Math @ Duke
|
Publications [#336893] of Vahid Tarokh
Papers Published
- Paterson, KG; Tarokh, V, On the existence and construction of good codes with low peak-to-average power ratios,
Hp Laboratories Technical Report no. 51
(April, 1999)
(last updated on 2023/06/01)
Abstract: The first lower bound on the peak-to-average power ratio (PAPR) of a constant energy code of a given length n, minimum Euclidean distance and rate is established. Conversely, using a non-constructive Varshamov-Gilbert style argument yields a lower bound on the achievable rate of a code of a given length, minimum Euclidean distance and maximum PAPR. The derivation of these bounds relies on a geometrical analysis of the PAPR of such a code. Further analysis shows that there exist asymptotically good codes whose PAPR is at most 8 log n. These bounds motivate the explicit construction of error-correcting codes with low PAPR. Bounds for exponential sums over Galois fields and rings are applied to obtain an upper bound of order (log n)2 on the PAPRs of a constructive class of codes, the trace codes. This class includes the binary simplex code, duals of binary, primitive BCH codes and a variety of their non-binary analogues. Some open problems are identified.
|
|
dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
| |
Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320
|
|