct the transmitter how to choose the code. Feedback can be combined with sub-optimal low complexity decoding of the component codes to match Maximum-Likelihood (ML) decoding performance of any individual code in the family. It can also be combined with ML decoding of the component codes to improve performance beyond ML decoding performance of any individual code. Prior analysis of code diversity did not take into account the effect of the mobile speed and the delay in the feedback channel. This paper demonstrates the practicality of code diversity in space-time coded systems by showing that predicted performance gains based on instantaneous feedback are largely preserved when the feedback is based on long-range prediction of rapidly time-varying correlated fading channels. Simulations are presented for two channel models; the first is the Jakes model where angles of arrival are uniformly distributed and the arrival rays have equal strengths, and the second is a model derived from a physical scattering environment where the parameters associated with the reflectors vary in time and the arrival rays have different strengths and non-symmetric arrival angles. © 2009 IEEE.}, Doi = {10.1109/ICEAA.2009.5297458}, Key = {fds235934} } @article{fds235935, Author = {Aggarwal, V and Applebaum, L and Bennatan, A and Calderbank, AR and Howard, SD and Searle, SJ}, Title = {Enhanced CDMA communications using compressed-sensing reconstruction methods}, Journal = {2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009}, Pages = {1211-1215}, Year = {2009}, url = {http://dx.doi.org/10.1109/ALLERTON.2009.5394537}, Abstract = {We propose a simple method for downlink communications based on second order Reed-Muller sequences which generalize the Walsh sequences that are used in orthogonal CDMA. In our approach, coding occurs at the chip level (i.e. we use a spreading factor of 1) and different users are not orthogonalized. Our decoding algorithm is borrowed from work on fast reconstruction of signals for compressed-sensing. This algorithm allows for low-complexity multiuser detection. ©2009 IEEE.}, Doi = {10.1109/ALLERTON.2009.5394537}, Key = {fds235935} } @article{fds235936, Author = {Qureshi, TR and Zoltowski, MD and Calderbank, R}, Title = {Target detection in MIMO radar using Golay complementary sequences in the presence of doppler}, Journal = {2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009}, Pages = {1490-1493}, Year = {2009}, url = {http://dx.doi.org/10.1109/ALLERTON.2009.5394498}, Abstract = {In this paper, we present a method for detecting a point target using multiple antennas when the relative motion between the receivers and the target induces a non-negligible Doppler shift. As a key illustrative example, we consider a 4 x 4 system employing a unitary matrix waveform set, e.g., formed from Golay complementary sequences. When a non-negligible Doppler shift is induced by the target motion, the waveform matrix formed from the complementary sequences is no longer unitary, resulting in significantly degraded target range estimates. To solve this problem, we adopt a subspace based approach exploiting the observation that the receive matrix formed from matched filtering of the reflected waveforms has a (non-trivial) null-space. Through processing of the waveforms with the appropriate vector from the null-space, we can significantly improve the detection performance. We provide simulation results to confirm the theoretical analysis. ©2009 IEEE.}, Doi = {10.1109/ALLERTON.2009.5394498}, Key = {fds235936} } @article{fds235937, Author = {Calderbank, R and Howard, S and Jafarpour, S}, Title = {A sublinear algorithm for sparse reconstruction with ℓ_{2}/ ℓ_{2}recovery guarantees}, Journal = {CAMSAP 2009 - 2009 3rd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing}, Pages = {209-212}, Year = {2009}, url = {http://dx.doi.org/10.1109/CAMSAP.2009.5413298}, Abstract = {Compressed Sensing aims to capture attributes of a sparse signal using very few measurements. Candès and Tao showed that sparse reconstruction is possible if the sensing matrix acts as a near isometry on all k-sparse signals. This property holds with overwhelming probability if the entries of the matrix are generated by an iid Gaussian or Bernoulli process. There has been significant recent interest in an alternative signal processing framework; exploiting deterministic sensing matrices that with overwhelming probability act as a near isometry on k-sparse vectors with uniformly random support, a geometric condition that is called the Statistical Restricted Isometry Property or StRIP. This paper considers a family of deterministic sensing matrices satisfying the StRIP that are based on Delsarte-Goethals Codes codes (binary chirps) and a k-sparse reconstruction algorithm with sublinear complexity. In the presence of stochastic noise in the data domain, this paper derives bounds on the ℓ2 accuracy of approximation in terms of the ℓ2 norm of the measurement noise and the accuracy of the best k-sparse approximation, also measured in the ℓ2 norm. This type of ℓ2/ℓ2 bound is tighter than the standard ℓ2/ℓ1 or ℓ1/ℓ1 bounds. © 2009 IEEE.}, Doi = {10.1109/CAMSAP.2009.5413298}, Key = {fds235937} } @article{fds235938, Author = {Bollapalli, KC and Wu, Y and Gulati, K and Khatri, S and Calderbank, AR}, Title = {Highly parallel decoding of space-time codes on graphics processing units}, Journal = {2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009}, Pages = {1262-1269}, Year = {2009}, url = {http://dx.doi.org/10.1109/ALLERTON.2009.5394528}, Abstract = {Graphics Processing Units (GPUs) with a few hundred extremely simple processors represent a paradigm shift for highly parallel computations. We use this emergent GPU architecture to provide a first demonstration of the feasibility of real time ML decoding (in software) of a high rate space-time block code that is representative of codes incorporated in 4th generation wireless standards such as WiMAX and LTE. The decoding algorithm is conditional optimization which reduces to a parallel calculation that is a natural fit to the architecture of low cost GPUs.Experimental results demonstrate that asymptotically the GPU implementation is more than 700 times faster than a standard serial implementation. These results suggest that GPU architectures have the potential to improve the cost / performance tradeoff of 4th generation wireless base stations. Additional benefits might include reducing the time required for system development and the time required for configuration and testing of wireless base stations. ©2009 IEEE.}, Doi = {10.1109/ALLERTON.2009.5394528}, Key = {fds235938} } @article{fds235939, Author = {Chi, Y and Calderbank, R and Pezeshki, A}, Title = {Golay complementary waveforms for sparse delay-Doppler radar imaging}, Journal = {CAMSAP 2009 - 2009 3rd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing}, Pages = {177-180}, Year = {2009}, url = {http://dx.doi.org/10.1109/CAMSAP.2009.5413308}, Abstract = {We present a new approach to radar imaging that exploits sparsity in the matched filter domain to enable high resolution imaging of targets in delay and Doppler. We show that the vector of radar cross-ambiguity values at any fixed test delay cell has a sparse representation in a Vandermonde frame that is obtained by discretizing the Doppler axis. The expansion coefficients are given by the auto-correlation functions of the transmitted waveforms. We show that the orthogonal matching pursuit (OMP) algorithm can then be easily used to identify the locations of the radar targets in delay and Doppler. Unambiguous imaging in delay is enabled by alternating between a Golay pair of phase coded waveforms at the transmission to eliminate delay sidelobe effects. We then extend our work to multi-channel radar, by developing a sparse recovery approach for dually-polarimetric radar. We exploit sparsity in a bank of matched filters, each of which is matched to an entry of an Alamouti matrix of Golay waveforms to recover a co-polar or cross-polar polarization scattering component. © 2009 IEEE.}, Doi = {10.1109/CAMSAP.2009.5413308}, Key = {fds235939} } @article{fds235940, Author = {Sirianunpiboon, S and Howard, SD and Calderbank, AR and Davis, LM}, Title = {Fully-polarimetric MIMO to improve throughput and reliability across propagation conditions}, Journal = {IEEE VTS ... Vehicular Technology Conference : VTC : [proceedings]}, Year = {2009}, ISSN = {1550-2252}, url = {http://dx.doi.org/10.1109/VETECF.2009.5379016}, Abstract = {Multiple-Input Multiple-Output (MIMO) functionality has been shown to dramatically increase the capacity of wireless communication systems when the environment provides rich multipath scattering. In a predominantly Line-of-Sight (LOS) environment, the loss of diversity reduces the potential gain considerably. This can be remedied in part by the use of dual-polarized antennas, which increases the rank of the wireless channel and introduces diversity, while minimizing the antenna's form factor. However the performance of a dual-polarized antenna is still degraded by antenna rotations that are typical of mobile terminal operation. This paper presents a solution which uses a triad antenna at the transmitter and a triad at the receiver, to provide a 8-10 dB gain over the baseline dual-polarized system. A triad is composed of three orthogonal dipoles oriented in perpendicular directions. A triad antenna can generate an arbitrary oscillating dipole moment at the transmitter and consequently an arbitrary polarized electric field at the receiver, subject only to the constraints imposed by the physics of the Electromagnetic (EM) field. We show that, in LOS environments, the capacity of the channel is invariant under arbitrary rotations of the transmit and/or receive antennas about their centres. Simulation results show that the performance is stable as the propagation environment varies from rich scattering to pure LOS. A full rate 3×3 Space-Time Block Code (STBC) is proposed for the triad system that is designed for low complexity decoding. © 2009 Crown.}, Doi = {10.1109/VETECF.2009.5379016}, Key = {fds235940} } @article{fds235941, Author = {Jafarpour, S and Willett, R and Raginsky, M and Calderbank, R}, Title = {Performance bounds for expander-based compressed sensing in the presence of Poisson noise}, Journal = {Conference Record of the Asilomar Conference on Signals, Systems and Computers}, Pages = {513-517}, Year = {2009}, ISSN = {1058-6393}, url = {http://dx.doi.org/10.1109/ACSSC.2009.5469879}, Abstract = {This paper provides performance bounds for compressed sensing in the presence of Poisson noise using expander graphs. The Poisson noise model is appropriate for a variety of applications, including low-light imaging and digital streaming, where the signal-independent and/or bounded noise models used in the compressed sensing literature are no longer applicable. In this paper, we develop a novel sensing paradigm based on expander graphs and propose a MAP algorithm for recovering sparse or compressible signals from Poisson observations. The geometry of the expander graphs and the positivity of the corresponding sensing matrices play a crucial role in establishing the bounds on the signal reconstruction error of the proposed algorithm. The geometry of the expander graphs makes them provably superior to random dense sensing matrices, such as Gaussian or partial Fourier ensembles, for the Poisson noise model.We support our results with experimental demonstrations. © 2009 IEEE.}, Doi = {10.1109/ACSSC.2009.5469879}, Key = {fds235941} } @article{fds235942, Author = {Sirianunpiboon, S and Howard, SD and Calderbank, AR}, Title = {A scheme for fully polarimetric MIMO multiuser detection}, Journal = {Conference Record of the Asilomar Conference on Signals, Systems and Computers}, Pages = {1461-1465}, Year = {2009}, ISSN = {1058-6393}, url = {http://dx.doi.org/10.1109/ACSSC.2009.5470081}, Abstract = {Multiple-Input Multiple-Output (MIMO) functionality has been shown to dramatically increase the capacity of wireless communication systems when the environment provides rich multipath scattering. In a predominantly Line-of-Sight (LOS) environment, the loss of diversity reduces the potential gain considerably. Recent studies have shown that systems which use a fully -polarimetric antenna such as triad antenna at the both end of the link can provides stability in performance across a full range of propagation environments from LOS to pure Rayleigh scattering. These systems also provide resilience to arbitrary rotations of the transmit and receive antennas. This paper considers the multiuser downlink where both the base station and each user is equipped with a triad antenna. The system uses a CDMA transmitting scheme in which each user is assigned a two dimensional subspace and the transmitted information symbol for each user is coded across this subspace. The received signal for each user after despreading is equivalent to the decoding problem of a single user with space-time block code (STBC) system. We demonstrate that the transmitted information symbols can be chosen to have the structure of STBC with full rate, full-diversity and low complexity decoding. We also show how to generalize our basic MIMO CDMA scheme to apply to an inhomogeneous multiuser scenario where the base station has two transmit antennas, but each user is equipped with either one or two receive antennas and wish to use different STBCs. © 2009 IEEE.}, Doi = {10.1109/ACSSC.2009.5470081}, Key = {fds235942} } @article{fds235943, Author = {Qureshi, T and Zoltowski, M and Calderbank, R}, Title = {Target detection in MIMO radar using golay complementary sequences in the presence of doppler}, Journal = {Conference Record of the Asilomar Conference on Signals, Systems and Computers}, Pages = {156-159}, Year = {2009}, ISSN = {1058-6393}, url = {http://dx.doi.org/10.1109/ACSSC.2009.5470143}, Abstract = {In this paper, we present a method for detecting a point target using multiple antennas when the relative motion between the receivers and the target induces a non-trivial Doppler shift. We consider a 4×4 system employing sets of unitary waveforms. In case of a non-trivial Doppler shift induced by the target motion, the waveforms are no longer unitary, and unambiguous target ranging is not possible. To solve this problem, we adopt a subspace based approach where we show that the unitary waveforms used have a non-empty null-space under certain conditions, and by processing the waveforms with vectors from the null-space, we can significantly improve the detection performance. © 2009 IEEE.}, Doi = {10.1109/ACSSC.2009.5470143}, Key = {fds235943} } @article{fds235944, Author = {Lau, C and Zoltowski, M and Calderbank, R}, Title = {Spatio-temporal scheduling of complementary sequences with application to MIMO-OFDM}, Journal = {Conference Record of the Asilomar Conference on Signals, Systems and Computers}, Pages = {503-507}, Year = {2009}, ISSN = {1058-6393}, url = {http://dx.doi.org/10.1109/ACSSC.2009.5469876}, Abstract = {In this paper, a new method of space-time processing is proposed for Orthogonal Frequency Division Multiplexing (OFDM) using complementary sequences derived from the rows of the DFT matrix. The autocorrelative properties of the complementary sequences allows multiple complex data signals at the transmitter with an arbitrary number of antennas to be perfectly separated at the receiver without prior channel knowledge while achieving full-rate. This new method is proposed and derived for multiple MIMO-OFDM systems with multipath fading; at the receiver, symbol estimation is effected via maximum likelhihood estimation (ML). © 2009 IEEE.}, Doi = {10.1109/ACSSC.2009.5469876}, Key = {fds235944} } @article{fds235945, Author = {Applebaum, L and Howard, SD and Searle, S and Calderbank, R}, Title = {Chirp sensing codes: Deterministic compressed sensing measurements for fast recovery}, Journal = {Applied and Computational Harmonic Analysis}, Volume = {26}, Number = {2}, Pages = {283-290}, Year = {2009}, ISSN = {1063-5203}, url = {http://dx.doi.org/10.1016/j.acha.2008.08.002}, Abstract = {Compressed sensing is a novel technique to acquire sparse signals with few measurements. Normally, compressed sensing uses random projections as measurements. Here we design deterministic measurements and an algorithm to accomplish signal recovery with computational efficiency. A measurement matrix is designed with chirp sequences forming the columns. Chirps are used since an efficient method using FFTs can recover the parameters of a small superposition. We show that this type of matrix is valid as compressed sensing measurements. This is done by bounding the eigenvalues of sub-matrices, as well as an empirical comparison with random projections. Further, by implementing our algorithm, simulations show successful recovery of signals with sparsity levels similar to those possible by matching pursuit with random measurements. For sufficiently sparse signals, our algorithm recovers the signal with computational complexity O (K log K) for K measurements. This is a significant improvement over existing algorithms. Crown Copyright © 2008.}, Doi = {10.1016/j.acha.2008.08.002}, Key = {fds235945} } @article{fds235946, Author = {Bennatan, A and Aggarwal, V and Wu, Y and Calderbank, AR and Hoydis, J and Chindapol, A}, Title = {Bounds and lattice-based transmission strategies for the phase-faded dirty-paper channel}, Journal = {IEEE Transactions on Wireless Communications}, Volume = {8}, Number = {7}, Pages = {3620-3627}, Year = {2009}, ISSN = {1536-1276}, url = {http://dx.doi.org/10.1109/TWC.2009.080569}, Abstract = {We consider a fading version of the dirty-paper problem, as proposed by Grover and Sahai. In this formulation, the various signals involved are complex-valued, and the interference (known only to the transmitter) is multiplied by a random complex-valued coefficient, whose phase is known only to the receiver. We focus on a compound channel formulation, and seek to maximize the worst-case performance. We present an achievable strategy modeled on the lattice-based approach of Erez, Shamai and Zamir and propose heuristic methods to optimize its parameters. We also derive an upper bound on the maximum achievable transmission rates. Our bounds are shown to be tight in some settings, yielding a complete characterization of capacity. We also provide simulation results, indicating the practical effectiveness of our approaches. © 2009 IEEE.}, Doi = {10.1109/TWC.2009.080569}, Key = {fds235946} } @article{fds235947, Author = {Rabiei, P and Al-Dhahir, N and Calderbank, R}, Title = {New rate-2 STBC design for 2 TX with reduced-complexity maximum likelihood decoding}, Journal = {IEEE Transactions on Wireless Communications}, Volume = {8}, Number = {4}, Pages = {1803-1813}, Year = {2009}, ISSN = {1536-1276}, url = {http://dx.doi.org/10.1109/TWC.2009.071323}, Abstract = {We propose a new full-rate space-time block code (STBC) for two transmit antennas which can be designed to achieve maximum diversity or maximum capacity while enjoying optimized coding gain and reduced-complexity maximum-likelihood (ML) decoding. The maximum transmit diversity (MTD) construction provides a diversity order of 2N r for any number of receive antennas N r at the cost of channel capacity loss. The maximum channel capacity (MCC) construction preserves the mutual information between the transmit and the received vectors while sacrificing diversity. The system designer can switch between the two constructions through a simple parameter change based on the operating signal-to-noise ratio (SNR), signal constellation size and number of receive antennas. Thanks to their special algebraic structure, both constructions enjoy low-complexity ML decoding proportional to the square of the signal constellation size making them attractive alternatives to existing full-diversity full-rate STBCs in [6], [3] which have high ML decoding complexity proportional to the fourth order of the signal constellation size. Furthermore, we design a differential transmission scheme for our proposed STBC, derive the exact ML differential decoding rule, and compare its performance with competitive schemes. Finally, we investigate transceiver design and performance of our proposed STBC in spatial multiple-access scenarios and over frequency-selective channels. © 2006 IEEE.}, Doi = {10.1109/TWC.2009.071323}, Key = {fds235947} } @article{fds235948, Author = {Wu, Y and Davis, LM and Calderbank, AR}, Title = {Finite precision analysis for space-time decoding}, Journal = {IEEE Transactions on Signal Processing}, Volume = {57}, Number = {12}, Pages = {4861-4870}, Year = {2009}, ISSN = {1053-587X}, url = {http://dx.doi.org/10.1109/TSP.2009.2026068}, Abstract = {Low complexity optimal (or nearly optimal) decoders for space-time codes have recently been under intensive investigation. For example, recent works by Sirianunpiboon and others show that the Silver code and the Golden code can be decoded optimally (or nearly optimally) with quadratic decoding complexity. Fast decodability makes them very attractive in practice. In implementing these decoders, floating-point to fixed-point conversion (FFC) needs to be carefully undertaken to minimize hardware cost while retaining decoding performance. The process of quantization for fixed-point representations is often ignored by research community and lacks investigation, and so FFC is often conducted heuristically based on simulations. This paper studies the effects of quantization to space-time coded systems from an information theoretic perspective. It shows the analytical relationship between quantization error and decoding performance deterioration. This paper also proposes a general finite precision implementation methodology including two FFC criteria for space-time coded systems within an integer optimization framework. As a particular example, this paper examines the finite precision implementation of the quadratic optimal decoding algorithm of the Silver code. However, our methodology and techniques can be applied to general space-time codes. © 2009 IEEE.}, Doi = {10.1109/TSP.2009.2026068}, Key = {fds235948} } @article{fds235949, Author = {Matz, G and Calderbank, R and Mecklenbrauker, C and Naguib, A and Viterbo, E}, Title = {Introduction to the issue on managing complexity in multiuser MIMO systems}, Journal = {IEEE Journal of Selected Topics in Signal Processing}, Volume = {3}, Number = {6}, Pages = {906-909}, Year = {2009}, ISSN = {1932-4553}, url = {http://dx.doi.org/10.1109/JSTSP.2009.2036955}, Doi = {10.1109/JSTSP.2009.2036955}, Key = {fds235949} } @article{fds235950, Author = {Wu, Y and Calderbank, R}, Title = {Code diversity in multiple antenna wireless communication}, Journal = {IEEE Journal of Selected Topics in Signal Processing}, Volume = {3}, Number = {6}, Pages = {928-938}, Year = {2009}, ISSN = {1932-4553}, url = {http://dx.doi.org/10.1109/JSTSP.2009.2035861}, Abstract = {The standard approach to the design of individual space-time codes is based on optimizing diversity and coding gains. This geometric approach leads to remarkable examples, such as perfect space-time block codes (Perfect space-time block codes. F. Oggier , Trans. Inf. Theory, vol. 52, no. 9, pp. 38853902, Sep. 2006), for which the complexity of maximum-likelihood (ML) decoding is considerable. Code diversity is an alternative and complementary approach where a small number of feedback bits are used to select from a family of space-time codes. Different codes lead to different induced channels at the receiver, where channel state information (CSI) is used to instruct the transmitter how to choose the code. This method of feedback provides gains associated with beamforming while minimizing the number of feedback bits. Thus, code diversity can be viewed as the integration of space-time coding with a fixed set of beams. It complements the standard approach to code design by taking advantage of different (possibly equivalent) realizations of a particular code design. Feedback can be combined with suboptimal low-complexity decoding of the component codes to match ML decoding performance of any individual code in the family. It can also be combined with ML decoding of the component codes to improve performance beyond ML decoding performance of any individual code. One method of implementing code diversity is the use of feedback to adapt the phase of a transmitted signal. The values of code diversity is verified in the simulations on 4 × 4 Quasi-Orthogonal space-time Block Code (QOSTBC), multi-user detection of Alamouti signaling and the Golden code. It shows that our code diversity scheme is more robust in the case of erroneous feedback compared with other low-rate feedback schemes such as transmit antenna selection and its variations. This paper introduces a family of full rate circulant codes which can be linearly decoded by Fourier decomposition of circulant matrices within the code diversity framework. © 2009 IEEE.}, Doi = {10.1109/JSTSP.2009.2035861}, Key = {fds235950} } @article{fds235951, Author = {Aggarwal, V and Sankar, L and Calderbank, AR and Poor, HV}, Title = {Ergodic layered erasure one-sided interference channels}, Journal = {2009 IEEE Information Theory Workshop, ITW 2009}, Pages = {574-578}, Year = {2009}, url = {http://dx.doi.org/10.1109/ITW.2009.5351176}, Abstract = {The sum capacity of a class of layered erasure onesided interference channels is developed under the assumption of no channel state information at the transmitters. Outer bounds are presented for this model and are shown to be tight for the following sub-classes: i) weak, ii) strong (mix of strong but not very strong (SnVS) and very strong (VS)), iii) ergodic very strong (mix of strong and weak), and (iv) a sub-class of mixed interference (mix of SnVS and weak). Each sub-class is uniquely defined by the fading statistics. © 2009 IEEE.}, Doi = {10.1109/ITW.2009.5351176}, Key = {fds235951} } @article{fds235777, Author = {Zoltowski, MD and Qureshi, TR and Calderbank, R and Moran, B}, Title = {Unitary Design of Radar Waveform Diversity Sets}, Journal = {Handbook on Array Processing and Sensor Networks}, Pages = {211-230}, Year = {2010}, url = {http://dx.doi.org/10.1002/9780470487068.ch7}, Doi = {10.1002/9780470487068.ch7}, Key = {fds235777} } @article{fds235952, Author = {Li, Y and Li, Z and Chiang, M and Calderbank, AR}, Title = {Intelligent video network engineering with distributed optimization: Two case studies}, Journal = {Studies in Computational Intelligence}, Volume = {280}, Pages = {253-290}, Year = {2010}, ISSN = {1860-949X}, url = {http://dx.doi.org/10.1007/978-3-642-11686-5_8}, Abstract = {Video is becoming the dominant traffic over the Internet. To provide better Quality of Service (QoS) to the end users, while also achieve network resource efficiency, is an important problem for both network operators, content providers and consumers. In this work, we present intelligent video networking solutions for IPTV and Peer-to-Peer (P2P) systems that optimizes the users' QoS experiences while under network resource constraints. Given the limited network bandwidth resources, how to provide Internet users with good video playback Quality of Service (QoS) is a key problem. For IPTV systems video clips competing bandwidth, we propose an approach of Content-Aware distortion-Fair (CAF) video delivery scheme, which is aware of the characteristics of video frames and ensures max-min distortion fair sharing among video flows. Different from bandwidth fair sharing, CAF targets end-to-end video playback quality fairness among users when bandwidth is insufficient, based on the fact that users directly care about video quality rather than bandwidth. The proposed CAF approach does not require rate-distortion modeling of the source, which is difficult to estimate, but instead, it exploits the temporal prediction structure of the video sequences along with a frame drop distortion metric to guide resource allocations and coordination. Experimental results show that the proposed approach operates with limited overhead in computation and communication, and yields better QoS, especially when the network is congested. For Internet based video broadcasting applications such as IPTV, the Peer-to-Peer (P2P) streaming scheme has been found to be an effective solution. An important issue in live broadcasting is to avoid playback buffer underflow. How to utilize the playback buffer and upload bandwidth of peers to minimize the freeze-ups in playback, is the problem we try to solve. We propose a successive water-filling (SWaF) algorithm for the video transmission scheduling in P2P live streaming system, to minimize the playback freeze-ups among peers. SWaF algorithm only needs each peer to optimally transmit (within its uploading bandwidth) part of its available video segments in the buffer to other peers requiring the content and pass small amount message to some other peers. Moreover, SWaF has low complexity and provable optimality. Numerical results demonstrated the effectiveness of the proposed algorithm. © 2010 Springer-Verlag Berlin Heidelberg.}, Doi = {10.1007/978-3-642-11686-5_8}, Key = {fds235952} } @article{fds235953, Author = {Hande, P and Chiang, M and Calderbank, R and Zhang, J}, Title = {Pricing under constraints in access networks: Revenue maximization and congestion management}, Journal = {Proceedings - IEEE INFOCOM}, Year = {2010}, ISSN = {0743-166X}, url = {http://dx.doi.org/10.1109/INFCOM.2010.5461954}, Abstract = {This paper investigates pricing of Internet connectivity services in the context of a monopoly ISP selling broadband access to consumers. We first study the optimal combination of flat-rate and usage-based access price components for maximization of ISP revenue, subject to a capacity constraint on the datarate demand. Next, we consider time-varying consumer utilities for broadband data rates that can result in uneven demand for data-rate over time. Practical considerations limit the viability of altering prices over time to smoothen out the demanded datarate. Despite such constraints on pricing, our analysis reveals that the ISP can retain the revenue by setting a low usage fee and dropping packets of consumer demanded data that exceed capacity. Regulatory attention on ISP congestion management discourages such "technical" practices and promotes economics based approaches. We characterize the loss in ISP revenue from an economics based approach. Regulatory requirements further impose limitations on price discrimination across consumers, and we derive the revenue loss to the ISP from such restrictions. We then develop partial recovery of revenue loss through non-linear pricing that does not explicitly discriminate across consumers. While determination of the access price is ultimately based on additional considerations beyond the scope of this paper, the analysis here can serve as a benchmark to structure access price in broadband access networks. ©2010 IEEE.}, Doi = {10.1109/INFCOM.2010.5461954}, Key = {fds235953} } @article{fds235954, Author = {Raginsky, M and Jafarpour, S and Willett, R and Calderbank, R}, Title = {Fishing in poisson streams: Focusing on the whales, ignoring the minnows}, Journal = {2010 44th Annual Conference on Information Sciences and Systems, CISS 2010}, Year = {2010}, url = {http://dx.doi.org/10.1109/CISS.2010.5464841}, Abstract = {This paper describes a low-complexity approach for reconstructing average packet arrival rates and instantaneous packet counts at a router in a communication network, where the arrivals of packets in each flow follow a Poisson process. Assuming that the rate vector of this Poisson process is sparse or approximately sparse, the goal is to maintain a compressed summary of the process sample paths using a small number of counters, such that at any time it is possible to reconstruct both the total number of packets in each flow and the underlying rate vector. We show that these tasks can be accomplished efficiently and accurately using compressed sensing with expander graphs. In particular, the compressive counts are a linear transformation of the underlying counting process by the adjacency matrix of an unbalanced expander. Such a matrix is binary and sparse, which allows for efficient incrementing when new packets arrive. We describe, analyze, and compare two methods that can be used to estimate both the current vector of total packet counts and the underlying vector of arrival rates. ©2010 IEEE.}, Doi = {10.1109/CISS.2010.5464841}, Key = {fds235954} } @article{fds235955, Author = {Chi, Y and Wu, Y and Calderbank, R}, Title = {Regularized blind detection for MIMO communications}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Pages = {2108-2112}, Year = {2010}, url = {http://dx.doi.org/10.1109/ISIT.2010.5513407}, Abstract = {Multiple-Input Multiple-Output (MIMO) systems improve the throughput and reliability of wireless communications. Perfect Channel State Information (CSI) is needed at the receiver to perform coherent detection and achieve the optimal gain of the system. In fast fading and low SNR regimes, it is hard or impossible to obtain perfect CSI, which leads the receiver to operate without knowledge of the CSI and perform blind detection. In reality CSI may be available to the receiver but this CSI may be insufficient to support coherent detection. In this paper, we fill the gap between coherent and blind detection by considering a more realistic model where the receiver knows the statistics of the channel, that is Channel Distribution Information (CDI). We propose a new detection algorithm, called Regularized Blind Detection (RBD), where coherent and blind detection can be viewed as special cases in our model. The algorithm estimates CDI from any training symbols that are available and maximizes performance given the estimated CDI. Simulations demonstrate significant improvement in performance over blind detection. Our work can be viewed as a systematic exploration of space between coherent and blind detection with a strong Bayesian statistic flavor. © 2010 IEEE.}, Doi = {10.1109/ISIT.2010.5513407}, Key = {fds235955} } @article{fds235956, Author = {Bajwa, WU and Calderbank, R and Jafarpour, S}, Title = {Model selection: Two fundamental measures of coherence and their algorithmic significance}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Pages = {1568-1572}, Year = {2010}, url = {http://dx.doi.org/10.1109/ISIT.2010.5513474}, Abstract = {The problem of model selection arises in a number of contexts, such as compressed sensing, subset selection in linear regression, estimation of structures in graphical models, and signal denoising. This paper generalizes the notion of incoherence in the existing literature on model selection and introduces two fundamental measures of coherence - termed as the worst-case coherence and the average coherence - among the columns of a design matrix. In particular, it utilizes these two measures of coherence to provide an in-depth analysis of a simple one-step thresholding (OST) algorithm for model selection. One of the key insights offered by the ensuing analysis is that OST is feasible for model selection as long as the design matrix obeys an easily verifiable property. In addition, the paper also characterizes the model-selection performance of OST in terms of the worst-case coherence, μ, and establishes that OST performs near-optimally in the low signal-to-noise ratio regime for N × C design matrices with μ ≈ O(N-1/2). Finally, in contrast to some of the existing literature on model selection, the analysis in the paper is nonasymptotic in nature, it does not require knowledge of the true model order, it is applicable to generic (random or deterministic) design matrices, and it neither requires submatrices of the design matrix to have full rank, nor does it assume a statistical prior on the values of the nonzero entries of the data vector. © 2010 IEEE.}, Doi = {10.1109/ISIT.2010.5513474}, Key = {fds235956} } @article{fds235957, Author = {Goel, S and Aggarwal, V and Yener, A and Calderbank, AR}, Title = {Modeling location uncertainty for eavesdroppers: A secrecy graph approach}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Pages = {2627-2631}, Year = {2010}, url = {http://dx.doi.org/10.1109/ISIT.2010.5513702}, Abstract = {In this paper, we consider end-to-end secure communication in a large wireless network, where the locations of eavesdroppers are uncertain. Our framework attempts to bridge the gap between physical layer security under uncertain channel state information of the eavesdropper and network level connectivity under security constraints, by modeling location uncertainty directly at the network level as correlated node and link failures in a secrecy graph. Bounds on the percolation threshold are obtained for square and triangular lattices, and bounds on mean degree are obtained for Poisson secrecy graphs. Both analytic and simulation results show the dramatic effect of uncertainty in location of eavesdroppers on connectivity in a secrecy graph. © 2010 IEEE.}, Doi = {10.1109/ISIT.2010.5513702}, Key = {fds235957} } @article{fds235958, Author = {Chiang, M and Hande, P and Kim, H and Ha, S and Calderbank, R}, Title = {Pricing broadband: Survey and open problems}, Journal = {ICUFN 2010 - 2nd International Conference on Ubiquitous and Future Networks}, Pages = {303-308}, Year = {2010}, url = {http://dx.doi.org/10.1109/ICUFN.2010.5547185}, Abstract = {Driven by the emerging directions from the FCC and the broadband market, this paper aims at answering the fundamental question of how to use pricing as a lever to enable universal broadband coverage and effective network management in the United States. We address differential pricing as a network management tool, i.e., what to charge, how to charge, and how much to charge. We also outline research towards multi-platform two-sided pricing focusing on ISP that charges both content and application providers. Open problems are highlghted. As a next step, through collaboration we will combine the access to large-scale empirical data with rigorous modeling and analysis; we will go all the way from data collection through mathematical analysis to practical impact on policy decisions and ISP business decisions, thus closing the loop in the study of network economics for universal broadband coverage. © 2010 IEEE.}, Doi = {10.1109/ICUFN.2010.5547185}, Key = {fds235958} } @article{fds235959, Author = {Chi, Y and Pezeshki, A and Scharf, L and Calderbank, R}, Title = {Sensitivity to basis mismatch in compressed sensing}, Journal = {IEEE International Conference on Acoustics Speech and Signal Processing}, Pages = {3930-3933}, Year = {2010}, ISSN = {1520-6149}, url = {http://dx.doi.org/10.1109/ICASSP.2010.5495800}, Abstract = {Compressed sensing theory suggests that successful inversion of an image of the physical world from its modal parameters can be achieved at measurement dimensions far lower than the image dimension, provided that the image is sparse in an a priori known basis. The assumed basis for sparsity typically corresponds to a gridding of the parameter space, e.g., an DFT grid in spectrum analysis. However, in reality no physical field is sparse in the DFT basis or in an a priori known basis. No matter how finely we grid the parameter space the sources may not lie in the center of the grid cells and there is always mismatch between the assumed and the actual bases for sparsity. In this paper, we study the sensitivity of compressed sensing (basis pursuit to be exact) to mismatch between the assumed and the actual sparsity bases. Our mathematical analysis and numerical examples show that the performance of basis pursuit degrades considerably in the presence of basis mismatch. ©2010 IEEE.}, Doi = {10.1109/ICASSP.2010.5495800}, Key = {fds235959} } @article{fds235960, Author = {Calderbank, R and Howard, S and Jafarpour, S}, Title = {Sparse reconstruction via the reed-muller sieve}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Pages = {1973-1977}, Year = {2010}, url = {http://dx.doi.org/10.1109/ISIT.2010.5513361}, Abstract = {This paper introduces the Reed Muller Sieve, a deterministic measurement matrix for compressed sensing. The columns of this matrix are obtained by exponentiating codewords in the quaternary second order Reed Muller code of length N. For k = O(N), the Reed Muller Sieve improves upon prior methods for identifying the support of a k-sparse vector by removing the requirement that the signal entries be independent. The Sieve also enables local detection; an algorithm is presented with complexity N2 log N that detects the presence or absence of a signal at any given position in the data domain without explicitly reconstructing the entire signal. Reconstruction is shown to be resilient to noise in both the measurement and data domains; the ℓ2/ℓ2 error bounds derived in this paper are tighter than the ℓ2/ℓ1 bounds arising from random ensembles and the ℓ1/ℓ1 bounds arising from expander-based ensembles. © 2010 IEEE.}, Doi = {10.1109/ISIT.2010.5513361}, Key = {fds235960} } @article{fds235961, Author = {Qureshi, TR and Zoltowski, MD and Calderbank, R}, Title = {Target detection in mimo radar in the presence of doppler using complementary sequences}, Journal = {IEEE International Conference on Acoustics Speech and Signal Processing}, Pages = {2766-2769}, Year = {2010}, ISSN = {1520-6149}, url = {http://dx.doi.org/10.1109/ICASSP.2010.5496206}, Abstract = {In this paper, we present a method for detecting a point target using multiple antennas when the relative motion between the receivers and the target induces a non-negligible Doppler shift. As a key illustrative example, we consider a 4x4 system employing a unitary matrix waveform set, e.g., formed from Golay complementary sequences. When a non-negligible Doppler shift is induced by the target motion, the waveform matrix formed from the complementary sequences is no longer unitary, resulting in significantly degraded target range estimates. To solve this problem, we adopt a subspace based approach exploiting the observation that the receive matrix formed from matched filtering of the reflected waveforms has a (non-trivial) null-space. Through processing of the waveforms with the appropriate vector from the null-space, we can significantly improve the detection performance. We provide simulation results to confirm the theoretical analysis. ©2010 IEEE.}, Doi = {10.1109/ICASSP.2010.5496206}, Key = {fds235961} } @article{fds235962, Author = {Wu, Y and Calderbank, R}, Title = {Circulant space-time codes for integration with beamforming}, Journal = {IEEE International Conference on Acoustics Speech and Signal Processing}, Pages = {2550-2553}, Year = {2010}, ISSN = {1520-6149}, url = {http://dx.doi.org/10.1109/ICASSP.2010.5496288}, Abstract = {This paper provides a framework for designing space-time codes to take advantage of a small number of feedback bits from the receiver. The new codes are based on circulant matrices and simple conditions are derived that guarantee full rate and full diversity. In the absence of feedback, Symbol Error Rate (SER) performance is shown to be similar to that of Diagonal Algebraic Space-Time (DAST) codes, both for Maximum Likelihood (ML) decoding and for suboptimal linear decoding. Decoding complexity of circulant codes is similar to the DAST codes and encoding is slightly less complex. In the presence of a small number of feedback bits from the receiver the circulant construction is shown to permit integration of space-time coding with a fixed set of beams by simply advancing the phase on one of the antennas. This integration is not possible within the DAST framework. Integration of space-time codes with beamforming makes it possible to achieve ML decoding performance with only linear decoding complexity or to improve upon ML performance of the original code. ©2010 IEEE.}, Doi = {10.1109/ICASSP.2010.5496288}, Key = {fds235962} } @article{fds235963, Author = {Wu, Y and Chi, Y and Calderbank, R}, Title = {Compressive blind source separation}, Journal = {Proceedings / ICIP ... International Conference on Image Processing}, Pages = {89-92}, Year = {2010}, ISSN = {1522-4880}, url = {http://dx.doi.org/10.1109/ICIP.2010.5652624}, Abstract = {The central goal of compressive sensing is to reconstruct a signal that is sparse or compressible in some basis using very few measurements. However reconstruction is often not the ultimate goal and it is of considerable interest to be able to deduce attributes of the signal from the measurements without explicitly reconstructing the full signal. This paper solves the blind source separation problem not in the high dimensional data domain, but in the low dimensional measurement domain. It develops a Bayesian inference framework that integrates hidden Markov models for sources with compressive measurement. Posterior probabilities are calculated using a Markov Chain Monte Carlo (MCMC) algorithm. Simulation results are provided for one-dimensional signals and for two-dimensional images, where hidden Markov tree models of the wavelet coefficients are considered. The integrated Bayesian framework is shown to outperform standard approaches where the mixtures are separated in the data domain. © 2010 IEEE.}, Doi = {10.1109/ICIP.2010.5652624}, Key = {fds235963} } @article{fds235964, Author = {Calderbank, R and Jafarpour, S}, Title = {Reed Muller sensing matrices and the LASSO (Invited paper)}, Journal = {Lecture notes in computer science}, Volume = {6338 LNCS}, Pages = {442-463}, Year = {2010}, ISSN = {0302-9743}, url = {http://dx.doi.org/10.1007/978-3-642-15874-2_37}, Abstract = {We construct two families of deterministic sensing matrices where the columns are obtained by exponentiating codewords in the quaternary Delsarte-Goethals code DG(m,r). This method of construction results in sensing matrices with low coherence and spectral norm. The first family, which we call Delsarte-Goethals frames, are 2m - dimensional tight frames with redundancy 2rm . The second family, which we call Delsarte-Goethals sieves, are obtained by subsampling the column vectors in a Delsarte-Goethals frame. Different rows of a Delsarte-Goethals sieve may not be orthogonal, and we present an effective algorithm for identifying all pairs of non-orthogonal rows. The pairs turn out to be duplicate measurements and eliminating them leads to a tight frame. Experimental results suggest that all DG(m,r) sieves with m ≤ 15 and r ≥ 2 are tight-frames; there are no duplicate rows. For both families of sensing matrices, we measure accuracy of reconstruction (statistical 0 - 1 loss) and complexity (average reconstruction time) as a function of the sparsity level k. Our results show that DG frames and sieves outperform random Gaussian matrices in terms of noiseless and noisy signal recovery using the LASSO. © 2010 Springer-Verlag.}, Doi = {10.1007/978-3-642-15874-2_37}, Key = {fds235964} } @article{fds235965, Author = {Wu, Y and Achtzehn, A and Petrova, M and Mähönen, P and Calderbank, R}, Title = {On the effect of feedback delay on limited-rate beamforming systems}, Journal = {GLOBECOM - IEEE Global Telecommunications Conference}, Year = {2010}, url = {http://dx.doi.org/10.1109/GLOCOM.2010.5684288}, Abstract = {The use of beamforming to enable higher data rates in telecommunications is widely appreciated, but performance gains are typically calculated assuming delay-free feedback from the receiver and neglecting processing time. This paper introduces a mathematical framework based on outage probability that measures the extent to which current channel state information is accurate. Performance gains from beamforming can then be evaluated as a function of the currency of system state. Results are provided for Multiple Input Single Output (MISO) and for Multiuser Multiple Input Multiple Output (MU-MIMO) systems. Outage probabilities and effective diversity orders are calculated for widely used methods of beamforming such as Transmit Antenna Selection as a function of the speed of channel variation. ©2010 IEEE.}, Doi = {10.1109/GLOCOM.2010.5684288}, Key = {fds235965} } @article{fds235966, Author = {Bajwa, WU and Calderbank, R and Jafarpour, S}, Title = {Revisiting model selection and recovery of sparse signals using one-step thresholding}, Journal = {2010 48th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2010}, Pages = {977-984}, Year = {2010}, url = {http://dx.doi.org/10.1109/ALLERTON.2010.5707015}, Abstract = {This paper studies non-asymptotic model selection and recovery of sparse signals in high-dimensional, linear inference problems. In contrast to the existing literature, the focus here is on the general case of arbitrary design matrices and arbitrary nonzero entries of the signal. In this regard, it utilizes two easily computable measures of coherence - termed as the worstcase coherence and the average coherence - among the columns of a design matrix to analyze a simple, model-order agnostic one-step thresholding (OST) algorithm. In particular, the paper establishes that if the design matrix has reasonably small worst-case and average coherence then OST performs near-optimal model selection when either (i) the energy of any nonzero entry of the signal is close to the average signal energy per nonzero entry or (ii) the signal-to-noise ratio (SNR) in the measurement system is not too high. Further, the paper shows that if the design matrix in addition has sufficiently small spectral norm then OST also exactly recovers most sparse signals whose nonzero entries have approximately the same magnitude even if the number of nonzero entries scales almost linearly with the number of rows of the design matrix. Finally, the paper also presents various classes of random and deterministic design matrices that can be used together with OST to successfully carry out near-optimal model selection and recovery of sparse signals under certain SNR regimes or for certain classes of signals. ©2010 IEEE.}, Doi = {10.1109/ALLERTON.2010.5707015}, Key = {fds235966} } @article{fds235967, Author = {Applebaum, L and Bajwa, WU and Duarte, MF and Calderbank, R}, Title = {Multiuser detection in asynchronous on-off random access channels using lasso}, Journal = {2010 48th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2010}, Pages = {130-137}, Year = {2010}, url = {http://dx.doi.org/10.1109/ALLERTON.2010.5706898}, Abstract = {This paper considers on-off random access channels where users transmit either a one or a zero to a base station. Such channels represent an abstraction of control channels used for scheduling requests in third-generation cellular systems and uplinks in wireless sensor networks deployed for target detection. This paper introduces a novel convex-optimization-based scheme for multiuser detection (MUD) in asynchronous on-off random access channels that does not require knowledge of the delays or the instantaneous received signal-to-noise ratios of the individual users at the base station. For any fixed number of temporal signal space dimensions N and maximum delay τ in the system, the proposed scheme can accommodate M ≲ exp(O(N1/3)) total users and k ≲ N/log M active users in the system-a significant improvement over the k ≤ M ≲ N scaling suggested by the use of classical matched-filtering- based approaches to MUD employing orthogonal signaling. Furthermore, the computational complexity of the proposed scheme differs from that of a similar oracle-based scheme with perfect knowledge of the user delays by at most a factor of log(N+τ). Finally, the results presented in here are non-asymptotic, in contrast to related previous work for synchronous channels that only guarantees that the probability of MUD error at the base station goes to zero asymptotically in M. ©2010 IEEE.}, Doi = {10.1109/ALLERTON.2010.5706898}, Key = {fds235967} } @article{fds235968, Author = {Lau, CC and Calderbank, R and Zoltowski, MD}, Title = {Space-time processing for MIMO-OFDM using DFT-based complementary sequences}, Journal = {Proceedings of SPIE - The International Society for Optical Engineering}, Volume = {7706}, Year = {2010}, ISSN = {0277-786X}, url = {http://dx.doi.org/10.1117/12.851020}, Abstract = {In this paper, a new space-time signaling scheme is proposed for Orthogonal Frequency Division Multiplexing (OFDM) using complementary sequences derived from the rows of the DFT matrix. The autocorrelative properties of the complementary sequences allows multiple complex data signals at the transmitter with an arbitrary number of antennas to be perfectly separated and reconstructed at the receiver without prior channel knowledge while achieving full-rate. This new method is proposed and derived for multiple MIMO-OFDM systems with multipath fading; at the receiver, symbol estimation is effected via maximum likelihood estimation (ML). © 2010 SPIE.}, Doi = {10.1117/12.851020}, Key = {fds235968} } @article{fds235969, Author = {Nastasescu, MM and Calderbank, AR}, Title = {The projective Kerdock code}, Journal = {2010 IEEE Information Theory Workshop, ITW 2010 - Proceedings}, Year = {2010}, url = {http://dx.doi.org/10.1109/CIG.2010.5592761}, Abstract = {Certain nonlinear binary codes can be constructed as binary images of Z4-linear codes under the Gray map. Examples include the second-order Reed-Muller code and the Kerdock and Preparata codes. In this paper, we consider a new quaternary code which is an additive subcode of the Z 4-linear Kerdock code. The Kerdock code is the direct sum of a one-dimensional quaternary code and the quaternary subcode examined in this paper. This paper calculates the weight distribution of the projective Kerdock code from which the weight distribution of the dual code can be computed. The dual code is a supercode of the quaternary Preparata code. The projective Kerdock code is used to construct a deterministic measurement matrix for compressed sensing. Numerical experiments are presented for sparse reconstruction using the LASSO that show improvement over random Gaussian matrices of the same size. © 2010 IEEE.}, Doi = {10.1109/CIG.2010.5592761}, Key = {fds235969} } @article{fds235970, Author = {Singh, A and Nowak, R and Calderbank, R}, Title = {Detecting weak but hierarchically-structured patterns in networks}, Journal = {Journal of machine learning research : JMLR}, Volume = {9}, Pages = {749-756}, Year = {2010}, ISSN = {1532-4435}, Abstract = {The ability to detect weak distributed activation patterns in networks is critical to several applications, such as identifying the onset of anomalous activity or incipient congestion in the Internet, or faint traces of a biochemical spread by a sensor network. This is a challenging problem since weak distributed patterns can be invisible in per node statistics as well as a global network-wide aggregate. Most prior work considers situations in which the activation/non-activation of each node is statistically independent, but this is unrealistic in many problems. In this paper, we consider structured patterns arising from statistical dependencies in the activation process. Our contributions are three-fold. First, we propose a sparsifying transform that succinctly represents structured activation patterns that conform to a hierarchical dependency graph. Second, we establish that the proposed transform facilitates detection of very weak activation patterns that cannot be detected with existing methods. Third, we show that the structure of the hierarchical dependency graph governing the activation process, and hence the network transform, can be learnt from very few (logarithmic in network size) independent snapshots of network activity. Copyright 2010 by the authors.}, Key = {fds235970} } @article{fds235971, Author = {Sirianunpiboon, S and Wu, Y and Calderbank, AR and Howard, SD}, Title = {Fast optimal decoding of multiplexed orthogonal designs by conditional optimization}, Journal = {IEEE Transactions on Information Theory}, Volume = {56}, Number = {3}, Pages = {1106-1113}, Year = {2010}, ISSN = {0018-9448}, url = {http://dx.doi.org/10.1109/TIT.2009.2039069}, Abstract = {This paper focuses on conditional optimization as a decoding primitive for high rate spacetime codes that are obtained by multiplexing in the spatial and code domains. The approach is a crystallization of the work of Hottinen which applies to spacetime codes that are assisted by quasi-orthogonality. It is independent of implementation and is more general in that it can be applied to spacetime codes such as the Golden Code and perfect spacetime block codes, that are not assisted by quasi-orthogonality, to derive fast decoders with essentially maximum likelihood (ML) performance. The conditions under which conditional optimization leads to reduced complexity ML decoding are captured in terms of the induced channel at the receiver. These conditions are then translated back to the transmission domain leading to codes that are constructed by multiplexing orthogonal designs. The methods are applied to several block spacetime codes obtained by multiplexing Alamouti blocks where it leads to ML decoding with complexity O(N2) where $N$ is the size of the underlying QAM signal constellation. A new code is presented that tests commonly accepted design principles and for which decoding by conditional optimization is both fast and ML. The two design principles for perfect spacetime codes are nonvanishing determinant of pairwise differences and cubic shaping, and it is cubic shaping that restricts the possible multiplexing structures. The new code shows that it is possible to give up on cubic shaping without compromising code performance or decoding complexity. © 2006 IEEE.}, Doi = {10.1109/TIT.2009.2039069}, Key = {fds235971} } @article{fds235972, Author = {Calderbank, R and Howard, S and Jafarpour, S}, Title = {Construction of a large class of deterministic sensing matrices that satisfy a statistical isometry property}, Journal = {IEEE Journal of Selected Topics in Signal Processing}, Volume = {4}, Number = {2}, Pages = {358-374}, Year = {2010}, ISSN = {1932-4553}, url = {http://dx.doi.org/10.1109/JSTSP.2010.2043161}, Abstract = {Compressed Sensing aims to capture attributes of κ-sparse signals using very few measurements. In the standard compressed sensing paradigm, the N × C measurement matrix Φ is required to act as a near isometry on the set of all κ-sparse signals (restricted isometry property or RIP). Although it is known that certain probabilistic processes generate N × C matrices that satisfy RIP with high probability, there is no practical algorithm for verifying whether a given sensing matrix Φ has this property, crucial for the feasibility of the standard recovery algorithms. In contrast, this paper provides simple criteria that guarantee that a deterministic sensing matrix satisfying these criteria acts as a near isometry on an overwhelming majority of κ-sparse signals; in particular, most such signals have a unique representation in the measurement domain. Probability still plays a critical role, but it enters the signal model rather than the construction of the sensing matrix. An essential element in our construction is that we require the columns of the sensing matrix to form a group under pointwise multiplication. The construction allows recovery methods for which the expected performance is sub-linear in C, and only quadratic in N, as compared to the super-linear complexity in C of the Basis Pursuit or Matching Pursuit algorithms; the focus on expected performance is more typical of mainstream signal processing than the worst case analysis that prevails in standard compressed sensing. Our framework encompasses many families of deterministic sensing matrices, including those formed from discrete chirps, DelsarteGoethals codes, and extended BCH codes. © IEEE.}, Doi = {10.1109/JSTSP.2010.2043161}, Key = {fds235972} } @article{fds235973, Author = {Li, Y and Tian, C and Diggavi, S and Chiang, M and Calderbank, A}, Title = {Network resource allocation for competing multiple description transmissions}, Journal = {IEEE Transactions on Communications}, Volume = {58}, Number = {5}, Pages = {1493-1504}, Year = {2010}, ISSN = {0090-6778}, url = {http://dx.doi.org/10.1109/TCOMM.2010.05.080551}, Abstract = {Providing real-time multimedia services over a besteffort network is challenging due to the stringent delay requirements in the presence of complex network dynamics. Multiple description (MD) coding is one approach to transmit the media over diverse (multiple) paths to reduce the detrimental effects caused by path failures or delay. The novelty of this work is to investigate the resource allocation in a network, where there are several competing MD coded streams. This is done by considering a framework that chooses the operating points for asymmetric MD coding to maximize total quality of the users, while these streams are sent over multiple routing paths. The framework is based on the theoretical modeling where we consider two descriptions and high source coding rate region approximated within small constants. We study the joint optimization of multimedia (source) coding and congestion control in wired networks. These ideas are extended to joint source coding and channel coding in wireless networks. In both situations, we propose distributed algorithms for optimal resource allocation. In the presence of path loss and competing users, the service quality to any particular MD stream could be uncertain. In such circumstances it might be tempting to expect that we need greater redundancy in the MD streams to protect against such failures. However, one surprising aspect of our study reveals that for large number of users who compete for the same resources, the overall system could benefit through opportunistic (hierarchical) strategies. In general networks, our studies indicate that the user composition varies from conservative to opportunistic operating points, depending on the number of users and their network vantage points. © 2006 IEEE.}, Doi = {10.1109/TCOMM.2010.05.080551}, Key = {fds235973} } @article{fds235974, Author = {Bajwa, WU and Calderbank, R and Jafarpour, S}, Title = {Why Gabor frames? Two fundamental measures of coherence and their role in model selection}, Journal = {Journal of Communications and Networks}, Volume = {12}, Number = {4}, Pages = {289-307}, Year = {2010}, ISSN = {1229-2370}, Abstract = {The problem of model selection arises in a number of contexts, such as subset selection in linear regression, estimation of structures in graphical models, and signal denoising. This paper studies non-asymptotic model selection for the general case of arbitrary (random or deterministic) design matrices and arbitrary nonzero entries of the signal. In this regard, it generalizes the notion of incoherence in the existing literature on model selection and introduces two fundamental measures of coherence- termed as the worst-case coherence and the average coherence-among the columns of a design matrix. It utilizes these two measures of coherence to provide an in-depth analysis of a simple, model-order agnostic one-step thresholding (OST) algorithm for model selection and proves that OST is feasible for exact as well as partial model selection as long as the design matrix obeys an easily verifiable property, which is termed as the coherence property. One of the key insights offered by the ensuing analysis in this regard is that OST can successfully carry out model selection even when methods based on convex optimization such as the lasso fail due to the rank deficiency of the submatrices of the design matrix. In addition, the paper establishes that if the design matrix has reasonably small worst-case and average coherence then OST performs near-optimally when either (i) the energy of any nonzero entry of the signal is close to the average signal energy per nonzero entry or (ii) the signal-to-noise ratio in the measurement system is not too high. Finally, two other key contributions of the paper are that (i) it provides bounds on the average coherence of Gaussian matrices and Gabor frames, and (ii) it extends the results on model selection using OST to low-complexity, model-order agnostic recovery of sparse signals with arbitrary nonzero entries. In particular, this part of the analysis in the paper implies that an Alltop Gabor frame together with OST can successfully carry out model selection and recovery of sparse signals irrespective of the phases of the nonzero entries even if the number of nonzero entries scales almost linearly with the number of rows of the Alltop Gabor frame. ©2010 KICS.}, Key = {fds235974} } @article{fds235975, Author = {Aggarwal, V and Calderbank, AR and Gilbert, G and Weinstein, YS}, Title = {Volume thresholds for quantum fault tolerance}, Journal = {Quantum Information Processing}, Volume = {9}, Number = {5}, Pages = {541-549}, Year = {2010}, ISSN = {1570-0755}, url = {http://dx.doi.org/10.1007/s11128-010-0181-2}, Abstract = {We introduce finite-level concatenation threshold regions for quantum fault tolerance. These volume thresholds are regions in an error probability manifold that allow for the implemented system dynamics to satisfy a prescribed implementation inaccuracy bound at a given level of quantum error correction concatenation. Satisfying this condition constitutes our fundamental definition of fault tolerance. The prescribed bound provides a halting condition identifying the attainment of fault tolerance that allows for the determination of the optimum choice of quantum error correction code(s) and number of concatenation levels. Our method is constructed to apply to finite levels of concatenation, does not require that error proabilities consistently decrease from one concatenation level to the next, and allows for analysis, without approximations, of physical systems characterized by non-equiprobable distributions of qubit error probabilities. We demonstrate the utility of this method via a general error model. © 2010 Springer Science+Business Media, LLC.}, Doi = {10.1007/s11128-010-0181-2}, Key = {fds235975} } @article{fds235976, Author = {Ashikhmin, A and Calderbank, AR}, Title = {Grassmannian packings from operator ReedMuller codes}, Journal = {IEEE Transactions on Information Theory}, Volume = {56}, Number = {11}, Pages = {5689-5714}, Year = {2010}, ISSN = {0018-9448}, url = {http://dx.doi.org/10.1109/TIT.2010.2070192}, Abstract = {This paper introduces multidimensional generalizations of binary Reed-Muller codes where the codewords are projection operators, and the corresponding subspaces are widely separated with respect to the chordal distance on Grassmannian space. Parameters of these Grassmannian packings are derived and a low complexity decoding algorithm is developed by modifying standard decoding algorithms for binary Reed-Muller codes. The subspaces are associated with projection operators determined by Pauli matrices appearing in the theory of quantum error correction and this connection with quantum stabilizer codes may be of independent interest. The Grassmannian packings constructed here find application in noncoherent wireless communication with multiple antennas, where separation with respect to the chordal distance on Grassmannian space guarantees closeness to the channel capacity. It is shown that the capacity of the noncoherent multiple-inputmultiple-output (MIMO) channel at both low and moderate signal-to-noise ratio (SNR) (under the constraint that only isotropically distributed unitary matrices are used for information transmission) is closely approximated by these packings. © 2006 IEEE.}, Doi = {10.1109/TIT.2010.2070192}, Key = {fds235976} } @article{fds235977, Author = {Wolff, J and Martens, M and Jafarpour, S and Daubechies, I and Calderbank, R}, Title = {Uncovering elements of style}, Journal = {IEEE International Conference on Acoustics Speech and Signal Processing}, Pages = {1017-1020}, Year = {2011}, ISSN = {1520-6149}, url = {http://dx.doi.org/10.1109/ICASSP.2011.5946579}, Abstract = {This paper relates the style of 16th century Flemish paintings by Goossen van der Weyden (GvdW) to the style of preliminary sketches or underpaintings made prior to executing the painting. Van der Weyden made underpaintings in markedly different styles for reasons as yet not understood by art historians. The analysis presented here starts from a classification of the underpaintings into four distinct styles by experts in art history. Analysis of the painted surfaces by a combination of wavelet analysis, hidden Markov trees and boosting algorithms can distinguish the four underpainting styles with greater than 90% cross-validation accuracy. On a subsequent blind test this classifier provided insight into the hypothesis by art historians that different patches of the finished painting were executed by different hands. © 2011 IEEE.}, Doi = {10.1109/ICASSP.2011.5946579}, Key = {fds235977} } @article{fds235978, Author = {Goparaju, S and Calderbank, AR and Carson, WR and Rodrigues, MRD and Perez-Cruz, F}, Title = {When to add another dimension when communicating over MIMO channels}, Journal = {IEEE International Conference on Acoustics Speech and Signal Processing}, Pages = {3100-3103}, Year = {2011}, ISSN = {1520-6149}, url = {http://dx.doi.org/10.1109/ICASSP.2011.5946351}, Abstract = {This paper introduces a divide and conquer approach to the design of transmit and receive filters for communication over a Multiple Input Multiple Output (MIMO) Gaussian channel subject to an average power constraint. It involves conversion to a set of parallel scalar channels, possibly with very different gains, followed by coding per sub-channel (i.e. over time) rather than coding across sub-channels (i.e. over time and space). The loss in performance is negligible at high signal-to-noise ratio (SNR) and not significant at medium SNR. The advantages are reduction in signal processing complexity and greater insight into the SNR thresholds at which a channel is first allocated power. This insight is a consequence of formulating the optimal power allocation in terms of an upper bound on error rate that is determined by parameters of the input lattice such as the minimum distance and kissing number. The resulting thresholds are given explicitly in terms of these lattice parameters. By contrast, when the optimization problem is phrased in terms of maximizing mutual information, the solution is mercury waterfilling, and the thresholds are implicit. © 2011 IEEE.}, Doi = {10.1109/ICASSP.2011.5946351}, Key = {fds235978} } @article{fds235979, Author = {Wu, Y and Zheng, H and Calderbank, R and Kulkarni, S and Poor, HV}, Title = {On optimal precoding in wireless multicast systems}, Journal = {IEEE International Conference on Acoustics Speech and Signal Processing}, Pages = {3068-3071}, Year = {2011}, ISSN = {1520-6149}, url = {http://dx.doi.org/10.1109/ICASSP.2011.5946306}, Abstract = {Precoding has been extensively studied for point-to-point communications, including the problems of constructing the precoding codebook and selecting the best precoder. This paper investigates precoding for a multicast channel in which a base station is sending the same information to all users and each user sends back the index of its best precoding matrix. It is assumed that users do not collaborate and that no channel state information is known at the base station. Optimization problems are formulated to reduce the packet drop rate. A set of probabilistic algorithms that effectively reduce the average package drop rate are presented. It is shown numerically that these new schemes lead to significant improvements. © 2011 IEEE.}, Doi = {10.1109/ICASSP.2011.5946306}, Key = {fds235979} } @article{fds235980, Author = {Kostina, V and Duarte, MF and Jafarpour, S and Calderbank, R}, Title = {The value of redundant measurement in compressed sensing}, Journal = {IEEE International Conference on Acoustics Speech and Signal Processing}, Pages = {3656-3659}, Year = {2011}, ISSN = {1520-6149}, url = {http://dx.doi.org/10.1109/ICASSP.2011.5947143}, Abstract = {The aim of compressed sensing is to recover attributes of sparse signals using very few measurements. Given an overall bit budget for quantization, this paper demonstrates that there is value to redundant measurement. The measurement matrices considered here are required to have the property that signal recovery is still possible even after dropping certain subsets of D measurements. It introduces the concept of a measurement matrix that is weakly democratic in the sense that the amount of information about the signal carried by each of the designated D-subsets is the same. Examples of deterministic measurement matrices that are weakly democratic are constructed by exponentiating codewords from the binary second order Reed Muller code. The value in rejecting D measurements that are on average larger, is to be able to provide a finer grid for vector quantization of the remaining measurements, even after discounting the original budget by the bits used to identify the reject set. Simulation results demonstrate that redundancy improves recovery SNR, sometimes by a wide margin. Optimum performance occurs when a significant fraction of measurements are rejected. © 2011 IEEE.}, Doi = {10.1109/ICASSP.2011.5947143}, Key = {fds235980} } @article{fds235981, Author = {Krishnamurthy, K and Bajwa, WU and Willett, R and Calderbank, R}, Title = {Fast level set estimation from projection measurements}, Journal = {IEEE Workshop on Statistical Signal Processing Proceedings}, Pages = {585-588}, Year = {2011}, url = {http://dx.doi.org/10.1109/SSP.2011.5967766}, Abstract = {Estimation of the level set of a function (i.e., regions where the function exceeds some value) is an important problem with applications in digital elevation maps, medical imaging, and astronomy. In many applications, however, the function of interest is acquired through indirect measurements, such as tomographic projections, coded-aperture measurements, or pseudo-random projections associated with compressed sensing. This paper describes a new methodology and associated theoretical analysis for rapid and accurate estimation of the level set from such projection measurements. The proposed method estimates the level set from projection measurements without an intermediate function reconstruction step, thereby leading to significantly faster computation. In addition, the coherence of the projection operator and McDiarmid's inequality are used to characterize the estimator's performance. © 2011 IEEE.}, Doi = {10.1109/SSP.2011.5967766}, Key = {fds235981} } @article{fds235982, Author = {Harms, A and Bajwa, WU and Calderbank, R}, Title = {Beating Nyquist through correlations: A constrained random demodulator for sampling of sparse bandlimited signals}, Journal = {IEEE International Conference on Acoustics Speech and Signal Processing}, Pages = {5968-5971}, Year = {2011}, ISSN = {1520-6149}, url = {http://dx.doi.org/10.1109/ICASSP.2011.5947721}, Abstract = {Technological constraints severely limit the rate at which analog-to-digital converters can reliably sample signals. Recently, Tropp et al. proposed an architecture, termed the random demodulator (RD), that attempts to overcome this obstacle for sparse bandlimited signals. One integral component of the RD architecture is a white noise-like, bipolar modulating waveform that changes polarity at a rate equal to the signal bandwidth. Since there is a hardware limitation to how fast analog waveforms can change polarity without undergoing shape distortion, this leads to the RD also having a constraint on the maximum allowable bandwidth. In this paper, an extension of the RD, termed the constrained random demodulator (CRD), is proposed that bypasses this bottleneck by replacing the original modulating waveform with a run-length limited (RLL) modulating waveform that changes polarity at a slower rate than the signal bandwidth. One of the main contributions of the paper is establishing that the CRD, despite employing a modulating waveform with correlations, enjoys some theoretical guarantees for certain RLL waveforms. In addition, for a given sampling rate and rate of change in the modulating waveform polarity, numerical simulations confirm that the CRD, using an appropriate RLL waveform, can sample a signal with an even wider bandwidth without a significant loss in performance. © 2011 IEEE.}, Doi = {10.1109/ICASSP.2011.5947721}, Key = {fds235982} } @article{fds235983, Author = {Applebaum, L and Bajwa, WU and Calderbank, AR and Haupt, J and Nowak, R}, Title = {Deterministic pilot sequences for sparse channel estimation in OFDM systems}, Journal = {17th DSP 2011 International Conference on Digital Signal Processing, Proceedings}, Year = {2011}, url = {http://dx.doi.org/10.1109/ICDSP.2011.6005024}, Abstract = {This paper examines the problem of multipath channel estimation in single-antenna orthogonal frequency division multiplexing (OFDM) systems. In particular, we study the problem of pilot assisted channel estimation in wideband OFDM systems, where the time-domain (discrete) channel is approximately sparse. Existing works on this topic established that techniques from the compressed sensing literature can yield accurate channel estimates using a relatively small number of pilot tones, provided the pilots are selected randomly. Here, we describe a general purpose procedure for deterministic selection of pilot tones to be used for channel estimation, and establish guarantees for channel estimation accuracy using these sequences along with recovery techniques from the compressed sensing literature. Simulation results are presented to demonstrate the effectiveness of the proposed procedure in practice. © 2011 IEEE.}, Doi = {10.1109/ICDSP.2011.6005024}, Key = {fds235983} } @article{fds235984, Author = {Mixon, DG and Bajwa, WU and Calderbank, R}, Title = {Frame coherence and sparse signal processing}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Pages = {663-667}, Year = {2011}, url = {http://dx.doi.org/10.1109/ISIT.2011.6034214}, Abstract = {The sparse signal processing literature often uses random sensing matrices to obtain performance guarantees. Unfortunately, in the real world, sensing matrices do not always come from random processes. It is therefore desirable to evaluate whether an arbitrary matrix, or frame, is suitable for sensing sparse signals. To this end, the present paper investigates two parameters that measure the coherence of a frame: worst-case and average coherence. We first provide several examples of frames that have small spectral norm, worst-case coherence, and average coherence. Next, we present a new lower bound on worst-case coherence and compare it to the Welch bound. Later, we propose an algorithm that decreases the average coherence of a frame without changing its spectral norm or worst-case coherence. Finally, we use worst-case and average coherence, as opposed to the Restricted Isometry Property, to garner near-optimal probabilistic guarantees on both sparse signal detection and reconstruction in the presence of noise. This contrasts with recent results that only guarantee noiseless signal recovery from arbitrary frames, and which further assume independence across the nonzero entries of the signalin a sense, requiring small average coherence replaces the need for such an assumption. © 2011 IEEE.}, Doi = {10.1109/ISIT.2011.6034214}, Key = {fds235984} } @article{fds235985, Author = {Calderbank, R and Jafarpour, S and Nastasescu, M}, Title = {Covering radius and the Restricted Isometry Property}, Journal = {2011 IEEE Information Theory Workshop, ITW 2011}, Pages = {558-562}, Year = {2011}, url = {http://dx.doi.org/10.1109/ITW.2011.6089564}, Abstract = {The Restricted Isometry Property or RIP introduced by Candes and Tao requires an n × p dictionary to act as a near isometry on all k-sparse signals. This paper provides a very simple condition under which a dictionary Φ (C) obtained by exponentiating codewords from a binary linear code C satisfies the RIP with high probability. The method is to bound the difference between the dictionary Φ(C) and a second dictionary A generated by a random Bernoulli process which is known to satisfy the RIP with high probability. The difference Δ-Φ (C) is controlled by the covering radius of C, a fundamental parameter that is bounded above by the number of weights in the dual code C ⊥ (the external distance of C). The main result complements a more sophisticated asymptotic analysis by Babadi and Tarokh of the distribution of eigenvalues of random submatrices of Φ(C). In this analysis, divergence from the distribution corresponding to the full Bernoulli matrix depends on a different fundamental parameter of C, namely the minimum distance of the dual code C ⊥. © 2011 IEEE.}, Doi = {10.1109/ITW.2011.6089564}, Key = {fds235985} } @article{fds235986, Author = {Gomaa, A and Chi, Y and Al-Dhahir, N and Calderbank, R}, Title = {On training signal design for multi-user MIMO-OFDM: Performance analysis and tradeoffs}, Journal = {IEEE VTS ... Vehicular Technology Conference : VTC : [proceedings]}, Year = {2011}, ISSN = {1550-2252}, url = {http://dx.doi.org/10.1109/VETECF.2011.6092844}, Abstract = {This paper addresses spectrally-efficient multiantenna multi-carrier uplink transmission scenarios where the users overlap in time and frequency and are separated using spatial processing at the base station. The robustness of the proposed training sequences to residual carrier frequency offset and phase noise is evaluated analytically. This analysis reveals an interesting design tradeoff between the Peak-to-Average Power Ratio of a training sequence and the increase in channel estimation mean squared error over the ideal case when these two impairments are not present. © 2011 IEEE.}, Doi = {10.1109/VETECF.2011.6092844}, Key = {fds235986} } @article{fds235987, Author = {Applebaum, L and Bajwa, WU and Calderbank, R and Howard, S}, Title = {Choir codes: Coding for full duplex interference management}, Journal = {2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011}, Pages = {1-8}, Year = {2011}, url = {http://dx.doi.org/10.1109/Allerton.2011.6120141}, Abstract = {Communication networks conventionally operate with half-duplex methods and interference avoiding schemes to manage multiple transceivers. Here we consider a method in which nodes transmit and receive in concert to achieve full duplex communication without transmitter coordination. We build on a recent framework for full-duplex communication in ad-hoc wireless networks recently proposed by Zhang, Luo and Guo. An individual node in the wireless network either transmits or it listens to transmissions from other nodes but it cannot do both at the same time. There might be as many nodes as there are MAC addresses but we assume that only a small subset of nodes contribute to the superposition received at any given node in the network. We develop deterministic algebraic coding methods that allow simultaneous communication across the entire network. We call such codes choir codes. Users are assigned subspaces of F 2m to define their transmit and listen times. Codewords on these subspaces are designed and proven to adhere to bounds on worst-case coherence and the associated matrix spectral norm. This in turn provides guarantees for multi-user detection using convex optimization. Further, we show that matrices for each receiver's listening times can be related by permutations, thus guaranteeing fairness between receivers. Compared with earlier work using random codes, our methods have significant improvements including reduced decoding/detection error and non-asymptotic results. Simulation results verify that, as a method to manage interference, our scheme has significant advantages over seeking to eliminate or align interference through extensive exchange of fine-grained channel state information. © 2011 IEEE.}, Doi = {10.1109/Allerton.2011.6120141}, Key = {fds235987} } @article{fds235988, Author = {Nokleby, M and Bajwa, WU and Calderbank, R and Aazhang, B}, Title = {Gossiping in groups: Distributed averaging over the wireless medium}, Journal = {2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011}, Pages = {1242-1249}, Year = {2011}, url = {http://dx.doi.org/10.1109/Allerton.2011.6120310}, Abstract = {We present an approach to gossip algorithms tailored to the practical considerations of wireless communications. Traditional gossip algorithms operate via the pairwise exchange of estimates, which fails to capture the broadcast and superposition nature of the wireless medium. Adapting the virtual full-duplex framework of Guo and Zhang, we construct a communications scheme in which each node can broadcast its estimate to its neighbors while simultaneously receiving its neighbors' estimates. This full-duplex scheme gives rise to group gossip, a more flexible family of gossip algorithms built on multilateral, rather than pairwise, exchanges. Our approach obviates the need for orthogonalization or medium access; only local information and synchronization are necessary. Additionally, group gossip has better convergence properties than does randomized gossip. Group gossip permits a tighter bound on the convergence speed than randomized gossip, and in general the upper bound on the convergence time is at most one-third that of randomized gossip. © 2011 IEEE.}, Doi = {10.1109/Allerton.2011.6120310}, Key = {fds235988} } @article{fds235989, Author = {Dang, W and Pezeshki, A and Howard, S and Moran, W and Calderbank, R}, Title = {Coordinating complementary waveforms for sidelobe suppression}, Journal = {Conference Record of the Asilomar Conference on Signals, Systems and Computers}, Pages = {2096-2100}, Year = {2011}, ISSN = {1058-6393}, url = {http://dx.doi.org/10.1109/ACSSC.2011.6190398}, Abstract = {We present a general method for constructing radar transmit pulse trains and receive filters for which the radar point-spread function in delay and Doppler, given by the cross-ambiguity function of the transmit pulse train and the pulse train used in the receive filter, is essentially free of range sidelobes inside a Doppler interval around the zero-Doppler axis. The transmit pulse train is constructed by coordinating the transmission of a pair of Golay complementary waveforms across time according to zeros and ones in a binary sequence P. The pulse train used to filter the received signal is constructed in a similar way, in terms of sequencing the Golay waveforms, but each waveform in the pulse train is weighted by an element from another sequence Q. We show that a spectrum jointly determined by P and Q sequences controls the size of the range sidelobes of the cross-ambiguity function and by properly choosing P and Q we can clear out the range sidelobes inside a Doppler interval around the zero-Doppler axis. The joint design of P and Q enables a tradeoff between the order of the spectral null for range sidelobe suppression and the signal-to-noise ratio at the receiver output. We establish this trade-off and derive a necessary and sufficient condition for the construction of P and Q sequences that produce a null of a desired order. © 2011 IEEE.}, Doi = {10.1109/ACSSC.2011.6190398}, Key = {fds235989} } @article{fds235990, Author = {Wu, Y and Viswanathan, H and Klein, T and Haner, M and Calderbank, R}, Title = {Capacity optimization in networks with heterogeneous radio access technologies}, Journal = {GLOBECOM - IEEE Global Telecommunications Conference}, Year = {2011}, url = {http://dx.doi.org/10.1109/GLOCOM.2011.6134226}, Abstract = {As it becomes common for wireless service providers (WSP) to employ multiple heterogeneous radio access technologies (RAT), the management of the combined resources across multiple RATs arises as an important issue. The WSP's objective is to assign different users to the different RATs so as to maximize network capacity (or total utility) while ensuring that individual users' quality of service (QoS) requirements are met. In this paper, we consider this resource allocation problem for two scenarios: voice communication and video communication. For voice communication, we propose a stable and optimal assignment scheme based on the deferred acceptance algorithm for both static and online cases. For video communication, identifying the NP-hardness of the problem, we propose and compare a set of heuristic algorithms including a low-complexity, high-performance scheme. © 2011 IEEE.}, Doi = {10.1109/GLOCOM.2011.6134226}, Key = {fds235990} } @article{fds235991, Author = {Li, Y and Papachristodoulou, A and Chiang, M and Calderbank, AR}, Title = {Congestion control and its stability in networks with delay sensitive traffic}, Journal = {Computer Networks}, Volume = {55}, Number = {1}, Pages = {20-32}, Year = {2011}, ISSN = {1389-1286}, url = {http://dx.doi.org/10.1016/j.comnet.2010.07.001}, Abstract = {We consider congestion control in a network with delay sensitive/ insensitive traffic, modelled by adding explicit delay terms to the utility function measuring user's happiness on the Quality of Service (QoS). A new Network Utility Maximization (NUM) problem is formulated and solved in a decentralized way via appropriate algorithms implemented at the users (primal) and/or links (dual). For the dual algorithm, delay-independent and delay-dependent stability conditions are derived when propagation delays are taken into account. A system with voice and data traffic is considered as example and the properties of the congestion control algorithm are assessed. © 2010 Elsevier B.V. All rights reserved.}, Doi = {10.1016/j.comnet.2010.07.001}, Key = {fds235991} } @article{fds235992, Author = {Chi, Y and Gomaa, A and Al-Dhahir, N and Calderbank, R}, Title = {MMSE-optimal training sequences for spectrally-efficient Multi-User MIMO-OFDM systems}, Journal = {European Signal Processing Conference}, Pages = {634-638}, Year = {2011}, ISSN = {2219-5491}, Abstract = {This paper proposes a new family of optimal training sequences in terms of minimizing the mean-square channel estimation error for spectrally-efficient Multi-User MIMO-OFDM systems with an arbitrary number of transmit antennas and an arbitrary number of training symbols. It addresses uplink transmission scenarios where the users overlap in time and frequency and are separated using spatial processing at the base station. In particular, optimal training sequences can be obtained easily from standard signal constellations such as QPSK with desired low PAPR, making it appealing for practical use. © 2011 EURASIP.}, Key = {fds235992} } @article{fds235993, Author = {Sirinaunpiboon, S and Calderbank, AR and Howard, SD}, Title = {Fast essentially maximum likelihood decoding of the Golden code}, Journal = {IEEE Transactions on Information Theory}, Volume = {57}, Number = {6}, Pages = {3537-3541}, Year = {2011}, ISSN = {0018-9448}, url = {http://dx.doi.org/10.1109/TIT.2011.2136870}, Abstract = {The Golden code is a full-rate full-diversity space-time code which has been incorporated in the IEEE 802.16 (WiMAX) standard. The worst case complexity of a tree-based sphere decoder for a square QAM constellation is O(N 3), where n is the size of the underlying QAM constellation; the worst case will dominate average decoding complexity on any channel with a significant line of sight component. In this paper, we present a simple algorithm with quadratic complexity for decoding the Golden code that can be employed by mobile terminals with either one or two receive antennas, that is resilient to near singularity of the channel matrix, and that gives essentially maximum likelihood (ML) performance. Dual use is an advantage, since there will likely be some IEEE 802.16 mobile terminals with one receive antenna and some with two antennas. The key to the quadratic algorithm is a maximization of the likelihood function with respect to one of the pair of signal points conditioned on the other. This choice is made by comparing the determinants of two covariance matrices, and the underlying geometry of the Golden code guarantees that one of these choices is good with high probability. © 2011 IEEE.}, Doi = {10.1109/TIT.2011.2136870}, Key = {fds235993} } @article{fds235994, Author = {Chi, Y and Scharf, LL and Pezeshki, A and Calderbank, AR}, Title = {Sensitivity to basis mismatch in compressed sensing}, Journal = {IEEE Transactions on Signal Processing}, Volume = {59}, Number = {5}, Pages = {2182-2195}, Year = {2011}, ISSN = {1053-587X}, url = {http://dx.doi.org/10.1109/TSP.2011.2112650}, Abstract = {The theory of compressed sensing suggests that successful inversion of an image of the physical world (broadly defined to include speech signals, radar/sonar returns, vibration records, sensor array snapshot vectors, 2-D images, and so on) for its source modes and amplitudes can be achieved at measurement dimensions far lower than what might be expected from the classical theories of spectrum or modal analysis, provided that the image is sparse in an apriori known basis. For imaging problems in spectrum analysis, and passive and active radar/sonar, this basis is usually taken to be a DFT basis. However, in reality no physical field is sparse in the DFT basis or in any apriori known basis. No matter how finely we grid the parameter space the sources may not lie in the center of the grid cells and consequently there is mismatch between the assumed and the actual bases for sparsity. In this paper, we study the sensitivity of compressed sensing to mismatch between the assumed and the actual sparsity bases. We start by analyzing the effect of basis mismatch on the best k-term approximation error, which is central to providing exact sparse recovery guarantees. We establish achievable bounds for the ℓ1 error of the best k-term approximation and show that these bounds grow linearly with the image (or grid) dimension and the mismatch level between the assumed and actual bases for sparsity. We then derive bounds, with similar growth behavior, for the basis pursuit ℓ1 recovery error, indicating that the sparse recovery may suffer large errors in the presence of basis mismatch. Although, we present our results in the context of basis pursuit, our analysis applies to any sparse recovery principle that relies on the accuracy of best k-term approximations for its performance guarantees. We particularly highlight the problematic nature of basis mismatch in Fourier imaging, where spillage from off-grid DFT components turns a sparse representation into an incompressible one. We substantiate our mathematical analysis by numerical examples that demonstrate a considerable performance degradation for image inversion from compressed sensing measurements in the presence of basis mismatch, for problem sizes common to radar and sonar. © 2011 IEEE.}, Doi = {10.1109/TSP.2011.2112650}, Key = {fds235994} } @article{fds235995, Author = {Thejaswi, PSC and Bennatan, A and Zhang, J and Calderbank, AR and Cochran, D}, Title = {Layered coding for interference channels with partial transmitter side information}, Journal = {IEEE Transactions on Information Theory}, Volume = {57}, Number = {5}, Pages = {2765-2780}, Year = {2011}, ISSN = {0018-9448}, url = {http://dx.doi.org/10.1109/TIT.2011.2119670}, Abstract = {A two-user interference channel is considered where each transmitter has access to a part of the information intended to the other destination. A primary objective is to maximize the information rates, by exploring the cooperation between the transmitters for interference mitigation, based on the partial side information. It is clear that full cooperation between the transmitters is not possible since each transmitter has only a part of the side information. With this insight, several "layered coding" schemes, consisting of binning and superposition at different stages, are developed. These schemes are are carefully built on coding strategies for the classical interference channel and node cooperation mechanisms. In particular, two layered coding schemes, which are based on a combination of MIMO broadcast coding and the HanKobayashi (HK) coding, are thoroughly studied : The first one, namely layered coding with binning, makes heavy use of the GelfandPinsker binning and the HK coding and the second one, namely layered superposition coding, involves superposition coding over different tiers. Rate regions corresponding to the proposed schemes are derived. Then the application of these coding schemes are illustrated for the Gaussian case and numerical results corroborate that the proposed layered coding schemes yield substantial gains at high SNR. © 2011 IEEE.}, Doi = {10.1109/TIT.2011.2119670}, Key = {fds235995} } @article{fds235996, Author = {Calderbank, R and Casazza, PG and Heinecke, A and Kutyniok, G and Pezeshki, A}, Title = {Sparse fusion frames: Existence and construction}, Journal = {Advances in Computational Mathematics}, Volume = {35}, Number = {1}, Pages = {1-31}, Year = {2011}, ISSN = {1019-7168}, url = {http://dx.doi.org/10.1007/s10444-010-9162-3}, Abstract = {Fusion frame theory is an emerging mathematical theory that provides a natural framework for performing hierarchical data processing. A fusion frame can be regarded as a frame-like collection of subspaces in a Hilbert space, and thereby generalizes the concept of a frame for signal representation. However, when the signal and/or subspace dimensions are large, the decomposition of the signal into its fusion frame measurements through subspace projections typically requires a large number of additions and multiplications, and this makes the decomposition intractable in applications with limited computing budget. To address this problem, in this paper, we introduce the notion of a sparse fusion frame, that is, a fusion frame whose subspaces are generated by orthonormal basis vectors that are sparse in a 'uniform basis' over all subspaces, thereby enabling low-complexity fusion frame decompositions. We study the existence and construction of sparse fusion frames, but our focus is on developing simple algorithmic constructions that can easily be adopted in practice to produce sparse fusion frames with desired (given) operators. By a desired (or given) operator we simply mean one that has a desired (or given) set of eigenvalues for the fusion frame operator. We start by presenting a complete characterization of Parseval fusion frames in terms of the existence of special isometries defined on an encompassing Hilbert space. We then introduce two general methodologies to generate new fusion frames from existing ones, namely the Spatial Complement Method and the Naimark Complement Method, and analyze the relationship between the parameters of the original and the new fusion frame. We proceed by establishing existence conditions for 2-sparse fusion frames for any given fusion frame operator, for which the eigenvalues are greater than or equal to two. We then provide an easily implementable algorithm for computing such 2-sparse fusion frames. © 2010 Springer Science+Business Media, LLC.}, Doi = {10.1007/s10444-010-9162-3}, Key = {fds235996} } @article{fds235997, Author = {Chi, Y and Gomaa, A and Al-Dhahir, N and Calderbank, AR}, Title = {Training signal design and tradeoffs for spectrally-efficient multi-user MIMO-OFDM systems}, Journal = {IEEE Transactions on Wireless Communications}, Volume = {10}, Number = {7}, Pages = {2234-2245}, Year = {2011}, ISSN = {1536-1276}, url = {http://dx.doi.org/10.1109/TWC.2011.042211.101100}, Abstract = {In this paper, we design MMSE-optimal training sequences for multi-user MIMO-OFDM systems with an arbitrary number of transmit antennas and an arbitrary number of training symbols. It addresses spectrally-efficient uplink transmission scenarios where the users overlap in time and frequency and are separated using spatial processing at the base station. The robustness of the proposed training sequences to residual carrier frequency offset and phase noise is evaluated. This analysis reveals an interesting design tradeoff between the peak-to-average power ratio of a training sequence and the increase in channel estimation mean squared error over the ideal case when these two impairments are not present. © 2011 IEEE.}, Doi = {10.1109/TWC.2011.042211.101100}, Key = {fds235997} } @article{fds235998, Author = {Qureshi, TR and Zoltowski, MD and Calderbank, R and Pezeshki, A}, Title = {Unitary design of radar waveform diversity sets}, Journal = {Digital Signal Processing}, Volume = {21}, Number = {5}, Pages = {552-567}, Year = {2011}, ISSN = {1051-2004}, url = {http://dx.doi.org/10.1016/j.dsp.2010.09.006}, Abstract = {In this work, multiple radar waveforms are simultaneously transmitted, emitted from different antennas. The goal is to process the returns in such a way that the overall ambiguity function is a sum of individual ambiguity functions, such that the sum better approximates the ideal thumbtack shape. A unitary design for the illustrative 4×4 example prescribes the scheduling of the waveforms over four transmit antennas over four PRIs. Further, it dictates how the matched filtering of the returns over four PRIs is combined in such a way so as to achieve both perfect separation (of the superimposed returns) AND perfect reconstruction. Perfect reconstruction implies that the sum of the time-autocorrelations associated with each of the four waveforms is a delta function. The net result of the processing of four PRIs over four virtual antennas yields 16 cross-correlations all of which ideally exhibit a sharp peak at the target delay. Conditions for both perfect separation and perfect reconstruction are developed, and a variety of waveform sets satisfying both are presented. Doppler compensation is achieved by a data-dependent weighting of the different PRI matched-filtered outputs prior to summing. Simulations are presented verifying the efficacy of the proposed unitary waveform matrix designs in conjunction with the proposed Doppler compensation technique. © 2010 Elsevier Inc. All rights reserved.}, Doi = {10.1016/j.dsp.2010.09.006}, Key = {fds235998} } @article{fds235999, Author = {Goel, S and Aggarwal, V and Yener, A and Calderbank, AR}, Title = {The effect of eavesdroppers on network connectivity: A secrecy graph approach}, Journal = {IEEE Transactions on Information Forensics and Security}, Volume = {6}, Number = {3 PART 1}, Pages = {712-724}, Year = {2011}, ISSN = {1556-6013}, url = {http://dx.doi.org/10.1109/TIFS.2011.2148714}, Abstract = {This paper investigates the effect of eavesdroppers on network connectivity, using a wiretap model and percolation theory. The wiretap model captures the effect of eavesdroppers on link security. A link exists between two nodes only if the secrecy capacity of that link is positive. Network connectivity is defined in a percolation sense, i.e., connectivity exists if an infinite connected component exists in the corresponding secrecy graph. We consider uncertainty in location of eavesdroppers, which is modeled directly at the network level as correlated failures in the secrecy graph. Our approach attempts to bridge the gap between physical layer security under uncertain channel state information and network level connectivity under secrecy constraints. For square and triangular lattice secrecy graphs, we obtain bounds on the percolation threshold, which is the critical value of the probability of occurrence of an eavesdropper, above which network connectivity does not exist. For Poisson secrecy graphs, degree distribution and mean value of upper and lower bounds on node degree are obtained. Further, inner and outer bounds on the achievable region for network connectivity are obtained. Both analytic and simulation results show that uncertainty in location of eavesdroppers has a dramatic effect on network connectivity in a secrecy graph. © 2011 IEEE.}, Doi = {10.1109/TIFS.2011.2148714}, Key = {fds235999} } @article{fds236000, Author = {Raginsky, M and Jafarpour, S and Harmany, ZT and Marcia, RF and Willett, RM and Calderbank, R}, Title = {Performance bounds for expander-based compressed sensing in poisson noise}, Journal = {IEEE Transactions on Signal Processing}, Volume = {59}, Number = {9}, Pages = {4139-4153}, Year = {2011}, ISSN = {1053-587X}, url = {http://dx.doi.org/10.1109/TSP.2011.2157913}, Abstract = {This paper provides performance bounds for compressed sensing in the presence of Poisson noise using expander graphs. The Poisson noise model is appropriate for a variety of applications, including low-light imaging and digital streaming, where the signal-independent and/or bounded noise models used in the compressed sensing literature are no longer applicable. In this paper, we develop a novel sensing paradigm based on expander graphs and propose a maximum a posteriori (MAP) algorithm for recovering sparse or compressible signals from Poisson observations. The geometry of the expander graphs and the positivity of the corresponding sensing matrices play a crucial role in establishing the bounds on the signal reconstruction error of the proposed algorithm. We support our results with experimental demonstrations of reconstructing average packet arrival rates and instantaneous packet counts at a router in a communication network, where the arrivals of packets in each flow follow a Poisson process. © 2011 IEEE.}, Doi = {10.1109/TSP.2011.2157913}, Key = {fds236000} } @article{fds235768, Author = {Simpson, MJ and Wilson, JW and Matthews, TE and Duarte, M and Calderbank, R and Warren, WS}, Title = {Imaging the distribution of melanin in human skin lesions with pump-probe microscopy}, Journal = {Optics InfoBase Conference Papers}, Year = {2011}, Month = {December}, Key = {fds235768} } @article{fds235779, Author = {Nokleby, M and Bajwa, WU and Calderbank, R and Aazhang, B}, Title = {Toward resource-optimal averaging consensus over the wireless medium}, Journal = {Conference Record of the Asilomar Conference on Signals, Systems and Computers}, Pages = {1197-1201}, Year = {2012}, ISSN = {1058-6393}, url = {http://dx.doi.org/10.1109/ACSSC.2012.6489211}, Abstract = {We carry out a comprehensive study of the resource costs of distributed averaging consensus in wireless sensor networks. In particular, we consider two metrics appropriate to the wireless medium: total transmit energy and time-bandwidth product. Most previous approaches, such as gossip algorithms, suppose a graphical network, which abstracts away crucial features of the wireless medium, and measure resource consumption only in terms of the total number of transmissions required to achieve consensus. Under a path-loss dominated protocol interference model, we study the performance of several popular gossip algorithms, showing that they are nearly order-optimal with respect to transmit energy but strictly sub-optimal with respect to time-bandwidth product. We also propose a new scheme, termed hierarchical averaging, which is tailored to the wireless medium, and show that in general this approach is nearly order-optimal with respect to time-bandwidth product but strictly sub-optimal with respect to transmit energy. For the special case of free-space propagation, however, the proposed hierarchical scheme is approximately order-optimal with respect to both metrics. © 2012 IEEE.}, Doi = {10.1109/ACSSC.2012.6489211}, Key = {fds235779} } @article{fds235780, Author = {Harms, A and Bajwa, WU and Calderbank, R}, Title = {Rapid sensing of underutilized, wideband spectrum using the Random Demodulator}, Journal = {Conference Record of the Asilomar Conference on Signals, Systems and Computers}, Pages = {1940-1944}, Year = {2012}, ISSN = {1058-6393}, url = {http://dx.doi.org/10.1109/ACSSC.2012.6489377}, Abstract = {Efficient spectrum sensing is an important problem given the large and increasing demand for wireless spectrum and the need to protect incumbent users. We can more efficiently use large swaths of underutilized spectrum by designing spectrum sensors that can quickly, and power-efficiently, find and opportunistically communicate over unused (or underutilized) pieces of spectrum, such as television bands. In this paper, we concentrate on a particular sensing architecture, the Random Demodulator (RD), and look at two aspects of the problem. First, we offer fundamental limits on how efficiently any algorithm can perform the sensing operation with the RD. Second, we analyze a very simple, low-complexity algorithm called one-step thresholding that has been shown to work near-optimally for certain measurement classes in a low SNR setting or when the non-zero input coefficients are nearly equal. We rigorously establish that the RD architecture is well-suited for near-optimal recovery of the locations of the non-zero frequency coefficients in similar settings using one-step thresholding and perform numerical experiments to offer some confirmation of our results. © 2012 IEEE.}, Doi = {10.1109/ACSSC.2012.6489377}, Key = {fds235780} } @article{fds235781, Author = {Jacobvitz, AN and Calderbank, R and Sorin, DJ}, Title = {Writing cosets of a convolutional code to increase the Lifetime of Flash memory}, Journal = {2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012}, Pages = {308-318}, Year = {2012}, url = {http://dx.doi.org/10.1109/Allerton.2012.6483234}, Abstract = {The goal of this paper is to extend the lifetime of Flash memory by reducing the frequency with which a given page of memory is erased. This is accomplished by increasing the number of writes that are possible before erasure is necessary. Redundancy is introduced into the write process to decrease the number of memory cells that are impacted by a given write, and to even out the impact of writing across an entire page of memory. Improvements are expressed in terms of write efficiency and lifetime gain. Write efficiency is the ratio of cells written to cells available, and lifetime gain is the ratio of coded writes to the baseline of uncoded writing. We use a physical model that allows multiple writes to a given region of memory. This can be realized with single level cells or with multi-level cells. Data is written to memory in the form of a coset of a convolutional code. The coset is represented by a binary vector that is selected by the Viterbi algorithm to minimize the number of cells impacted by the write (Hamming weight) and to even out the number of writes to each cell within a given page. Several different Viterbi metrics are evaluated. It is shown that page write efficiencies of over 85% and lifetime gains of over 500% are possible with only modest encoding and decoding complexity. It is also straightforward to integrate lifetime extension with standard methods of error correction by requiring that the coset representative be drawn from an error correcting code. An example is provided where single error correction is provided using a Hamming code. © 2012 IEEE.}, Doi = {10.1109/Allerton.2012.6483234}, Key = {fds235781} } @article{fds235783, Author = {Wu, Y and Jia, T and Calderbank, R and Duel-Hallen, A and Hallen, H}, Title = {Enabling code diversity for mobile radio channels using long-range fading prediction}, Journal = {IEEE Transactions on Wireless Communications}, Volume = {11}, Number = {12}, Pages = {4362-4371}, Year = {2012}, ISSN = {1536-1276}, url = {http://dx.doi.org/10.1109/TWC.2012.101712.111884}, Abstract = {Code diversity integrates space-time coding with beamforming by using a small number of feedback bits to select from a family of space-time codes. Different codes lead to different induced channels at the receiver, where Channel State Information (CSI) is used to instruct the transmitter how to choose the code. Feedback can be combined with sub-optimal low complexity decoding of the component codes to match Maximum-Likelihood (ML) decoding performance of any individual code in the family. It can also be combined with ML decoding of the component codes to improve performance beyond ML decoding performance of any individual code. Prior analysis of code diversity did not take into account the effect of the mobile speed and the delay in the feedback channel. This paper demonstrates the practicality of code diversity in space-time coded systems by showing that performance gains based on instantaneous feedback are largely preserved when long-range prediction of time-varying correlated fading channels is employed to compensate for the effect of the feedback delay. To maintain prediction accuracy for realistic SNR, noise reduction that employs oversampled pilots is used prior to fading prediction. We also propose a robust low pilot rate method that utilizes interleaving to improve the spectral efficiency. Simulations are presented for two channel models: the conventional Jakes model and a realistic physical channel model where the parameters associated with the reflectors vary in time and the arrival rays have different strengths and asymmetric arrival angles. © 2002-2012 IEEE.}, Doi = {10.1109/TWC.2012.101712.111884}, Key = {fds235783} } @article{fds235786, Author = {Carson, WR and Chen, M and Rodrigues, MRD and Calderbank, R and Carin, L}, Title = {Communications-inspired projection design with application to compressive sensing}, Journal = {SIAM Journal on Imaging Sciences}, Volume = {5}, Number = {4}, Pages = {1182-1212}, Year = {2012}, ISSN = {1936-4954}, url = {http://hdl.handle.net/10161/8952 Duke open access}, Abstract = {We consider the recovery of an underlying signal x ∈ ℂm based on projection measurements of the form y = Mx+w, where y ∈ ℂℓ and w is measurement noise; we are interested in the case ℓ ≪ m. It is assumed that the signal model p(x) is known and that w ~ CN(w; 0,Σw) for known Σ w. The objective is to design a projection matrix M ∈ ℂℓ×m to maximize key information-theoretic quantities with operational significance, including the mutual information between the signal and the projections I(x; y) or the Rényi entropy of the projections hα (y) (Shannon entropy is a special case). By capitalizing on explicit characterizations of the gradients of the information measures with respect to the projection matrix, where we also partially extend the well-known results of Palomar and Verdu ́ from the mutual information to the Rényi entropy domain, we reveal the key operations carried out by the optimal projection designs: mode exposure and mode alignment. Experiments are considered for the case of compressive sensing (CS) applied to imagery. In this context, we provide a demonstration of the performance improvement possible through the application of the novel projection designs in relation to conventional ones, as well as justification for a fast online projection design method with which state-of-the-art adaptive CS signal recovery is achieved. © 2012 Society for Industrial and Applied Mathematics.}, Doi = {10.1137/120878380}, Key = {fds235786} } @article{fds236001, Author = {Jafarpour, S and Duarte, MF and Calderbank, R}, Title = {Beyond worst-case reconstruction in deterministic compressed sensing}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Pages = {1852-1856}, Year = {2012}, url = {http://dx.doi.org/10.1109/ISIT.2012.6283601}, Abstract = {The role of random measurement in compressive sensing is analogous to the role of random codes in coding theory. In coding theory, decoders that can correct beyond the minimum distance of a code allow random codes to achieve the Shannon limit. In compressed sensing, the counterpart of minimum distance is the spark of the measurement matrix, i.e., the size of the smallest set of linearly dependent columns. This paper constructs a family of measurement matrices where the columns are formed by exponentiating codewords from a classical binary error-correcting code of block length M. The columns can be partitioned into mutually unbiased bases, and the spark of the corresponding measurement matrix is shown to be O(√M) by identifying a configuration of columns that plays a role similar to that of the Dirac comb in classical Fourier analysis. Further, an explicit basis for the null space of these measurement matrices is given in terms of indicator functions of binary self-dual codes. Reliable reconstruction of k-sparse inputs is shown for k of order M/log(M) which is best possible and far beyond the worst case lower bound provided by the spark. © 2012 IEEE.}, Doi = {10.1109/ISIT.2012.6283601}, Key = {fds236001} } @article{fds236002, Author = {Zeng, M and Calderbank, R and Cui, S}, Title = {On design of rateless codes over dying binary erasure channel}, Journal = {IEEE Transactions on Communications}, Volume = {60}, Number = {4}, Pages = {889-894}, Year = {2012}, ISSN = {0090-6778}, url = {http://dx.doi.org/10.1109/TCOMM.2012.022712.110038}, Abstract = {In this paper, we study a practical coding scheme for the dying binary erasure channel (DBEC), which is a binary erasure channel (BEC) subject to a random fatal failure. We consider the rateless codes and optimize the degree distribution to maximize the average recovery probability. In particular, we first study the upper bound of the average recovery probability, based on which we define the objective function as the gap between the upper bound and the average recovery probability achieved by a particular degree distribution. We then seek the optimal degree distribution by minimizing the objective function. A simple and heuristic approach is also proposed to provide a suboptimal but good degree distribution. Simulation results are presented to show the significant performance gain over the conventional LT codes. © 2012 IEEE.}, Doi = {10.1109/TCOMM.2012.022712.110038}, Key = {fds236002} } @article{fds236003, Author = {Applebaum, L and Bajwa, WU and Duarte, MF and Calderbank, R}, Title = {Asynchronous code-division random access using convex optimization}, Journal = {Physical Communication}, Volume = {5}, Number = {2}, Pages = {129-147}, Year = {2012}, ISSN = {1874-4907}, url = {http://dx.doi.org/10.1016/j.phycom.2011.09.006}, Abstract = {Many applications in cellular systems and sensor networks involve a random subset of a large number of users asynchronously reporting activity to a base station. This paper examines the problem of multiuser detection (MUD) in random access channels for such applications. Traditional orthogonal signaling ignores the random nature of user activity in this problem and limits the total number of users to be on the order of the number of signal space dimensions. Contention-based schemes, on the other hand, suffer from delays caused by colliding transmissions and the hidden node problem. In contrast, this paper presents a novel pairing of an asynchronous non-orthogonal code-division random access scheme with a convex optimization-based MUD algorithm that overcomes the issues associated with orthogonal signaling and contention-based methods. Two key distinguishing features of the proposed MUD algorithm are that it does not require knowledge of the delay or channel state information of every user and it has polynomial-time computational complexity. The main analytical contribution of this paper is the relationship between the performance of the proposed MUD algorithm in the presence of arbitrary or random delays and two simple metrics of the set of user codewords. The study of these metrics is then focused on two specific sets of codewords, random binary codewords and specially constructed algebraic codewords, for asynchronous random access. The ensuing analysis confirms that the proposed scheme together with either of these two codeword sets significantly outperforms the orthogonal signaling-based random access in terms of the total number of users in the system. © 2011 Elsevier B.V.}, Doi = {10.1016/j.phycom.2011.09.006}, Key = {fds236003} } @article{fds236004, Author = {Bajwa, WU and Calderbank, R and Mixon, DG}, Title = {Two are better than one: Fundamental parameters of frame coherence}, Journal = {Applied and Computational Harmonic Analysis}, Volume = {33}, Number = {1}, Pages = {58-78}, Year = {2012}, ISSN = {1063-5203}, url = {http://dx.doi.org/10.1016/j.acha.2011.09.005}, Abstract = {This paper investigates two parameters that measure the coherence of a frame: worst-case and average coherence. We first use worst-case and average coherence to derive near-optimal probabilistic guarantees on both sparse signal detection and reconstruction in the presence of noise. Next, we provide a catalog of nearly tight frames with small worst-case and average coherence. Later, we find a new lower bound on worst-case coherence; we compare it to the Welch bound and use it to interpret recently reported signal reconstruction results. Finally, we give an algorithm that transforms frames in a way that decreases average coherence without changing the spectral norm or worst-case coherence. © 2011 Elsevier Inc. All rights reserved.}, Doi = {10.1016/j.acha.2011.09.005}, Key = {fds236004} } @article{fds236005, Author = {Wu, Y and Jia, T and Calderbank, R and Duel-Hallen, A and Hallen, H}, Title = {Enabling Code Diversity for Mobile Radio Channels using Long-Range Fading Prediction}, Journal = {IEEE Transactions on Wireless Communications}, Year = {2012}, ISSN = {1536-1276}, url = {http://dx.doi.org/10.1109/TWC.2012.101712.111884}, Abstract = {Code diversity integrates space-time coding with beamforming by using a small number of feedback bits to select from a family of space-time codes. Different codes lead to different induced channels at the receiver, where Channel State Information (CSI) is used to instruct the transmitter how to choose the code. Feedback can be combined with sub-optimal low complexity decoding of the component codes to match Maximum-Likelihood (ML) decoding performance of any individual code in the family. It can also be combined with ML decoding of the component codes to improve performance beyond ML decoding performance of any individual code. Prior analysis of code diversity did not take into account the effect of the mobile speed and the delay in the feedback channel. This paper demonstrates the practicality of code diversity in space-time coded systems by showing that performance gains based on instantaneous feedback are largely preserved when long-range prediction of time-varying correlated fading channels is employed to compensate for the effect of the feedback delay. To maintain prediction accuracy for realistic SNR, noise reduction that employs oversampled pilots is used prior to fading prediction. We also propose a robust low pilot rate method that utilizes interleaving to improve the spectral efficiency. Simulations are presented for two channel models: the conventional Jakes model and a realistic physical channel model where the parameters associated with the reflectors vary in time and the arrival rays have different strengths and asymmetric arrival angles.}, Doi = {10.1109/TWC.2012.101712.111884}, Key = {fds236005} } @article{fds236077, Author = {Chen, M and Carson, W and Rodrigues, M and Calderbank, R and Carin, L}, Title = {Communications inspired linear discriminant analysis}, Journal = {Proceedings of the 29th International Conference on Machine Learning, ICML 2012}, Volume = {1}, Pages = {919-926}, Year = {2012}, url = {http://hdl.handle.net/10161/8956 Duke open access}, Abstract = {We study the problem of supervised linear dimensionality reduction, taking an information-theoretic viewpoint. The linear projection matrix is designed by maximizing the mutual information between the projected signal and the class label. By harnessing a recent theoretical result on the gradient of mutual information, the above optimization problem can be solved directly using gradient descent, without requiring simplification of the objective function. Theoretical analysis and empirical comparison are made between the proposed method and two closely related methods, and comparisons are also made with a method in which Rényi entropy is used to define the mutual information (in this case the gradient may be computed simply, under a special parameter setting). Relative to these alternative approaches, the proposed method achieves promising results on real datasets. Copyright 2012 by the author(s)/owner(s).}, Key = {fds236077} } @article{fds236078, Author = {Chi, Y and Eldar, YC and Calderbank, R}, Title = {PETRELS: Subspace estimation and tracking from partial observations}, Journal = {IEEE International Conference on Acoustics Speech and Signal Processing}, Pages = {3301-3304}, Year = {2012}, ISSN = {1520-6149}, url = {http://dx.doi.org/10.1109/ICASSP.2012.6288621}, Abstract = {We consider the problem of reconstructing a data stream from a small subset of its entries, where the data stream is assumed to lie in a low-dimensional linear subspace, possibly corrupted by noise. It is also important to track the change of underlying subspace for many applications. This problem can be viewed as a sequential low-rank matrix completion problem in which the subspace is learned in an online fashion. The proposed algorithm, called Parallel Estimation and Tracking by REcursive Least Squares (PETRELS), identifies the underlying low-dimensional subspace via a recursive procedure for each row of the subspace matrix in parallel, and then reconstructs the missing entries via least-squares estimation if required. PETRELS outperforms previous approaches by discounting observations in order to capture long-term behavior of the data stream and be able to adapt to it. Numerical examples are provided for direction-of-arrival estimation and matrix completion, comparing PETRELS with state of the art batch algorithms. © 2012 IEEE.}, Doi = {10.1109/ICASSP.2012.6288621}, Key = {fds236078} } @article{fds236079, Author = {Qureshi, TR and Zoltowski, MD and Calderbank, R}, Title = {A novel approach to Doppler compensation and estimation for multiple targets in MIMO radar with unitary waveform matrix scheduling}, Journal = {IEEE International Conference on Acoustics Speech and Signal Processing}, Pages = {2473-2476}, Year = {2012}, ISSN = {1520-6149}, url = {http://dx.doi.org/10.1109/ICASSP.2012.6288417}, Abstract = {In this paper, we present a method of detecting the range and Doppler phase of a point target using multiple antennas. As a key illustrative example, we consider a 4 x 4 system employing a unitary matrix waveform set, e.g., formed from Golay complementary sequences. When a non-negligible Doppler shift is induced by the target motion, the waveform matrix formed from the complementary sequences is no longer unitary, resulting in significantly degraded target range estimates. To solve this problem, we adopt a subspace based approach exploiting the observation that the receive matrix formed from matched filtering of the reflected waveforms has a (non-trivial) null-space. Through processing of the waveforms with the appropriate vector from the null-space, we can significantly improve the range detection performance. Also, another very important target aspect is the velocity with which the target is moving, and to determine that, the exact Doppler phase shift induced by the target motion needs to be estimated with reasonable accuracy. To accomplish this task, we develop a strategy that uses the MUSIC algorithm to estimate the Doppler phase, and we use simulations to show that the phase estimates obtained are reasonably accurate even at low SNRs. © 2012 IEEE.}, Doi = {10.1109/ICASSP.2012.6288417}, Key = {fds236079} } @article{fds236080, Author = {Carson, WR and Rodrigues, MRD and Chen, M and Carin, L and Calderbank, R}, Title = {How to focus the discriminative power of a dictionary}, Journal = {IEEE International Conference on Acoustics Speech and Signal Processing}, Pages = {1365-1368}, Year = {2012}, ISSN = {1520-6149}, url = {http://dx.doi.org/10.1109/ICASSP.2012.6288144}, Abstract = {This paper is motivated by the challenge of high fidelity processing of images using a relatively small set of projection measurements. This is a problem of great interest in many sensing applications, for example where high photodetector counts are precluded by a combination of available power, form factor and expense. The emerging methods of dictionary learning and compressive sensing offer great potential for addressing this challenge. Combining these methods requires that the signals of interest be representable as a sparse combination of elements of some dictionary. This paper develops a method that aligns the discriminative power of such a dictionary with the physical limitations of the imaging system. Alignment is accomplished by designing a projection matrix that exposes and then aligns the modes of the noise with those of the dictionary. The design algorithm is obtained by modifying an algorithm for designing the pre-filter to maximize the rate and reliability of a Multiple Input Multiple Output (MIMO) communications channel. The difference is that in the communications problem a source is being matched to a channel, whereas in the imaging problem a channel, or equivalently the noise covariance, is being matched to a source. Our results shown that using the proposed communications design framework we can reduce reconstruction error between 20%, after only 20 projections of a 28 x 28 image, and 10% after 100 projections. Furthermore, we noticeably see the superior quality of the reconstructed images. © 2012 IEEE.}, Doi = {10.1109/ICASSP.2012.6288144}, Key = {fds236080} } @article{fds236081, Author = {Nokleby, M and Bajwa, WU and Calderbank, R and Aazhang, B}, Title = {Hierarchical averaging over wireless sensor networks}, Journal = {IEEE International Conference on Acoustics Speech and Signal Processing}, Pages = {3121-3124}, Year = {2012}, ISSN = {1520-6149}, url = {http://dx.doi.org/10.1109/ICASSP.2012.6288576}, Abstract = {We introduce an approach to gossip algorithms that exploits three aspects of the wireless medium: superposition, broadcast, and power control. Instead of sending pairwise messages between neighbors on a fixed network topology, we construct gossip algorithms in which nodes can simultaneously recover multiple neighbors' messages and in which nodes can adjust the set of their neighbors by adjusting transmit power. We present two averaging algorithms, each based on a hierarchical clustering of the network. In the first algorithm, clusters of nodes transmit their estimates locally and randomly select a representative node for communications at the next level. In the second, each cluster mutually averages and then cooperatively transmits at the next level. For path-loss environments, these schemes achieve order-optimal or near order-optimal performance. © 2012 IEEE.}, Doi = {10.1109/ICASSP.2012.6288576}, Key = {fds236081} } @article{fds236082, Author = {Xie, Y and Chi, Y and Applebaum, L and Calderbank, R}, Title = {Compressive demodulation of mutually interfering signals}, Journal = {2012 IEEE Statistical Signal Processing Workshop, SSP 2012}, Pages = {592-595}, Year = {2012}, url = {http://dx.doi.org/10.1109/SSP.2012.6319768}, Abstract = {The challenge of Multiuser Detection (MUD) is that of demodulating mutually interfering signals given that at any time instant the number of active users is typically small. The promise of compressed sensing is the demodulation of sparse superpositions of signature waveforms from very few measurements. This paper considers signature waveforms that are are drawn from a Gabor frame. It describes a MUD architecture that uses subsampling to convert analog input to a digital signal, and then uses iterative matching pursuit to recover the active users. Compressive demodulation requires K logN samples to recover K active users whereas standard MUD requires N samples. The paper provides theoretical performance guarantees and consistent numerical simulations. © 2012 IEEE.}, Doi = {10.1109/SSP.2012.6319768}, Key = {fds236082} } @article{fds236083, Author = {Calderbank, R and Jafarpour, S}, Title = {Finding needles in compressed haystacks}, Journal = {IEEE International Conference on Acoustics Speech and Signal Processing}, Pages = {3441-3444}, Year = {2012}, ISSN = {1520-6149}, url = {http://dx.doi.org/10.1109/ICASSP.2012.6288656}, Abstract = {In this paper, we investigate the problem of compressed learning, i.e. learning directly in the compressed domain. In particular, we provide tight bounds demonstrating that the linear kernel SVMs classifier in the measurement domain, with high probability, has true accuracy close to the accuracy of the best linear threshold classifier in the data domain. Furthermore, we indicate that for a family of well-known deterministic compressed sensing matrices, compressed learning is provided on the fly. Finally, we support our claims with experimental results in the texture analysis application. © 2012 IEEE.}, Doi = {10.1109/ICASSP.2012.6288656}, Key = {fds236083} } @article{fds236084, Author = {Duarte, MF and Matthews, TE and Warren, WS and Calderbank, R}, Title = {Melanoma classification from hidden Markov tree features}, Journal = {IEEE International Conference on Acoustics Speech and Signal Processing}, Pages = {685-688}, Year = {2012}, ISSN = {1520-6149}, url = {http://dx.doi.org/10.1109/ICASSP.2012.6287976}, Abstract = {Melanoma detection relies on visual inspection of skin samples under the microscope via a qualitative set of indicators, causing large discordance among pathologists. New developments in pump-probe imaging enable the extraction of melanin intensity levels from skin samples and provide baseline qualitative figures for melanoma detection and classification. However, such basic figures do not capture the diverse types of cellular structure that distinguish different stages of melanoma. In this paper, we propose an initial approach for feature extraction for classification purposes via Hidden Markov Tree models trained on skin sample melanin intensity images. Our experimental results show that the proposed features provide a mathematical microscope that is able to better discriminate cellular structure, enabling successful classification of skin samples that are mislabeled when the baseline melanin intensity qualitative figures are used. © 2012 IEEE.}, Doi = {10.1109/ICASSP.2012.6287976}, Key = {fds236084} } @article{fds303202, Author = {Harms, A and Bajwa, WU and Calderbank, R}, Title = {A Constrained Random Demodulator for Sub-Nyquist Sampling}, Journal = {IEEE Trans. Signal Processing, vol. 61, no. 3, pp. 707-723, Feb. 2013}, Year = {2012}, Month = {April}, url = {http://arxiv.org/abs/1204.0839v3}, Abstract = {This paper presents a significant modification to the Random Demodulator (RD) of Tropp et al. for sub-Nyquist sampling of frequency-sparse signals. The modification, termed constrained random demodulator, involves replacing the random waveform, essential to the operation of the RD, with a constrained random waveform that has limits on its switching rate because fast switching waveforms may be hard to generate cleanly. The result is a relaxation on the hardware requirements with a slight, but manageable, decrease in the recovery guarantees. The paper also establishes the importance of properly choosing the statistics of the constrained random waveform. If the power spectrum of the random waveform matches the distribution on the tones of the input signal (i.e., the distribution is proportional to the power spectrum), then recovery of the input signal tones is improved. The theoretical guarantees provided in the paper are validated through extensive numerical simulations and phase transition plots.}, Doi = {10.1109/TSP.2012.2231077}, Key = {fds303202} } @article{fds303201, Author = {Chi, Y and Eldar, YC and Calderbank, R}, Title = {PETRELS: Parallel Subspace Estimation and Tracking by Recursive Least Squares from Partial Observations}, Year = {2012}, Month = {July}, url = {http://arxiv.org/abs/1207.6353v2}, Abstract = {Many real world data sets exhibit an embedding of low-dimensional structure in a high-dimensional manifold. Examples include images, videos and internet traffic data. It is of great significance to reduce the storage requirements and computational complexity when the data dimension is high. Therefore we consider the problem of reconstructing a data stream from a small subset of its entries, where the data is assumed to lie in a low-dimensional linear subspace, possibly corrupted by noise. We further consider tracking the change of the underlying subspace, which can be applied to applications such as video denoising, network monitoring and anomaly detection. Our problem can be viewed as a sequential low-rank matrix completion problem in which the subspace is learned in an on-line fashion. The proposed algorithm, dubbed Parallel Estimation and Tracking by REcursive Least Squares (PETRELS), first identifies the underlying low-dimensional subspace via a recursive procedure for each row of the subspace matrix in parallel with discounting for previous observations, and then reconstructs the missing entries via least-squares estimation if required. Numerical examples are provided for direction-of-arrival estimation and matrix completion, comparing PETRELS with state of the art batch algorithms.}, Doi = {10.1109/TSP.2013.2282910}, Key = {fds303201} } @article{fds303200, Author = {Nokleby, M and Bajwa, WU and Calderbank, R and Aazhang, B}, Title = {Toward Resource-Optimal Consensus over the Wireless Medium}, Journal = {IEEE J. Select. Topics Signal Processing, vol. 7, no. 2, pp. 284-295, Apr. 2013}, Year = {2012}, Month = {August}, url = {http://arxiv.org/abs/1208.3251v2}, Abstract = {We carry out a comprehensive study of the resource cost of averaging consensus in wireless networks. Most previous approaches suppose a graphical network, which abstracts away crucial features of the wireless medium, and measure resource consumption only in terms of the total number of transmissions required to achieve consensus. Under a path-loss dominated model, we study the resource requirements of consensus with respect to three wireless-appropriate metrics: total transmit energy, elapsed time, and time-bandwidth product. First we characterize the performance of several popular gossip algorithms, showing that they may be order-optimal with respect to transmit energy but are strictly suboptimal with respect to elapsed time and time-bandwidth product. Further, we propose a new consensus scheme, termed hierarchical averaging, and show that it is nearly order-optimal with respect to all three metrics. Finally, we examine the effects of quantization, showing that hierarchical averaging provides a nearly order-optimal tradeoff between resource consumption and quantization error.}, Doi = {10.1109/JSTSP.2013.2246765}, Key = {fds303200} } @article{fds303203, Author = {Chi, Y and Calderbank, R}, Title = {Coherence-Based Performance Guarantees of Orthogonal Matching Pursuit}, Year = {2012}, Month = {September}, url = {http://arxiv.org/abs/1209.6267v1}, Abstract = {In this paper, we present coherence-based performance guarantees of Orthogonal Matching Pursuit (OMP) for both support recovery and signal reconstruction of sparse signals when the measurements are corrupted by noise. In particular, two variants of OMP either with known sparsity level or with a stopping rule are analyzed. It is shown that if the measurement matrix $X\in\mathbb{C}^{n\times p}$ satisfies the strong coherence property, then with $n\gtrsim\mathcal{O}(k\log p)$, OMP will recover a $k$-sparse signal with high probability. In particular, the performance guarantees obtained here separate the properties required of the measurement matrix from the properties required of the signal, which depends critically on the minimum signal to noise ratio rather than the power profiles of the signal. We also provide performance guarantees for partial support recovery. Comparisons are given with other performance guarantees for OMP using worst-case analysis and the sorted one step thresholding algorithm.}, Key = {fds303203} } @article{fds235778, Author = {Jacobvitz, AN and Calderbank, R and Sorin, DJ}, Title = {Coset coding to extend the lifetime of memory}, Journal = {Proceedings - International Symposium on High-Performance Computer Architecture}, Pages = {222-233}, Year = {2013}, ISSN = {1530-0897}, url = {http://dx.doi.org/10.1109/HPCA.2013.6522321}, Abstract = {Some recent memory technologies, including phase change memory (PCM), have lifetime reliabilities that are affected by write operations. We propose the use of coset coding to extend the lifetimes of these memories. The key idea of coset coding is that it performs a one-to-many mapping from each dataword to a coset of vectors, and having multiple possible vectors provides the flexibility to choose the vector to write that optimizes lifetime. Our technique, FlipMin, uses coset coding and, for each write, selects the vector that minimizes the number of bits that must flip. We also show how FlipMin can be synergistically combined with the ability to tolerate bit erasures. Thus, our techniques help to prevent bits from wearing out and can then tolerate those bits that do wear out. © 2013 IEEE.}, Doi = {10.1109/HPCA.2013.6522321}, Key = {fds235778} } @article{fds235782, Author = {Duarte, MF and Jafarpour, S and Calderbank, AR}, Title = {Performance of the Delsarte-Goethals frame on clustered sparse vectors}, Journal = {IEEE Transactions on Signal Processing}, Volume = {61}, Number = {8}, Pages = {1998-2008}, Year = {2013}, ISSN = {1053-587X}, url = {http://dx.doi.org/10.1109/TSP.2013.2242064}, Abstract = {The Delsarte-Goethals frame (DGF) has been proposed for deterministic compressive sensing of sparse and compressible signals. Results in compressive sensing theory show that the DGF enables successful recovery of an overwhelming majority of sufficiently sparse signals. However, these results do not give a characterization of the sparse vectors for which the recovery procedure fails. In this paper, we present a formal analysis of the DGF that highlights the presence of clustered sparse vectors within its null space. This in turn implies that sparse recovery performance is diminished for sparse vectors that have their nonzero entries clustered together. Such clustered structure is present in compressive imaging applications, where commonly-used raster scannings of 2-D discrete wavelet transform representations yield clustered sparse representations for natural images. Prior work leverages this structure by proposing specially tailored sparse recovery algorithms that partition the recovery of the input vector into known clustered and unclustered portions. Alternatively, we propose new randomized and deterministic raster scannings for clustered coefficient vectors that improve recovery performance. Experimental results verify the aforementioned analysis and confirm the predicted improvements for both noiseless and noisy measurement regimes. © 1991-2012 IEEE.}, Doi = {10.1109/TSP.2013.2242064}, Key = {fds235782} } @article{fds235761, Author = {Wang, L and Carlson, D and Rodrigues, MD and Wilcox, D and Calderbank, R and Carin, L}, Title = {Designed measurements for vector count data}, Journal = {Advances in Neural Information Processing Systems}, Year = {2013}, Month = {January}, ISSN = {1049-5258}, Abstract = {We consider design of linear projection measurements for a vector Poisson signal model. The projections are performed on the vector Poisson rate,X ∈ ℝ + n , and the observed data are a vector of counts, Y ∈ ℤ + m . The projection matrix is designed by maximizing mutual information between Y and X, I(Y;X). When there is a latent class label C ∈ {1; : : : ;L} associated with X, we onsider the mutual information with respect to Y and C, I(Y ;C). New analytic expressions for the gradient of I(Y ;X) and I(Y ;C) are presented, with gradient performed with respect to the measurement matrix. Connections are made to the more widely studied Gaussian measurement model. Example results are presented for compressive topic modeling of a document corpora (word counting), and hyperspectral compressive sensing for chemical classification (photon counting).}, Key = {fds235761} } @article{fds322367, Author = {Nokleby, M and Bajwa, WU and Calderbank, R and Aazhang, B}, Title = {Toward resource-optimal consensus over the wireless medium}, Journal = {IEEE Journal of Selected Topics in Signal Processing}, Volume = {7}, Number = {2}, Pages = {284-295}, Year = {2013}, Month = {January}, url = {http://dx.doi.org/10.1109/JSTSP.2013.2246765}, Abstract = {We carry out a comprehensive study of the resource cost of averaging consensus in wireless networks. Most previous approaches suppose a graphical network, which abstracts away crucial features of the wireless medium, and measure resource consumption only in terms of the total number of transmissions required to achieve consensus. Under a path-loss model, we study the resource requirements of consensus with respect to three wireless- appropriate metrics: total transmit energy, elapsed time, and time-bandwidth product. First, we characterize the performance of several popular gossip algorithms, showing that they may be order-optimal with respect to transmit energy but are strictly suboptimal with respect to elapsed time and time-bandwidth product. Further, we propose a new consensus scheme, termed hierarchical averaging, and show that it is nearly order-optimal with respect to all three metrics. Finally, we examine the effects of quantization, showing that hierarchical averaging provides a nearly orderoptimal tradeoff between resource consumption and quantization error. © 2013 IEEE.}, Doi = {10.1109/JSTSP.2013.2246765}, Key = {fds322367} } @article{fds303199, Author = {Reboredo, H and Renna, F and Calderbank, R and Rodrigues, MRD}, Title = {Compressive Classification}, Year = {2013}, Month = {February}, url = {http://arxiv.org/abs/1302.4660v1}, Abstract = {This paper derives fundamental limits associated with compressive classification of Gaussian mixture source models. In particular, we offer an asymptotic characterization of the behavior of the (upper bound to the) misclassification probability associated with the optimal Maximum-A-Posteriori (MAP) classifier that depends on quantities that are dual to the concepts of diversity gain and coding gain in multi-antenna communications. The diversity, which is shown to determine the rate at which the probability of misclassification decays in the low noise regime, is shown to depend on the geometry of the source, the geometry of the measurement system and their interplay. The measurement gain, which represents the counterpart of the coding gain, is also shown to depend on geometrical quantities. It is argued that the diversity order and the measurement gain also offer an optimization criterion to perform dictionary learning for compressive classification applications.}, Key = {fds303199} } @article{fds303198, Author = {Goparaju, S and Rouayheb, SE and Calderbank, R and Poor, HV}, Title = {Data Secrecy in Distributed Storage Systems under Exact Repair}, Year = {2013}, Month = {April}, url = {http://arxiv.org/abs/1304.3156v2}, Abstract = {The problem of securing data against eavesdropping in distributed storage systems is studied. The focus is on systems that use linear codes and implement exact repair to recover from node failures.The maximum file size that can be stored securely is determined for systems in which all the available nodes help in repair (i.e., repair degree $d=n-1$, where $n$ is the total number of nodes) and for any number of compromised nodes. Similar results in the literature are restricted to the case of at most two compromised nodes. Moreover, new explicit upper bounds are given on the maximum secure file size for systems with $d<n-1$. The key ingredients for the contribution of this paper are new results on subspace intersection for the data downloaded during repair. The new bounds imply the interesting fact that the maximum data that can be stored securely decreases exponentially with the number of compromised nodes.}, Key = {fds303198} } @article{fds303197, Author = {Goparaju, S and Tamo, I and Calderbank, R}, Title = {An Improved Sub-Packetization Bound for Minimum Storage Regenerating Codes}, Year = {2013}, Month = {May}, url = {http://arxiv.org/abs/1305.3498v1}, Abstract = {Distributed storage systems employ codes to provide resilience to failure of multiple storage disks. Specifically, an $(n, k)$ MDS code stores $k$ symbols in $n$ disks such that the overall system is tolerant to a failure of up to $n-k$ disks. However, access to at least $k$ disks is still required to repair a single erasure. To reduce repair bandwidth, array codes are used where the stored symbols or packets are vectors of length $\ell$. MDS array codes have the potential to repair a single erasure using a fraction $1/(n-k)$ of data stored in the remaining disks. We introduce new methods of analysis which capitalize on the translation of the storage system problem into a geometric problem on a set of operators and subspaces. In particular, we ask the following question: for a given $(n, k)$, what is the minimum vector-length or sub-packetization factor $\ell$ required to achieve this optimal fraction? For \emph{exact recovery} of systematic disks in an MDS code of low redundancy, i.e. $k/n > 1/2$, the best known explicit codes \cite{WTB12} have a sub-packetization factor $\ell$ which is exponential in $k$. It has been conjectured \cite{TWB12} that for a fixed number of parity nodes, it is in fact necessary for $\ell$ to be exponential in $k$. In this paper, we provide a new log-squared converse bound on $k$ for a given $\ell$, and prove that $k \le 2\log_2\ell\left(\log_{\delta}\ell+1\right)$, for an arbitrary number of parity nodes $r = n-k$, where $\delta = r/(r-1)$.}, Key = {fds303197} } @article{fds303196, Author = {Renna, F and Calderbank, R and Carin, L and Rodrigues, MRD}, Title = {Reconstruction of Signals Drawn from a Gaussian Mixture from Noisy Compressive Measurements}, Year = {2013}, Month = {July}, url = {http://arxiv.org/abs/1307.0861v2}, Abstract = {This paper determines to within a single measurement the minimum number of measurements required to successfully reconstruct a signal drawn from a Gaussian mixture model in the low-noise regime. The method is to develop upper and lower bounds that are a function of the maximum dimension of the linear subspaces spanned by the Gaussian mixture components. The method not only reveals the existence or absence of a minimum mean-squared error (MMSE) error floor (phase transition) but also provides insight into the MMSE decay via multivariate generalizations of the MMSE dimension and the MMSE power offset, which are a function of the interaction between the geometrical properties of the kernel and the Gaussian mixture. These results apply not only to standard linear random Gaussian measurements but also to linear kernels that minimize the MMSE. It is shown that optimal kernels do not change the number of measurements associated with the MMSE phase transition, rather they affect the sensed power required to achieve a target MMSE in the low-noise regime. Overall, our bounds are tighter and sharper than standard bounds on the minimum number of measurements needed to recover sparse signals associated with a union of subspaces model, as they are not asymptotic in the signal dimension or signal sparsity.}, Doi = {10.1109/TSP.2014.2309560}, Key = {fds303196} } @article{fds303195, Author = {Calderbank, R and Thompson, A and Xie, Y}, Title = {On block coherence of frames}, Year = {2013}, Month = {July}, url = {http://arxiv.org/abs/1307.7544v4}, Abstract = {Block coherence of matrices plays an important role in analyzing the performance of block compressed sensing recovery algorithms (Bajwa and Mixon, 2012). In this paper, we characterize two block coherence metrics: worst-case and average block coherence. First, we present lower bounds on worst-case block coherence, in both the general case and also when the matrix is constrained to be a union of orthobases. We then present deterministic matrix constructions based upon Kronecker products which obtain these lower bounds. We also characterize the worst-case block coherence of random subspaces. Finally, we present a flipping algorithm that can improve the average block coherence of a matrix, while maintaining the worst-case block coherence of the original matrix. We provide numerical examples which demonstrate that our proposed deterministic matrix construction performs well in block compressed sensing.}, Key = {fds303195} } @article{fds235773, Author = {Renna, F and Rodrigues, MRD and Chen, M and Calderbank, R and Carin, L}, Title = {Compressive sensing for incoherent imaging systems with optical constraints}, Journal = {IEEE International Conference on Acoustics Speech and Signal Processing}, Pages = {5484-5488}, Year = {2013}, Month = {October}, ISSN = {1520-6149}, url = {http://dx.doi.org/10.1109/ICASSP.2013.6638712}, Abstract = {We consider the problem of linear projection design for incoherent optical imaging systems. We propose a computationally efficient method to obtain effective measurement kernels that satisfy the physical constraints imposed by an optical system, starting first from arbitrary kernels, including those that satisfy a less demanding power constraint. Performance is measured in terms of mutual information between the source input and the projection measurement, as well as reconstruction error for real world images. A clear improvement in the quality of image reconstructions is shown with respect to both random and adaptive projection designs in the literature. © 2013 IEEE.}, Doi = {10.1109/ICASSP.2013.6638712}, Key = {fds235773} } @article{fds235774, Author = {Wang, M and Xu, W and Calderbank, R}, Title = {Compressed sensing with corrupted participants}, Journal = {IEEE International Conference on Acoustics Speech and Signal Processing}, Pages = {4653-4657}, Year = {2013}, Month = {October}, ISSN = {1520-6149}, url = {http://dx.doi.org/10.1109/ICASSP.2013.6638542}, Abstract = {Compressed sensing (CS) theory promises one can recover real-valued sparse signal from a small number of linear measurements. Motivated by network monitoring with link failures, we for the first time consider the problem of recovering signals that contain both real-valued entries and corruptions, where the real entries represent transmission delays on normal links and the corruptions represent failed links. Unlike conventional CS, here a measurement is real-valued only if it does not include a failed link, and it is corrupted otherwise. We prove that O((d + 1)max(d, k) log n) nonadaptive measurements are enough to recover all n-dimensional signals that contain k nonzero real entries and d corruptions. We provide explicit constructions of measurements and recovery algorithms. We also analyze the performance of signal recovery when the measurements contain errors. © 2013 IEEE.}, Doi = {10.1109/ICASSP.2013.6638542}, Key = {fds235774} } @article{fds235775, Author = {Chi, Y and Calderbank, R}, Title = {Knowledge-enhanced matching pursuit}, Journal = {IEEE International Conference on Acoustics Speech and Signal Processing}, Pages = {6576-6580}, Year = {2013}, Month = {October}, ISSN = {1520-6149}, url = {http://dx.doi.org/10.1109/ICASSP.2013.6638933}, Abstract = {Compressive Sensing is possible when the sensing matrix acts as a near isometry on signals of interest that can be sparsely or compressively represented. The attraction of greedy algorithms such as Orthogonal Matching Pursuit is their simplicity. However they fail to take advantage of both the structure of the sensing matrix and any prior information about the sparse signal. This paper introduces an oblique projector to matching pursuit algorithms to enhance detection of a component that is present in the signal by reducing interference from other candidate components based on prior information about the signal as well as the structure of the sensing matrix. Numerical examples demonstrate that performance as a function of SNR is superior to conventional matching pursuit. © 2013 IEEE.}, Doi = {10.1109/ICASSP.2013.6638933}, Key = {fds235775} } @article{fds235764, Author = {Xie, Y and Chi, Y and Calderbank, R}, Title = {Low-rank matrix recovery with poison noise}, Journal = {2013 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2013 - Proceedings}, Pages = {622}, Year = {2013}, Month = {December}, url = {http://dx.doi.org/10.1109/GlobalSIP.2013.6736959}, Abstract = {Estimating an image M* + m 1 ×m 2 from its linear measurements under Poisson noise is an important problem arises from applications such as optical imaging, nuclear medicine and x-ray imaging [1]. When the image M* has a low-rank structure, we can use a small number of linear measurements to recover M*, also known as low-rank matrix recovery. This is related to compressed sensing, where the goal is to develop efficient data acquisition systems by exploiting sparsity of underlying signals. © 2013 IEEE.}, Doi = {10.1109/GlobalSIP.2013.6736959}, Key = {fds235764} } @article{fds235765, Author = {Wu, T and Polatkan, G and Steel, D and Brown, W and Daubechies, I and Calderbank, R}, Title = {Painting analysis using wavelets and probabilistic topic models}, Journal = {2013 IEEE International Conference on Image Processing, ICIP 2013 - Proceedings}, Pages = {3264-3268}, Year = {2013}, Month = {December}, url = {http://dx.doi.org/10.1109/ICIP.2013.6738672}, Abstract = {In this paper, computer-based techniques for stylistic analysis of paintings are applied to the five panels of the 14th century Peruzzi Altarpiece by Giotto di Bondone. Features are extracted by combining a dual-tree complex wavelet transform with a hidden Markov tree (HMT) model. Hierarchical clustering is used to identify stylistic keywords in image patches, and keyword frequencies are calculated for sub-images that each contains many patches. A generative hierarchical Bayesian model learns stylistic patterns of keywords; these patterns are then used to characterize the styles of the sub-images; this in turn, permits to discriminate between paintings. Results suggest that such unsupervised probabilistic topic models can be useful to distill characteristic elements of style. © 2013 IEEE.}, Doi = {10.1109/ICIP.2013.6738672}, Key = {fds235765} } @article{fds235766, Author = {Renna, F and Calderbank, R and Carin, L and Rodrigues, MRD}, Title = {Reconstruction of Gaussian mixture models from compressive measurements: A phase transition view}, Journal = {2013 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2013 - Proceedings}, Pages = {628}, Year = {2013}, Month = {December}, url = {http://dx.doi.org/10.1109/GlobalSIP.2013.6736965}, Abstract = {We characterize the minimum number of measurements needed to drive to zero the minimum mean squared error (MMSE) of Gaussian mixture model (GMM) input signals in the low-noise regime. The result also hints at almost phase-transition optimal recovery procedures based on a classification and reconstruction approach. © 2013 IEEE.}, Doi = {10.1109/GlobalSIP.2013.6736965}, Key = {fds235766} } @article{fds235767, Author = {Reboredo, H and Renna, F and Calderbank, R and Rodrigues, MRD}, Title = {Projections designs for compressive classification}, Journal = {2013 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2013 - Proceedings}, Pages = {1029-1032}, Year = {2013}, Month = {December}, url = {http://dx.doi.org/10.1109/GlobalSIP.2013.6737069}, Abstract = {This paper puts forth projections designs for compressive classification of Gaussian mixture models. In particular, we capitalize on the asymptotic characterization of the behavior of an (upper bound to the) misclassification probability associated with the optimal Maximum-A-Posteriori (MAP) classifier, which depends on quantities that are dual to the concepts of the diversity gain and coding gain in multi-antenna communications, to construct measurement designs that maximize the diversity-order of the measurement model. Numerical results demonstrate that the new measurement designs substantially outperform random measurements. Overall, the analysis and the designs cast geometrical insight about the mechanics of compressive classification problems. © 2013 IEEE.}, Doi = {10.1109/GlobalSIP.2013.6737069}, Key = {fds235767} } @article{fds235770, Author = {Nokleby, M and Calderbank, R and Rodrigues, MRD}, Title = {Information-theoretic limits on the classification of Gaussian mixtures: Classification on the Grassmann manifold}, Journal = {2013 IEEE Information Theory Workshop, ITW 2013}, Year = {2013}, Month = {December}, url = {http://dx.doi.org/10.1109/ITW.2013.6691253}, Abstract = {Motivated by applications in high-dimensional signal processing, we derive fundamental limits on the performance of compressive linear classifiers. By analogy with Shannon theory, we define the classification capacity, which quantifies the maximum number of classes that can be discriminated with low probability of error, and the diversity-discrimination tradeoff, which quantifies the tradeoff between the number of classes and the probability of classification error. For classification of Gaussian mixture models, we identify a duality between classification and communications over non-coherent multiple-antenna channels. This duality allows us to characterize the classification capacity and diversity-discrimination tradeoff using existing results from multiple-antenna communication. We also identify the easiest possible classification problems, which correspond to low-dimensional subspaces drawn from an appropriate Grassmann manifold. © 2013 IEEE.}, Doi = {10.1109/ITW.2013.6691253}, Key = {fds235770} } @article{fds235776, Author = {Goparaju, S and Calderbank, R}, Title = {A new sub-packetization bound for minimum storage regenerating codes}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Pages = {1616-1620}, Year = {2013}, Month = {December}, ISSN = {2157-8095}, url = {http://dx.doi.org/10.1109/ISIT.2013.6620500}, Abstract = {Codes for distributed storage systems are often designed to sustain failure of multiple storage disks. Specifically, an (n, k) MDS code stores k symbols in n disks such that the overall system is tolerant to a failure of up to n - k disks. However, access to at least k disks is still required to repair a single erasure. To reduce repair bandwidth, array codes are used where the stored symbols or packets are vectors of length ℓ. MDS array codes can potentially repair a single erasure using a fraction l/(n - k) of data stored in the surviving nodes. We ask the following question: for a given (n, k), what is the minimum vector-length or sub-packetization factor ℓ required to achieve this optimal fraction? For exact recovery of systematic disks in an MDS code of low redundancy, i.e. k/n > 1/2, the best known explicit codes [1] have a sub-packetization factor I which is exponential in k. It has been conjectured [2] that for a fixed number of parity nodes, it is in fact necessary for ℓ to be exponential in k. In this paper, we provide new converse bounds on k for a given ℓ We prove that k ≤ ℓ 2 for an arbitrary but fixed number of parity nodes r = n ™ k. For the practical case of 2 parity nodes, we prove a stronger result that k ≤ 4ℓ. © 2013 IEEE.}, Doi = {10.1109/ISIT.2013.6620500}, Key = {fds235776} } @article{fds235749, Author = {Calderbank, R and Thompson, A and Xie, Y}, Title = {On block coherence of frames}, Journal = {Applied and Computational Harmonic Analysis}, Volume = {38}, Number = {1}, Pages = {50-71}, Year = {2014}, Month = {January}, ISSN = {1063-5203}, url = {http://dx.doi.org/10.1016/j.acha.2014.03.003}, Abstract = {© 2014 Elsevier Inc. All rights reserved. Block coherence of matrices plays an important role in analyzing the performance of block compressed sensing recovery algorithmns (Bajwa and Mixon, 2012). In this paper, we characterize two block coheremice metrics: worst-case and average block coherence. First, we present lower bounds on worst-case block coherence, in both the general case and also when the mnatrix is constrained to be a union of orthobases. We then present determninistic mnatrix constructions based upon Kronecker products which obtain these lower bounds. We also characterize the worst-case block coherence of randomn suibspaces. Finally, we present a flipping algorithmn that can imnprove the average block coherence of a mnatrix, w}ule mnaintaining the worst- case block coherence of the original mnatrix. We provide nuimnerical examnples which demnonstrate that our proposed determninistic mnatrix construction performns well in block comnpressed sensing.}, Doi = {10.1016/j.acha.2014.03.003}, Key = {fds235749} } @article{fds235751, Author = {Goparaju, S and El Rouayheb and S and Calderbank, R}, Title = {New codes and inner bounds for exact repair in distributed storage systems}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Pages = {1036-1040}, Year = {2014}, Month = {January}, ISSN = {2157-8095}, url = {http://dx.doi.org/10.1109/ISIT.2014.6874990}, Abstract = {We study the exact-repair tradeoff between storage and repair bandwidth in distributed storage systems. We give new inner bounds for the tradeoff region and provide code constructions that achieve these bounds. © 2014 IEEE.}, Doi = {10.1109/ISIT.2014.6874990}, Key = {fds235751} } @article{fds235752, Author = {Nokleby, M and Rodrigues, M and Calderbank, R}, Title = {Discrimination on the grassmann manifold: Fundamental limits of subspace classifiers}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Pages = {3012-3016}, Year = {2014}, Month = {January}, ISSN = {2157-8095}, url = {http://dx.doi.org/10.1109/ISIT.2014.6875387}, Abstract = {Repurposing tools and intuitions from Shannon theory, we derive fundamental limits on the reliable classification of high-dimensional signals from low-dimensional features. We focus on the classification of linear and affine subspaces and suppose the features to be noisy linear projections. Leveraging a syntactic equivalence of discrimination between subspaces and communications over vector wireless channels, we derive asymptotic bounds on classifier performance. First, we define the classification capacity, which characterizes necessary and sufficient relationships between the signal dimension, the number of features, and the number of classes to be discriminated, as all three quantities approach infinity. Second, we define the diversitydiscrimination tradeoff, which characterizes relationships between the number of classes and the misclassification probability as the signal-to-noise ratio approaches infinity. We derive inner and outer bounds on these measures, revealing precise relationships between signal dimension and classifier performance. © 2014 IEEE.}, Doi = {10.1109/ISIT.2014.6875387}, Key = {fds235752} } @article{fds235753, Author = {Goparaju, S and Calderbank, R}, Title = {Binary cyclic codes that are locally repairable}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Pages = {676-680}, Year = {2014}, Month = {January}, ISSN = {2157-8095}, url = {http://dx.doi.org/10.1109/ISIT.2014.6874918}, Abstract = {Codes for storage systems aim to minimize the repair locality, which is the number of disks (or nodes) that participate in the repair of a single failed disk. Simultaneously, the code must sustain a high rate, operate on a small finite field to be practically significant and be tolerant to a large number of erasures. To this end, we construct new families of binary linear codes that have an optimal dimension (rate) for a given minimum distance and locality. Specifically, we construct cyclic codes that are locally repairable for locality 2 and distances 2, 6 and 10. In doing so, we discover new upper bounds on the code dimension, and prove the optimality of enabling local repair by provisioning disjoint groups of disks. Finally, we extend our construction to build codes that have multiple repair sets for each disk. © 2014 IEEE.}, Doi = {10.1109/ISIT.2014.6874918}, Key = {fds235753} } @article{fds235754, Author = {Nokleby, M and Rodrigues, M and Calderbank, R}, Title = {Information-theoretic criteria for the design of compressive subspace classifiers}, Journal = {IEEE International Conference on Acoustics Speech and Signal Processing}, Pages = {3067-3071}, Year = {2014}, Month = {January}, ISSN = {1520-6149}, url = {http://dx.doi.org/10.1109/ICASSP.2014.6854164}, Abstract = {Using Shannon theory, we derive fundamental, asymptotic limits on the classification of low-dimensional subspaces from compressive measurements. We identify a syntactic equivalence between the classification of subspaces and the communication of codewords over non-coherent, multiple-antenna channels, from which we derive sharp bounds on the number of classes that can be discriminated with low misclassification probability as a function of the signal dimensionality and the signal-to-noise ratio. While the bounds are asymptotic in the limit of high dimension, they provide intuition for classifier design at finite dimension. We validate this intuition via an application to face recognition. © 2014 IEEE.}, Doi = {10.1109/ICASSP.2014.6854164}, Key = {fds235754} } @article{fds235755, Author = {Carpenter, K and Sprechmann, P and Fiori, M and Calderbank, R and Egger, H and Sapiro, G}, Title = {Questionnaire simplification for fast risk analysis of children's mental health}, Journal = {IEEE International Conference on Acoustics Speech and Signal Processing}, Pages = {6009-6013}, Year = {2014}, Month = {January}, ISSN = {1520-6149}, url = {http://dx.doi.org/10.1109/ICASSP.2014.6854757}, Abstract = {Early detection and treatment of psychiatric disorders on children has shown significant impact in their subsequent development and quality of life. The assessment of psychopathology in childhood is commonly carried out by performing long comprehensive interviews such as the widely used Preschool Age Psychiatric Assessment (PAPA). Unfortunately, the time required to complete a full interview is too long to apply it at the scale of the actual population at risk, and most of the population goes undiagnosed or is diagnosed significantly later than desired. In this work, we aim to learn from unique and very rich previously collected PAPA examples the inter-correlations between different questions in order to provide a reliable risk analysis in the form of a much shorter interview. This helps to put such important risk analysis at the hands of regular practitioners, including teachers and family doctors. We use for this purpose the alternating decision trees algorithm, which combines decision trees with boosting to produce small and interpretable decision rules. Rather than a binary prediction, the algorithm provides a measure of confidence in the classification outcome. This is highly desirable from a clinical perspective, where it is preferable to abstain a decision on the low-confidence cases and recommend further screening. In order to prevent over-fitting, we propose to use network inference analysis to predefine a set of candidate question with consistent high correlation with the diagnosis. We report encouraging results with high levels of prediction using two independently collected datasets. The length and accuracy of the developed method suggests that it could be a valuable tool for preliminary evaluation in everyday care. © 2014 IEEE.}, Doi = {10.1109/ICASSP.2014.6854757}, Key = {fds235755} } @article{fds235756, Author = {Goparaju, S and Rouayheb, SE and Calderbank, R}, Title = {New codes and inner bounds for exact repair in distributed storage systems}, Journal = {2014 48th Annual Conference on Information Sciences and Systems, CISS 2014}, Year = {2014}, Month = {January}, url = {http://dx.doi.org/10.1109/CISS.2014.6814148}, Abstract = {We study the exact-repair tradeoff between storage and repair bandwidth in distributed storage systems (DSS). We give new inner bounds for the tradeoff region and provide code constructions that achieve these bounds. © 2014 IEEE.}, Doi = {10.1109/CISS.2014.6814148}, Key = {fds235756} } @article{fds235759, Author = {Bennatan, A and Shamai, S and Calderbank, AR}, Title = {Soft-Decoding-Based Strategies for Relay and Interference Channels: Analysis and Achievable Rates Using LDPC Codes}, Journal = {IEEE Transactions on Information Theory}, Volume = {60}, Number = {4}, Pages = {1977-2009}, Year = {2014}, Month = {April}, ISSN = {0018-9448}, url = {http://dx.doi.org/10.1109/TIT.2013.2294373}, Doi = {10.1109/TIT.2013.2294373}, Key = {fds235759} } @article{fds235760, Author = {Liming Wang, and Carlson, DE and Rodrigues, MRD and Calderbank, R and Carin, L}, Title = {A Bregman Matrix and the Gradient of Mutual Information for Vector Poisson and Gaussian Channels}, Journal = {IEEE Transactions on Information Theory}, Volume = {60}, Number = {5}, Pages = {2611-2629}, Year = {2014}, Month = {May}, ISSN = {0018-9448}, url = {http://dx.doi.org/10.1109/TIT.2014.2307068}, Doi = {10.1109/TIT.2014.2307068}, Key = {fds235760} } @article{fds290773, Author = {Wang, L and Huang, J and Yuan, X and Krishnamurthy, K and Greenberg, J and Cevher, V and Rodrigues, MRD and Brady, D and Calderbank, R and Carin, L}, Title = {Signal Recovery and System Calibration from Multiple Compressive Poisson Measurements}, Journal = {SIAM Journal on Imaging Sciences}, Volume = {8}, Number = {3}, Pages = {1923-1954}, Year = {2015}, Month = {January}, url = {http://dx.doi.org/10.1137/140998779}, Doi = {10.1137/140998779}, Key = {fds290773} } @article{fds235747, Author = {Harms, A and Bajwa, WU and Calderbank, R}, Title = {Identification of Linear Time-Varying Systems Through Waveform Diversity}, Journal = {IEEE Transactions on Signal Processing}, Volume = {63}, Number = {8}, Pages = {2070-2084}, Year = {2015}, Month = {April}, ISSN = {1053-587X}, url = {http://dx.doi.org/10.1109/TSP.2015.2407319}, Doi = {10.1109/TSP.2015.2407319}, Key = {fds235747} } @article{fds235748, Author = {Nokleby, M and Rodrigues, M and Calderbank, R}, Title = {Discrimination on the Grassmann Manifold: Fundamental Limits of Subspace Classifiers}, Journal = {IEEE Transactions on Information Theory}, Volume = {61}, Number = {4}, Pages = {2133-2147}, Year = {2015}, Month = {April}, ISSN = {0018-9448}, url = {http://dx.doi.org/10.1109/TIT.2015.2407368}, Doi = {10.1109/TIT.2015.2407368}, Key = {fds235748} } @article{fds235746, Author = {Bajwa, WU and Duarte, MF and Calderbank, R}, Title = {Conditioning of Random Block Subdictionaries With Applications to Block-Sparse Recovery and Regression}, Journal = {IEEE Transactions on Information Theory}, Volume = {61}, Number = {7}, Pages = {4060-4079}, Year = {2015}, Month = {July}, ISSN = {0018-9448}, url = {http://dx.doi.org/10.1109/TIT.2015.2429632}, Doi = {10.1109/TIT.2015.2429632}, Key = {fds235746} } @article{fds326756, Author = {Carpenter, KLH and Sprechmann, P and Calderbank, R and Sapiro, G and Egger, HL}, Title = {Quantifying Risk for Anxiety Disorders in Preschool Children: A Machine Learning Approach.}, Journal = {PloS one}, Volume = {11}, Number = {11}, Pages = {e0165524}, Year = {2016}, Month = {January}, url = {http://dx.doi.org/10.1371/journal.pone.0165524}, Abstract = {Early childhood anxiety disorders are common, impairing, and predictive of anxiety and mood disorders later in childhood. Epidemiological studies over the last decade find that the prevalence of impairing anxiety disorders in preschool children ranges from 0.3% to 6.5%. Yet, less than 15% of young children with an impairing anxiety disorder receive a mental health evaluation or treatment. One possible reason for the low rate of care for anxious preschoolers is the lack of affordable, timely, reliable and valid tools for identifying young children with clinically significant anxiety. Diagnostic interviews assessing psychopathology in young children require intensive training, take hours to administer and code, and are not available for use outside of research settings. The Preschool Age Psychiatric Assessment (PAPA) is a reliable and valid structured diagnostic parent-report interview for assessing psychopathology, including anxiety disorders, in 2 to 5 year old children. In this paper, we apply machine-learning tools to already collected PAPA data from two large community studies to identify sub-sets of PAPA items that could be developed into an efficient, reliable, and valid screening tool to assess a young child's risk for an anxiety disorder. Using machine learning, we were able to decrease by an order of magnitude the number of items needed to identify a child who is at risk for an anxiety disorder with an accuracy of over 96% for both generalized anxiety disorder (GAD) and separation anxiety disorder (SAD). Additionally, rather than considering GAD or SAD as discrete/binary entities, we present a continuous risk score representing the child's risk of meeting criteria for GAD or SAD. Identification of a short question-set that assesses risk for an anxiety disorder could be a first step toward development and validation of a relatively short screening tool feasible for use in pediatric clinics and daycare/preschool settings.}, Doi = {10.1371/journal.pone.0165524}, Key = {fds326756} } @article{fds326890, Author = {Huang, J and Qiu, Q and Calderbank, R}, Title = {The Role of Principal Angles in Subspace Classification}, Journal = {IEEE Transactions on Signal Processing}, Volume = {64}, Number = {8}, Pages = {1933-1945}, Year = {2016}, Month = {April}, url = {http://dx.doi.org/10.1109/TSP.2015.2500889}, Doi = {10.1109/TSP.2015.2500889}, Key = {fds326890} } @article{fds326754, Author = {Qiu, Q and Thompson, A and Calderbank, R and Sapiro, G}, Title = {Data Representation Using the Weyl Transform}, Journal = {IEEE Transactions on Signal Processing}, Volume = {64}, Number = {7}, Pages = {1844-1853}, Year = {2016}, Month = {April}, url = {http://dx.doi.org/10.1109/TSP.2015.2505661}, Doi = {10.1109/TSP.2015.2505661}, Key = {fds326754} } @article{fds326887, Author = {Sokolic, J and Renna, F and Calderbank, R and Rodrigues, MRD}, Title = {Mismatch in the Classification of Linear Subspaces: Sufficient Conditions for Reliable Classification}, Journal = {IEEE Transactions on Signal Processing}, Volume = {64}, Number = {12}, Pages = {3035-3050}, Year = {2016}, Month = {June}, url = {http://dx.doi.org/10.1109/TSP.2016.2537272}, Doi = {10.1109/TSP.2016.2537272}, Key = {fds326887} } @article{fds326884, Author = {Vahid, A and Calderbank, R}, Title = {Two-User Erasure Interference Channels With Local Delayed CSIT}, Journal = {IEEE Transactions on Information Theory}, Volume = {62}, Number = {9}, Pages = {4910-4923}, Year = {2016}, Month = {September}, url = {http://dx.doi.org/10.1109/TIT.2016.2594224}, Doi = {10.1109/TIT.2016.2594224}, Key = {fds326884} } @article{fds326883, Author = {Thompson, A and Robles, FE and Wilson, JW and Deb, S and Calderbank, R and Warren, WS}, Title = {Dual-wavelength pump-probe microscopy analysis of melanin composition.}, Journal = {Scientific Reports}, Volume = {6}, Pages = {36871}, Year = {2016}, Month = {November}, url = {http://dx.doi.org/10.1038/srep36871}, Abstract = {Pump-probe microscopy is an emerging technique that provides detailed chemical information of absorbers with sub-micrometer spatial resolution. Recent work has shown that the pump-probe signals from melanin in human skin cancers correlate well with clinical concern, but it has been difficult to infer the molecular origins of these differences. Here we develop a mathematical framework to describe the pump-probe dynamics of melanin in human pigmented tissue samples, which treats the ensemble of individual chromophores that make up melanin as Gaussian absorbers with bandwidth related via Frenkel excitons. Thus, observed signals result from an interplay between the spectral bandwidths of the individual underlying chromophores and spectral proximity of the pump and probe wavelengths. The model is tested using a dual-wavelength pump-probe approach and a novel signal processing method based on gnomonic projections. Results show signals can be described by a single linear transition path with different rates of progress for different individual pump-probe wavelength pairs. Moreover, the combined dual-wavelength data shows a nonlinear transition that supports our mathematical framework and the excitonic model to describe the optical properties of melanin. The novel gnomonic projection analysis can also be an attractive generic tool for analyzing mixing paths in biomolecular and analytical chemistry.}, Doi = {10.1038/srep36871}, Key = {fds326883} } @article{fds326749, Author = {Campbell, K and Carpenter, KLH and Espinosa, S and Hashemi, J and Qiu, Q and Tepper, M and Calderbank, R and Sapiro, G and Egger, HL and Baker, JP and Dawson, G}, Title = {Use of a Digital Modified Checklist for Autism in Toddlers - Revised with Follow-up to Improve Quality of Screening for Autism.}, Journal = {The Journal of Pediatrics}, Volume = {183}, Pages = {133-139.e1}, Year = {2017}, Month = {April}, url = {http://dx.doi.org/10.1016/j.jpeds.2017.01.021}, Abstract = {To assess changes in quality of care for children at risk for autism spectrum disorders (ASD) due to process improvement and implementation of a digital screening form.The process of screening for ASD was studied in an academic primary care pediatrics clinic before and after implementation of a digital version of the Modified Checklist for Autism in Toddlers - Revised with Follow-up with automated risk assessment. Quality metrics included accuracy of documentation of screening results and appropriate action for positive screens (secondary screening or referral). Participating physicians completed pre- and postintervention surveys to measure changes in attitudes toward feasibility and value of screening for ASD. Evidence of change was evaluated with statistical process control charts and χ2 tests.Accurate documentation in the electronic health record of screening results increased from 54% to 92% (38% increase, 95% CI 14%-64%) and appropriate action for children screening positive increased from 25% to 85% (60% increase, 95% CI 35%-85%). A total of 90% of participating physicians agreed that the transition to a digital screening form improved their clinical assessment of autism risk.Implementation of a tablet-based digital version of the Modified Checklist for Autism in Toddlers - Revised with Follow-up led to improved quality of care for children at risk for ASD and increased acceptability of screening for ASD. Continued efforts towards improving the process of screening for ASD could facilitate rapid, early diagnosis of ASD and advance the accuracy of studies of the impact of screening.}, Doi = {10.1016/j.jpeds.2017.01.021}, Key = {fds326749} } @article{fds326748, Author = {Wang, L and Chen, M and Rodrigues, M and Wilcox, D and Calderbank, R and Carin, L}, Title = {Information-Theoretic Compressive Measurement Design.}, Journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence}, Volume = {39}, Number = {6}, Pages = {1150-1164}, Year = {2017}, Month = {June}, url = {http://dx.doi.org/10.1109/tpami.2016.2568189}, Abstract = {An information-theoretic projection design framework is proposed, of interest for feature design and compressive measurements. Both Gaussian and Poisson measurement models are considered. The gradient of a proposed information-theoretic metric (ITM) is derived, and a gradient-descent algorithm is applied in design; connections are made to the information bottleneck. The fundamental solution structure of such design is revealed in the case of a Gaussian measurement model and arbitrary input statistics. This new theoretical result reveals how ITM parameter settings impact the number of needed projection measurements, with this verified experimentally. The ITM achieves promising results on real data, for both signal recovery and classification.}, Doi = {10.1109/tpami.2016.2568189}, Key = {fds326748} } %% Conference articles PUBLISHED @article{fds331061, Author = {Calderbank, AR}, Title = {Binary covering codes and high speed data transmission}, Journal = {Lecture notes in computer science}, Volume = {514 LNCS}, Pages = {319-336}, Year = {1991}, Month = {January}, ISBN = {9783540543039}, url = {http://dx.doi.org/10.1007/3-540-54303-1_143}, Abstract = {© Springer-Verlag Berlin Heidelberg 1991. There has been a great deal of recent interest in the covering radius of binary codes. We shall describe how good covering codes can be used to make high speed data transmission more reliable.}, Doi = {10.1007/3-540-54303-1_143}, Key = {fds331061} } @article{fds326908, Author = {CALDERBANK, R and FISHBURN, P and SIEGEL, P}, Title = {STATE-SPACE CHARACTERIZATION OF VITERBI DETECTOR PATH METRIC DIFFERENCES}, Journal = {CONFERENCE RECORD OF THE TWENTY-SIXTH ASILOMAR CONFERENCE ON SIGNALS, SYSTEMS & COMPUTERS, VOLS 1 AND 2}, Pages = {940-944}, Year = {1992}, ISBN = {0-8186-3160-0}, Key = {fds326908} } @article{fds331057, Author = {Calderbank, AR and Fishburn, PC and Rabinovich, A}, Title = {Sequence based methods for data transmission and source compression}, Journal = {Lecture notes in computer science}, Volume = {673 LNCS}, Pages = {1-12}, Year = {1993}, Month = {January}, ISBN = {9783540566861}, Abstract = {© 1993, Springer Verlag. All rights reserved. In the last 10 years the invention of trellis coded modulation has revolutionized communication over bandlimited channels and is starting to be used in magnetic storage. Part of the reason is that sophisticated signal processing systems involving finite state machines can now be fabricated inexpensively. This paper discusses new developments in the performance analysis of finite state machines. This is the extended abstract of an invited lecture to be given at the 10th International Symposium on Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes, Puerto Rico, May 10-14, 1993.}, Key = {fds331057} } @article{fds333193, Author = {Hammons, AR and Kumar, PV and Calderbank, AR and Sloane, NJA and Solé, P}, Title = {On the apparent duality of the kerdock and preparata codes}, Journal = {Lecture notes in computer science}, Volume = {673 LNCS}, Pages = {13-24}, Year = {1993}, Month = {January}, ISBN = {9783540566861}, Abstract = {© 1993, Springer Verlag. All rights reserved. The Kerdock and extended Preparata codes are something of an enigma in coding theory since they are both Hamming-distance invariant and have weight enumerators that are MacWilliams duals just as if they were dual linear codes. In this paper, we explain, by constructing in a natural way a Preparata-like code PL from the Kerdock code K, why the existence of a distance-invariant code with weight distribution that is the McWilliams transform of that of the Kerdock code is only to be expected. The construction involves quaternary codes over the ring ℤ 4 of integers modulo 4. We exhibit a quaternary code Q and its quaternary dual P ⊥ which, under the Gray mapping, give rise to the Kerdock code K, and Preparata-like code P L , respectively. The code P L is identical in weight and distance distribution to the extended Preparata code. The linearity of Q and P ⊥ ensures that the binary codes K and P L are distance invariant, while their duality as quaternary codes guarantees that K and P L have dual weight distributions. The quaternary code Q is the ℤ 4 -analog of the first-order Reed-Muller code. As a result, P L has a simple description in the ℤ 4 -domain that admits a simple syndrome decoder. At length 16, the code P L coincides with the Preparata code.}, Key = {fds333193} } @article{fds331054, Author = {Tarokh, V and Jafarkhani, H and Calderbank, AR}, Title = {The application of orthogonal designs to wireless communication}, Journal = {1998 Information Theory Workshop, ITW 1998}, Pages = {46-47}, Year = {1998}, Month = {January}, ISBN = {0780344081}, url = {http://dx.doi.org/10.1109/ITW.1998.706408}, Abstract = {© 1998 IEEE. We introduce space-block codzng, a new paradigm for transmission over Rayleigh fading channels using multiple transmit antennas. Data is encoded using a space-block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas. The received signal at each receive antenna is a linear superposition of the n transmitted signal perturbed by noise. Decoding is achieved in a simple way using the orthogonal structure of tlie space-block code and maximum likelihood decoding algorithm is totally based on linear processing at the receiver. Space-black codes are designed to achieve the maximum diversity gain of transmit and receive antennas with the constraint of having a simple decoding algorithm. It is shown that the classical mathematical framework of orthogonal designs can be applied to construct cliannel codes which have a simple decoding algorithm, while providing tlie full spatial diversity order. Space-block codes constructed in this way only exist for few sporadic values of n and therefore there is a need for a new mathematical theory. In this light, we introduce the theory of Generalzzed Deszgns which provides codes for both real and complex constellations for any number of transmit antennas. Using this theory, we construct space-block codes that achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as PAM. For any arbitrary complex constellation such as PSK and QAM, we construct space-block codes that achieve half of the maximum possible transmission rate for any number of transmit antennas. For tlie specific cases of two, three and four transmit antennas, we provide space-block codes that achieve respectively the whole, 3/4 and 3/4 of maximum possible transmission rate using arbitrary complex constellations. The best trade-off between tlie decoding delay and the number of transmit antennas is also computed and it is shown that the designed codes are optimal in this sense as well. Various fundamental problems are posed which are both inatliematically appealing and have immediate application to the design of a physical layer for wireless communication systems.}, Doi = {10.1109/ITW.1998.706408}, Key = {fds331054} } @article{fds326907, Author = {Naguib, AF and Calderbank, R}, Title = {Space-time coding and signal processing for high data rate wireless communications}, Journal = {WIRELESS COMMUNICATION TECHNOLOGIES: NEW MULTIMEDIA SYSTEMS}, Volume = {564}, Pages = {23-59}, Year = {2000}, ISBN = {0-7923-7900-4}, Key = {fds326907} } @article{fds235784, Author = {Das, S and Al-Dhahir, N and Diggavi, S and Calderbank, R and IEEE}, Title = {Opportunistic space-time block codes}, Pages = {2025-2029}, Year = {2005}, ISBN = {0-7803-9152-7}, ISSN = {1090-3038}, url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000235046902131&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92}, Key = {fds235784} } @article{fds235785, Author = {Calderbank, R and Das, S and Al-Dhahir, N and Diggavi, S and IEEE}, Title = {A novel full-rate full-diversity STBC with application to WiMAX}, Pages = {1791-1795}, Year = {2005}, ISBN = {0-7803-9152-7}, ISSN = {1090-3038}, url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000235046902082&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92}, Key = {fds235785} } @article{fds322368, Author = {Souvik, D and Thangaraj, A and McLaughlin, SW and Calderbank, AR}, Title = {Linear-time decodable secrecy codes for binary erasure wiretap channels}, Journal = {43rd Annual Allerton Conference on Communication, Control and Computing 2005}, Volume = {3}, Pages = {1548-1556}, Year = {2005}, Month = {January}, ISBN = {9781604234916}, Abstract = {In this paper we consider encoder and decoder design for codes achieving perfect secrecy on the wiretap channel. We consider the special case of a noiseless main channel and binary erasure channel (BEC) as the wiretapper's channel and show that it is possible to construct linear-time decodable secrecy codes based on LDPC codes that achieve perfect secrecy.}, Key = {fds322368} } @article{fds322370, Author = {Diggavi, S and Dusad, S and Calderbank, AR and Al-Dhahir, N}, Title = {On embedded diversity codes}, Journal = {43rd Annual Allerton Conference on Communication, Control and Computing 2005}, Volume = {2}, Pages = {1046-1055}, Year = {2005}, Month = {January}, ISBN = {9781604234916}, Abstract = {Diversity-embedded codes for fading channels are high-rate codes that are de-signed so that they have a high-diversity code embedded within them [3, 4]. This is equivalent to coding the data into two streams such that the high-priority stream has higher r eliability (designed in terms of diversity order) than the low-priority stream. These codes also allow a form of opportunistic communication where the high-rate code opportunistically takes advantage of good channel realizations whereas the embedded high-diversity code ensures that at least part of the infor-mation is received reliably. In this paper we give the design for a class of such codes for a fixed transmit alphabet constraint. These constructions are a natural generalization of multilevel codes to diversity embedding. These codes give prov-able performance guarantees by using binary matrices with rank guarantees as the building blocks to generate the desired diversity embedding in the complex do-main. We also investigate the systems implications of these codes by examining its applications to unequal error protection, rate opportunism and packet delay optimization. Preliminary results in these applications demonstrate that diversity-embedded codes can outperform traditional single-layer codes in moderate SNR regimes.}, Key = {fds322370} } @article{fds322369, Author = {Ashikhmin, A and Calderbank, AR}, Title = {The first order space-time reed-muller codes}, Journal = {43rd Annual Allerton Conference on Communication, Control and Computing 2005}, Volume = {2}, Pages = {1086-1095}, Year = {2005}, Month = {January}, ISBN = {9781604234916}, Abstract = {We present a family of Space-Time codes for the noncoherent MIMO channel. These space-time codes are strongly related to standard binary fist order Reed-Muller codes. In particular, their decoder can be built from several parallel decoders of first order Reed-Muller codes. We show that these codes allow transmission with rates close to the MIMO noncoherent unitary space-time codes capacity in the low signal to noise ratio (SNR) regime.}, Key = {fds322369} } @article{fds326904, Author = {Wu, Y and Calderbank, R and IEEE}, Title = {Code Diversity in Multiple Antenna Wireless Communication}, Journal = {2008 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY PROCEEDINGS, VOLS 1-6}, Pages = {1078-1082}, Year = {2008}, ISBN = {978-1-4244-2256-2}, url = {http://dx.doi.org/10.1109/ISIT.2008.4595153}, Doi = {10.1109/ISIT.2008.4595153}, Key = {fds326904} } @article{fds326901, Author = {Zoltowski, MD and Qureshi, TR and Calderbank, R and IEEE}, Title = {Channel Estimation for MIMO-OFDM using Complementary Codes}, Journal = {IEEE Radio and Wireless Symposium, RWS}, Pages = {151-+}, Year = {2009}, ISBN = {978-1-4244-2698-0}, Key = {fds326901} } @article{fds326902, Author = {Calderbank, R and Howard, S and Jafarpour, S and IEEE}, Title = {A Sublinear Algorithm for Sparse Reconstruction with (2) Recovery Guarantees}, Journal = {2009 3RD IEEE INTERNATIONAL WORKSHOP ON COMPUTATIONAL ADVANCES IN MULTI-SENSOR ADAPTIVE PROCESSING (CAMSAP)}, Pages = {209-212}, Year = {2009}, Key = {fds326902} } @article{fds326903, Author = {Chi, Y and Calderbank, R and Pezeshki, A and IEEE}, Title = {Golay Complementary Waveforms for Sparse Delay-Doppler Radar Imaging}, Journal = {2009 3RD IEEE INTERNATIONAL WORKSHOP ON COMPUTATIONAL ADVANCES IN MULTI-SENSOR ADAPTIVE PROCESSING (CAMSAP)}, Pages = {177-180}, Year = {2009}, Key = {fds326903} } @article{fds326899, Author = {Harms, A and Bajwa, WU and Calderbank, R and IEEE}, Title = {Shaping the Power Spectra of Bipolar Sequences with Application to Sub-Nyquist Sampling}, Journal = {2013 IEEE 5TH INTERNATIONAL WORKSHOP ON COMPUTATIONAL ADVANCES IN MULTI-SENSOR ADAPTIVE PROCESSING (CAMSAP 2013)}, Pages = {236-+}, Year = {2013}, ISBN = {978-1-4673-3144-9}, Key = {fds326899} } @article{fds326900, Author = {Harms, A and Bajwa, WU and Calderbank, R and IEEE}, Title = {Resource-Efficient Parametric Recovery of Linear Time-Varying Systems}, Journal = {2013 IEEE 5TH INTERNATIONAL WORKSHOP ON COMPUTATIONAL ADVANCES IN MULTI-SENSOR ADAPTIVE PROCESSING (CAMSAP 2013)}, Pages = {200-+}, Year = {2013}, ISBN = {978-1-4673-3144-9}, Key = {fds326900} } @article{fds235750, Author = {Wang, L and Razi, A and Dias Rodrigues and M and Calderbank, R and Carin, L}, Title = {Nonlinear information-theoretic compressive measurement design}, Journal = {31st International Conference on Machine Learning, ICML 2014}, Volume = {4}, Pages = {2896-2907}, Year = {2014}, Month = {January}, ISBN = {9781634393973}, Abstract = {Copyright © (2014) by the International Machine Learning Society (IMLS) All rights reserved. We investigate design of general nonlinear functions for mapping high-dimensional data into a lower-dimensional (compressive) space. The nonlinear measurements are assumed contaminated by additive Gaussian noise. Depending on the application, we are either interested in recovering the high-dimensional data from the nonlinear compressive measurements, or performing classification directly based on these measurements. The latter case corresponds to classification based on nonlinearly constituted and noisy features. The nonlinear measurement functions are designed based on constrained mutual- information optimization. New analytic results are developed for the gradient of mutual information in this setting, for arbitrary input-signal statistics. We make connections to kernel-based methods, such as the support vector machine. Encouraging results are presented on multiple datasets, for both signal recovery and classification. The nonlinear approach is shown to be particularly valuable in high-noise scenarios.}, Key = {fds235750} } @article{fds235744, Author = {Harms, A and Bajwa, W and Calderbank, R}, Title = {Efficient linear time-varying system identification using chirp waveforms}, Journal = {Conference Record of the Asilomar Conference on Signals, Systems and Computers}, Volume = {2015-April}, Pages = {854-858}, Year = {2015}, Month = {January}, ISBN = {9781479982974}, ISSN = {1058-6393}, url = {http://dx.doi.org/10.1109/ACSSC.2014.7094572}, Abstract = {© 2014 IEEE. Linear, time-varying (LTV) systems are operators composed of time shifts, frequency shifts, and complex amplitude scalings that act on continuous finite-energy waveforms. This paper builds upon a novel, resource-efficient method previously proposed by the authors for identifying the parametric description of such systems from the sampled response to linear frequency modulated (LFM) waveforms. If the LTV operator is probed with a sufficiently diverse set of LFM pulses, more LFM pulses than reflectors, then the system can be identified with high accuracy. The accuracy is shown to be proportional to the uncertainty in the estimated frequencies and confirmed with numerical experiments.}, Doi = {10.1109/ACSSC.2014.7094572}, Key = {fds235744} } @article{fds322362, Author = {Xian, Y and Thompson, A and Qiu, Q and Nolte, L and Nowacek, D and Lu, J and Calderbank, R}, Title = {Classification of whale vocalizations using the Weyl transform}, Journal = {IEEE International Conference on Acoustics Speech and Signal Processing}, Volume = {2015-August}, Pages = {773-777}, Year = {2015}, Month = {January}, ISBN = {9781467369978}, url = {http://dx.doi.org/10.1109/ICASSP.2015.7178074}, Abstract = {© 2015 IEEE. In this paper, we apply the Weyl transform to represent the vocalization of marine mammals. In contrast to other popular representation methods, such as the MFCC and the Chirplet transform, the Weyl transform captures the global information of signals. This is especially useful when the signal has low order polynomial phase. We can reconstruct the signal from the coefficients obtained from the Weyl transform, and perform classification based on these coefficients. Experimental results show that classification using features extracted from the Weyl transform outperforms the MFCC and the Chirplet transform on our collected whales data.}, Doi = {10.1109/ICASSP.2015.7178074}, Key = {fds322362} } @article{fds322363, Author = {Huang, J and Qiu, Q and Calderbank, R and Rodrigues, M and Sapiro, G}, Title = {Alignment with intra-class structure can improve classification}, Journal = {IEEE International Conference on Acoustics Speech and Signal Processing}, Volume = {2015-August}, Pages = {1921-1925}, Year = {2015}, Month = {January}, ISBN = {9781467369978}, url = {http://dx.doi.org/10.1109/ICASSP.2015.7178305}, Abstract = {© 2015 IEEE. High dimensional data is modeled using low-rank subspaces, and the probability of misclassification is expressed in terms of the principal angles between subspaces. The form taken by this expression motivates the design of a new feature extraction method that enlarges inter-class separation, while preserving intra-class structure. The method can be tuned to emphasize different features shared by members within the same class. Classification performance is compared to that of state-of-the-art methods on synthetic data and on the real face database. The probability of misclassification is decreased when intra-class structure is taken into account.}, Doi = {10.1109/ICASSP.2015.7178305}, Key = {fds322363} } @article{fds322364, Author = {Huang, J and Yuan, X and Calderbank, R}, Title = {Multi-scale Bayesian reconstruction of compressive X-ray image}, Journal = {IEEE International Conference on Acoustics Speech and Signal Processing}, Volume = {2015-August}, Pages = {1618-1622}, Year = {2015}, Month = {January}, ISBN = {9781467369978}, url = {http://dx.doi.org/10.1109/ICASSP.2015.7178244}, Abstract = {© 2015 IEEE. A novel multi-scale dictionary based Bayesian reconstruction algorithm is proposed for compressive X-ray imaging, which encodes the material's spectrum by Poisson measurements. Inspired by recently developed compressive X-ray imaging systems [1], th is work aims to recover the material's spectrum from the compressive coded image by leveraging a reference spectrum library. Instead of directly using the huge and redundant library as a dictionary, which is cumbersome in computation and difficult for selecting those active dictionary atoms, a multi-scale tree structured dictionary is refined from the spectrum library, and following this a Bayesian reconstruction algorithm is developed. Experimental results on real data demonstrate superior performance in comparison with traditional methods.}, Doi = {10.1109/ICASSP.2015.7178244}, Key = {fds322364} } @article{fds322365, Author = {Yuan, X and Huang, J and Calderbank, R}, Title = {Polynomial-phase signal direction-finding and source-tracking with a single acoustic vector sensor}, Journal = {IEEE International Conference on Acoustics Speech and Signal Processing}, Volume = {2015-August}, Pages = {2559-2563}, Year = {2015}, Month = {January}, ISBN = {9781467369978}, url = {http://dx.doi.org/10.1109/ICASSP.2015.7178433}, Abstract = {© 2015 IEEE. This paper introduces a new ESPRIT-based algorithm to estimate the direction-of-arrival of an arbitrary degree polynomial-phase signal with a single acoustic vector-sensor. The proposed time-invariant ESPRIT algorithm is based on a matrix-pencil pair derived from the time-delayed data-sets collected by a single acoustic vector-sensor. This approach requires neither a prior knowledge of the polynomial-phase signal's coefficients nor a prior knowledge of the polynomial-phase signal's frequency-spectrum. Furthermore, a preprocessing technique is proposed to incorporate the single-forgetting-factor algorithm and multiple-forgetting-factor adaptive tracking algorithm to track a polynomial-phase signal using one acoustic vector sensor. Simulation results verify the efficacy of the proposed direction finding and source tracking algorithms.}, Doi = {10.1109/ICASSP.2015.7178433}, Key = {fds322365} } @article{fds322366, Author = {Huang, J and Yuan, X and Calderbank, R}, Title = {Collaborative compressive X-ray image reconstruction}, Journal = {IEEE International Conference on Acoustics Speech and Signal Processing}, Volume = {2015-August}, Pages = {3282-3286}, Year = {2015}, Month = {January}, ISBN = {9781467369978}, url = {http://dx.doi.org/10.1109/ICASSP.2015.7178578}, Abstract = {© 2015 IEEE. The Poisson Factor Analysis (PFA) is applied to recover signals from a Poisson compressive sensing system. Motivated by the recently developed compressive X-ray imaging system, Coded Aperture Coherent Scatter Spectral Imaging (CACSSI) [1], we propose a new Bayesian reconstruction algorithm. The proposed Poisson-Gamma (PG) approach uses multiple measurements to refine our knowledge on both sensing matrix and background noise to overcome the uncertainties and inaccuracy of the hardware system. Therefore, a collaborative compressive X-ray image reconstruction algorithm is proposed under a Bayesian framework. Experimental results on real data show competitive performance in comparison with point estimation based methods.}, Doi = {10.1109/ICASSP.2015.7178578}, Key = {fds322366} } @article{fds326898, Author = {Michelusi, N and Nokleby, M and Mitra, U and Calderbank, R}, Title = {Dynamic spectrum estimation with minimal overhead via multiscale information exchange}, Journal = {2015 IEEE Global Communications Conference, GLOBECOM 2015}, Year = {2015}, Month = {January}, ISBN = {9781479959525}, url = {http://dx.doi.org/10.1109/GLOCOM.2014.7417532}, Abstract = {© 2015 IEEE. In this paper, a multiscale approach to spectrum sensing in cognitive cellular networks is analyzed. Observing that wireless interference decays with distance, and that estimating the entire spectrum occupancy across the network entails substantial energy cost and communication overhead, a protocol for distributed spectrum estimation is defined by which secondary users maintain fine-grained estimates of the spectrum occupancy of nearby cells, but coarse-grained estimates of that of distant cells. This is accomplished by arranging the cellular network into a hierarchy of increasingly coarser macro-cells and having secondary users fuse local spectrum estimates up the hierarchy. The spectrum occupancy is modeled as a Markov process, and the system is optimized by defining a probabilistic framework for spectrum sensing and information exchange that balances improvements in spectrum estimation against energy costs. The performance of the multiscale scheme is evaluated numerically, showing that it offers substantial improvements in energy efficiency over local estimation. On the other hand, it is shown that schemes that attempt to estimate the state of the whole network perform poorly, due to the excessive cost of performing information exchange with far away cells, and to the fact that, knowing the spectrum occupancy of distant cells, which experience low interference levels, results in a small increase in reward.}, Doi = {10.1109/GLOCOM.2014.7417532}, Key = {fds326898} } @article{fds326755, Author = {Huang, J and Qiu, Q and Calderbank, R and Sapiro, G}, Title = {Geometry-aware deep transform}, Journal = {Proceedings / IEEE International Conference on Computer Vision. IEEE International Conference on Computer Vision}, Volume = {2015 International Conference on Compute}, Pages = {4139-4147}, Year = {2015}, Month = {February}, ISBN = {9781467383912}, url = {http://dx.doi.org/10.1109/ICCV.2015.471}, Abstract = {© 2015 IEEE. Many recent efforts have been devoted to designing sophisticated deep learning structures, obtaining revolutionary results on benchmark datasets. The success of these deep learning methods mostly relies on an enormous volume of labeled training samples to learn a huge number of parameters in a network, therefore, understanding the generalization ability of a learned deep network cannot be overlooked, especially when restricted to a small training set, which is the case for many applications. In this paper, we propose a novel deep learning objective formulation that unifies both the classification and metric learning criteria. We then introduce a geometry-aware deep transform to enable a non-linear discriminative and robust feature transform, which shows competitive performance on small training sets for both synthetic and real-world data. We further support the proposed framework with a formal (K)-robustness analysis.}, Doi = {10.1109/ICCV.2015.471}, Key = {fds326755} } @article{fds326894, Author = {Vahid, A and Calderbank, R}, Title = {Impact of local delayed CSIT on the capacity region of the two-user interference channel}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Volume = {2015-June}, Pages = {2421-2425}, Year = {2015}, Month = {September}, ISBN = {9781467377041}, url = {http://dx.doi.org/10.1109/ISIT.2015.7282890}, Abstract = {© 2015 IEEE. The coherence time of a wireless channel is often smaller than the delay with which channel state information is available at transmitters. In this paper, we aim to find the most important subset of the channel state information that transmitters need to learn with delay. We characterize the capacity region of the two-user interference channel with local delayed channel state information at transmitters. We propose a transmission strategy that only relies on the delayed knowledge of the outgoing links at each transmitter and achieves the outer-bound for the scenario in which transmitters learn the entire channel state with delay. We also show that the delayed knowledge of the outgoing links is the minimum delayed knowledge that is required to outperform the no knowledge assumption.}, Doi = {10.1109/ISIT.2015.7282890}, Key = {fds326894} } @article{fds326895, Author = {Sokolić, J and Renna, F and Calderbank, R and Rodrigues, MRD}, Title = {Mismatch in the classification of linear subspaces: Upper bound to the probability of error}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Volume = {2015-June}, Pages = {2201-2205}, Year = {2015}, Month = {September}, ISBN = {9781467377041}, url = {http://dx.doi.org/10.1109/ISIT.2015.7282846}, Abstract = {© 2015 IEEE. This paper studies the performance associated with the classification of linear subspaces corrupted by noise with a mismatched classifier. In particular, we consider a problem where the classifier observes a noisy signal, the signal distribution conditioned on the signal class is zero-mean Gaussian with low-rank covariance matrix, and the classifier knows only the mismatched parameters in lieu of the true parameters. We derive an upper bound to the misclassification probability of the mismatched classifier and characterize its behaviour. Specifically, our characterization leads to sharp sufficient conditions that describe the absence of an error floor in the low-noise regime, and that can be expressed in terms of the principal angles and the overlap between the true and the mismatched signal subspaces.}, Doi = {10.1109/ISIT.2015.7282846}, Key = {fds326895} } @article{fds326896, Author = {Beirami, A and Calderbank, R and Duffy, K and Medard, M}, Title = {Quantifying computational security subject to source constraints, guesswork and inscrutability}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Volume = {2015-June}, Pages = {2757-2761}, Year = {2015}, Month = {September}, ISBN = {9781467377041}, url = {http://dx.doi.org/10.1109/ISIT.2015.7282958}, Abstract = {© 2015 IEEE. Guesswork forms the mathematical framework for quantifying computational security subject to brute-force determination by query. In this paper, we consider guesswork subject to a per-symbol Shannon entropy budget. We introduce inscrutability rate as the asymptotic rate of increase in the exponential number of guesses required of an adversary to determine one or more secret strings. We prove that the inscrutability rate of any string-source supported on a finite alphabet χ, if it exists, lies between the per-symbol Shannon entropy constraint and log χ. We further prove that the inscrutability rate of any finite-order Markov string-source with hidden statistics remains the same as the unhidden case, i.e., the asymptotic value of hiding the statistics per each symbol is vanishing. On the other hand, we show that there exists a string-source that achieves the upper limit on the inscrutability rate, i.e., log χ, under the same Shannon entropy budget.}, Doi = {10.1109/ISIT.2015.7282958}, Key = {fds326896} } @article{fds326897, Author = {Tamo, I and Barg, A and Goparaju, S and Calderbank, R}, Title = {Cyclic LRC codes and their subfield subcodes}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Volume = {2015-June}, Pages = {1262-1266}, Year = {2015}, Month = {September}, ISBN = {9781467377041}, url = {http://dx.doi.org/10.1109/ISIT.2015.7282658}, Abstract = {© 2015 IEEE. We consider linear cyclic codes with the locality property, or locally recoverable codes (LRC codes). A family of LRC codes that generalizes the classical construction of Reed-Solomon codes was constructed in a recent paper by I. Tamo and A. Barg (IEEE Trans. IT, no. 8, 2014). In this paper we focus on the optimal cyclic codes that arise from the general construction. We give a characterization of these codes in terms of their zeros, and observe that there are many equivalent ways of constructing optimal cyclic LRC codes over a given field. We also study subfield subcodes of cyclic LRC codes (BCH-like LRC codes) and establish several results about their locality and minimum distance.}, Doi = {10.1109/ISIT.2015.7282658}, Key = {fds326897} } @article{fds326758, Author = {Renna, F and Wang, L and Yuan, X and Yang, J and Reeves, G and Calderbank, R and Carin, L and Rodrigues, MRD}, Title = {Classification and reconstruction of compressed GMM signals with side information}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Volume = {2015-June}, Pages = {994-998}, Year = {2015}, Month = {September}, ISBN = {9781467377041}, url = {http://dx.doi.org/10.1109/ISIT.2015.7282604}, Abstract = {© 2015 IEEE. This paper offers a characterization of performance limits for classification and reconstruction of high-dimensional signals from noisy compressive measurements, in the presence of side information. We assume the signal of interest and the side information signal are drawn from a correlated mixture of distributions/components, where each component associated with a specific class label follows a Gaussian mixture model (GMM). We provide sharp sufficient and/or necessary conditions for the phase transition of the misclassification probability and the reconstruction error in the low-noise regime. These conditions, which are reminiscent of the well-known Slepian-Wolf and Wyner-Ziv conditions, are a function of the number of measurements taken from the signal of interest, the number of measurements taken from the side information signal, and the geometry of these signals and their interplay.}, Doi = {10.1109/ISIT.2015.7282604}, Key = {fds326758} } @article{fds326757, Author = {Eslami, A and Velasco, A and Vahid, A and Mappouras, G and Calderbank, R and Sorin, DJ}, Title = {Writing without disturb on phase change memories by integrating coding and layout design}, Journal = {ACM International Conference Proceeding Series}, Volume = {05-08-October-2015}, Pages = {71-77}, Year = {2015}, Month = {October}, ISBN = {9781450336048}, url = {http://dx.doi.org/10.1145/2818950.2818962}, Abstract = {© 2015 ACM. We integrate coding techniques and layout design to elimi- nate write-disturb in phase change memories (PCMs), while enhancing lifetime and host-visible capacity. We first pro- pose a checkerboard confguration for cell layout to elimi- nate write-disturb while doubling the memory lifetime. We then introduce two methods to jointly design Write-Once- Memory (WOM) codes and layout. The first WOM-layout design improves the lifetime by more than double without compromising the host-visible capacity. The second design applies WOM codes to even more dense layouts to achieve both lifetime and capacity gains. The constructions demon- strate that substantial improvements to lifetime and host- visible capacity are possible by co-designing coding and cell layout in PCM.}, Doi = {10.1145/2818950.2818962}, Key = {fds326757} } @article{fds326893, Author = {Nokleby, M and Beirami, A and Calderbank, R}, Title = {A rate-distortion framework for supervised learning}, Journal = {IEEE International Workshop on Machine Learning for Signal Processing : [proceedings]. IEEE International Workshop on Machine Learning for Signal Processing}, Volume = {2015-November}, Year = {2015}, Month = {November}, ISBN = {9781467374545}, url = {http://dx.doi.org/10.1109/MLSP.2015.7324319}, Abstract = {© 2015 IEEE. An information-theoretic framework is presented for bounding the number of samples needed for supervised learning in a parametric Bayesian setting. This framework is inspired by an analogy with rate-distortion theory, which characterizes tradeoffs in the lossy compression of random sources. In a parametric Bayesian environment, the maximum a posteriori classifier can be viewed as a random function of the model parameters. Labeled training data can be viewed as a finite-rate encoding of that source, and the excess loss due to using the learned classifier instead of the MAP classifier can be viewed as distortion. A strict bound on the loss-measured in terms of the expected total variation-is derived, providing a minimum number of training samples needed to drive the expected total variation to within a specified tolerance. The tightness of this bound is demonstrated on the classification of Gaus-sians, for which one can derive closed-form expressions for the bound.}, Doi = {10.1109/MLSP.2015.7324319}, Key = {fds326893} } @article{fds326892, Author = {Thompson, A and Calderbank, R}, Title = {Compressive imaging using fast transform coding}, Journal = {Proceedings of SPIE - The International Society for Optical Engineering}, Volume = {9992}, Year = {2016}, Month = {January}, ISBN = {9781510603882}, url = {http://dx.doi.org/10.1117/12.2239999}, Abstract = {© 2016 SPIE. We propose deterministic sampling strategies for compressive imaging based on Delsarte-Goethals frames. We show that these sampling strategies result in multi-scale measurements which can be related to the 2D Haar wavelet transform. We demonstrate the effectiveness of our proposed strategies through numerical experiments.}, Doi = {10.1117/12.2239999}, Key = {fds326892} } @article{fds326891, Author = {Goparaju, S and Rouayheb, SE and Calderbank, R}, Title = {Can linear minimum storage regenerating codes be universally secure?}, Journal = {Conference Record of the Asilomar Conference on Signals, Systems and Computers}, Volume = {2016-February}, Pages = {549-553}, Year = {2016}, Month = {February}, ISBN = {9781467385763}, url = {http://dx.doi.org/10.1109/ACSSC.2015.7421189}, Abstract = {© 2015 IEEE. We study the problem of making a distributed storage system information-theoretically secure against a passive eavesdropper, and aim to characterize coding schemes that are universally secure for up to a given number of eavesdropped nodes. Specifically, we consider minimum storage regenerating (MSR) codes and ask the following question: For an MSR code where a failed node is repaired using all the remaining nodes, is it possible to simultaneously be optimally secure using a single linear coding scheme? We define a pareto-optimality associated with this simultaneity and show that there exists at least one linear coding scheme that is pareto-optimal.}, Doi = {10.1109/ACSSC.2015.7421189}, Key = {fds326891} } @article{fds326888, Author = {Beirami, A and Calderbank, R and Christiansen, M and Duffy, K and Makhdoumi, A and Medard, M}, Title = {A geometric perspective on guesswork}, Journal = {2015 53rd Annual Allerton Conference on Communication, Control, and Computing, Allerton 2015}, Pages = {941-948}, Year = {2016}, Month = {April}, ISBN = {9781509018239}, url = {http://dx.doi.org/10.1109/ALLERTON.2015.7447109}, Abstract = {© 2015 IEEE. Guesswork is the position at which a random string drawn from a given probability distribution appears in the list of strings ordered from the most likely to the least likely. We define the tilt operation on probability distributions and show that it parametrizes an exponential family of distributions, which we refer to as the tilted family of the source. We prove that two sources result in the same guesswork, i.e., the same ordering from most likely to least likely on all strings, if and only if they belong to the same tilted family. We also prove that the strings whose guesswork is smaller than a given string are concentrated on the tilted family. Applying Laplace's method, we derive precise approximations on the distribution of guesswork on i.i.d. sources. The simulations show a good match between the approximations and the actual guesswork for i.i.d. sources.}, Doi = {10.1109/ALLERTON.2015.7447109}, Key = {fds326888} } @article{fds326889, Author = {Vahid, A and Shomorony, I and Calderbank, R}, Title = {Informational bottlenecks in two-unicast wireless networks with delayed CSIT}, Journal = {2015 53rd Annual Allerton Conference on Communication, Control, and Computing, Allerton 2015}, Pages = {1256-1263}, Year = {2016}, Month = {April}, ISBN = {9781509018239}, url = {http://dx.doi.org/10.1109/ALLERTON.2015.7447152}, Abstract = {© 2015 IEEE. We study the impact of delayed channel state information at the transmitters (CSIT) in two-unicast wireless networks with a layered topology and arbitrary connectivity. We introduce a technique to obtain outer bounds to the degrees-of-freedom (DoF) region through the new graph-theoretic notion of bottleneck nodes. Such nodes act as informational bottlenecks only under the assumption of delayed CSIT, and imply asymmetric DoF bounds of the form mD1 + D2 ≤ m. Combining this outer-bound technique with new achievability schemes, we characterize the sum DoF of a class of two-unicast wireless networks, which shows that, unlike in the case of instantaneous CSIT, the DoF of two-unicast networks with delayed CSIT can take an infinite set of values.}, Doi = {10.1109/ALLERTON.2015.7447152}, Key = {fds326889} } @article{fds326753, Author = {Wang, L and Renna, F and Yuan, X and Rodrigues, M and Calderbank, R and Carin, L}, Title = {A general framework for reconstruction and classification from compressive measurements with side information}, Journal = {IEEE International Conference on Acoustics Speech and Signal Processing}, Volume = {2016-May}, Pages = {4239-4243}, Year = {2016}, Month = {May}, ISBN = {9781479999880}, url = {http://dx.doi.org/10.1109/ICASSP.2016.7472476}, Abstract = {© 2016 IEEE. We develop a general framework for compressive linear-projection measurements with side information. Side information is an additional signal correlated with the signal of interest. We investigate the impact of side information on classification and signal recovery from low-dimensional measurements. Motivated by real applications, two special cases of the general model are studied. In the first, a joint Gaussian mixture model is manifested on the signal and side information. The second example again employs a Gaussian mixture model for the signal, with side information drawn from a mixture in the exponential family. Theoretical results on recovery and classification accuracy are derived. The presence of side information is shown to yield improved performance, both theoretically and experimentally.}, Doi = {10.1109/ICASSP.2016.7472476}, Key = {fds326753} } @article{fds326885, Author = {Nokleby, M and Beirami, A and Calderbank, R}, Title = {Rate-distortion bounds on Bayes risk in supervised learning}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Volume = {2016-August}, Pages = {2099-2103}, Year = {2016}, Month = {August}, ISBN = {9781509018062}, url = {http://dx.doi.org/10.1109/ISIT.2016.7541669}, Abstract = {© 2016 IEEE. An information-theoretic framework is presented for estimating the number of labeled samples needed to train a classifier in a parametric Bayesian setting. Ideas from rate-distortion theory are used to derive bounds for the average L 1 or L ∞ distance between the learned classifier and the true maximum a posteriori classifier in terms of familiar information-theoretic quantities and the number of training samples available. The maximum a posteriori classifier is viewed as a random source, labeled training data are viewed as a finite-rate encoding of the source, and the L 1 or L ∞ Bayes risk is viewed as the average distortion. The result is a framework dual to the well-known probably approximately correct (PAC) framework. PAC bounds characterize worst-case learning performance of a family of classifiers whose complexity is captured by the Vapnik-Chervonenkis (VC) dimension. The rate-distortion framework, on the other hand, characterizes the average-case performance of a family of data distributions in terms of a quantity called the interpolation dimension, which represents the complexity of the family of data distributions. The resulting bounds do not suffer from the pessimism typical of the PAC framework, particularly when the training set is small.}, Doi = {10.1109/ISIT.2016.7541669}, Key = {fds326885} } @article{fds326886, Author = {Vahid, A and Calderbank, R}, Title = {When does spatial correlation add value to delayed channel state information?}, Journal = {IEEE International Symposium on Information Theory - Proceedings}, Volume = {2016-August}, Pages = {2624-2628}, Year = {2016}, Month = {August}, ISBN = {9781509018062}, url = {http://dx.doi.org/10.1109/ISIT.2016.7541774}, Abstract = {© 2016 IEEE. Fast fading wireless networks with delayed knowledge of the channel state information have received significant attention in recent years. An exception is networks where channels are spatially correlated. This paper characterizes the capacity region of two-user erasure interference channels with delayed knowledge of the channel state information and spatially correlated channels. There are instances where spatial correlation eliminates any potential gain from delayed channel state information and instances where it enables the same performance that is possible with instantaneous knowledge of channel state. The key is an extremal entropy inequality for spatially correlated channels that separates the two types of instances. It is also shown that to achieve the capacity region, each transmitter only needs to rely on the delayed knowledge of the channels to which it is connected.}, Doi = {10.1109/ISIT.2016.7541774}, Key = {fds326886} } @article{fds326752, Author = {Mappouras, G and Vahid, A and Calderbank, R and Sorin, DJ}, Title = {Methuselah flash: Rewriting codes for extra long storage lifetime}, Journal = {Proceedings - 46th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, DSN 2016}, Pages = {180-191}, Year = {2016}, Month = {September}, ISBN = {9781467388917}, url = {http://dx.doi.org/10.1109/DSN.2016.25}, Abstract = {© 2016 IEEE. Motivated by embedded systems and datacenters that require long-life components, we extend the lifetime of Flash memory using rewriting codes that allow for multiple writes to a page before it needs to be erased. Although researchers have previously explored rewriting codes for this purpose, we make two significant contributions beyond prior work. First, we remove the assumption of idealized - and unrealistically optimistic - Flash cells used in prior work on endurance codes. Unfortunately, current Flash technology has a non-ideal interface, due to its underlying physical design, and does not, for example, allow all seemingly possible increases in a cell's level. We show how to provide the ideal multi-level cell interface, by developing a virtual Flash cell, and we evaluate its impact on existing endurance codes. Our second contribution is our development of novel endurance codes, called Methuselah Flash Codes (MFC), that provide better cost/lifetime trade-offs than previously studied codes.}, Doi = {10.1109/DSN.2016.25}, Key = {fds326752} } @article{fds326751, Author = {Kumar, S and Calderbank, R and Pfister, HD}, Title = {Beyond double transitivity: Capacity-achieving cyclic codes on erasure channels}, Journal = {2016 IEEE Information Theory Workshop, ITW 2016}, Pages = {241-245}, Year = {2016}, Month = {October}, ISBN = {9781509010905}, url = {http://dx.doi.org/10.1109/ITW.2016.7606832}, Abstract = {© 2016 IEEE. Recently, sequences of error-correcting codes with doubly-transitive permutation groups were shown to achieve capacity on erasure channels under symbol-wise maximum a posteriori (MAP) decoding. From this, it follows that Reed-Muller and primitive narrow-sense BCH codes achieve capacity in the same setting. In this article, we extend this result to a large family of cyclic codes by considering codes whose permutation groups satisfy a condition weaker than double transitivity. The article combines two simple technical contributions. First, we show that the transition width of a monotone boolean function is O(1/log k), where k is the size of the smallest orbit induced by its symmetry group. The proof is based on Talagrand's lower bound on influences for monotone boolean functions. Second, we consider the extrinsic information transfer (EXIT) function of an Fq-linear cyclic code whose blocklength N divides q t -1 and is coprime with q-1. We show that this EXIT function is a monotone boolean function whose symmetry group contains no orbits of size smaller than the smallest prime divisor of t. Combining these, we show that sequences of cyclic codes, whose blocklengths satisfy the above conditions, achieve capacity on the q-ary erasure channel if all prime divisors of t tend to infinity.}, Doi = {10.1109/ITW.2016.7606832}, Key = {fds326751} } @article{fds326750, Author = {Renna, F and Wang, L and Yuan, X and Yang, J and Reeves, G and Calderbank, R and Carin, L and Rodrigues, MRD}, Title = {Classification and Reconstruction of High-Dimensional Signals From Low-Dimensional Features in the Presence of Side Information}, Journal = {IEEE Transactions on Information Theory}, Volume = {62}, Number = {11}, Pages = {6459-6492}, Year = {2016}, Month = {November}, url = {http://dx.doi.org/10.1109/TIT.2016.2606646}, Doi = {10.1109/TIT.2016.2606646}, Key = {fds326750} } @article{fds326882, Author = {Reboredo, H and Renna, F and Calderbank, R and Rodrigues, MRD}, Title = {Bounds on the Number of Measurements for Reliable Compressive Classification}, Journal = {IEEE Transactions on Signal Processing}, Volume = {64}, Number = {22}, Pages = {5778-5793}, Year = {2016}, Month = {November}, url = {http://dx.doi.org/10.1109/TSP.2016.2599496}, Doi = {10.1109/TSP.2016.2599496}, Key = {fds326882} } @article{fds326881, Author = {Hadani, R and Rakib, S and Tsatsanis, M and Monk, A and Goldsmith, AJ and Molisch, AF and Calderbank, R}, Title = {Orthogonal time frequency space modulation}, Journal = {IEEE Wireless Communications and Networking Conference}, Year = {2017}, Month = {May}, ISBN = {9781509041831}, url = {http://dx.doi.org/10.1109/WCNC.2017.7925924}, Abstract = {© 2017 IEEE. A new two-dimensional modulation technique called Orthogonal Time Frequency Space (OTFS) modulation designed in the delay-Doppler domain is introduced. Through this design, which exploits full diversity over time and frequency, OTFS coupled with equalization converts the fading, time-varying wireless channel experienced by modulated signals such as OFDM into a time-independent channel with a complex channel gain that is roughly constant for all symbols. Thus, transmitter adaptation is not needed. This extraction of the full channel diversity allows OTFS to greatly simplify system operation and significantly improves performance, particular in systems with high Doppler, short packets, and large antenna arrays. Simulation results indicate at least several dB of block error rate performance improvement for OTFS over OFDM in all of these settings. In addition these results show that even at very high Dopplers (500 km/h), OTFS approaches channel capacity through linear scaling of throughput with the MIMO order, whereas the performance of OFDM under typical design parameters breaks down completely.}, Doi = {10.1109/WCNC.2017.7925924}, Key = {fds326881} } @article{fds332945, Author = {Cnaan-On, I and Harms, A and Krolik, JL and Calderbank, AR}, Title = {Run-length limited codes for backscatter communication}, Journal = {IEEE International Conference on Acoustics Speech and Signal Processing}, Pages = {6110-6114}, Year = {2017}, Month = {June}, ISBN = {9781509041176}, url = {http://dx.doi.org/10.1109/ICASSP.2017.7953330}, Abstract = {© 2017 IEEE. In backscatter communications, ultra-low power devices signal by modulating the reflection of radio frequency signals emitted from an external source. Unlike conventional one-way communication, the backscatter channel experiences unique self-interference and spread Doppler clutter. Run-length limited (RLL) codes provide a method for spectrum shaping that requires no hardware changes to the communicating devices. The proposed coding framework is suitable for any arbitrarily-shaped pulse train or continuous wave reader waveform. It exploits the unique channel Doppler spread statistics to offer a trade-off between interference rejection and data rate. Analysis shows that code rates of 1 and 4/5 are achievable when dealing with low spread Doppler channels, which is an improvement over the current rate 1/2 with current mainstream backscatter communication techniques. Simulation results with realistic channel assumptions are analyzed and discussed to confirm the theoretical analysis.}, Doi = {10.1109/ICASSP.2017.7953330}, Key = {fds332945} }