Math @ Duke

Publications [#235815] of Robert Calderbank
Papers Published
 Calderbank, AR; Seshadri, N, Multilevel codes for unequal error protection,
Ieee Transactions on Information Theory, vol. 39 no. 4
(July, 1993),
pp. 12341248 [doi]
(last updated on 2018/11/18)
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 6dB coding gain) for some fraction (for example, 25%) of the data while providing a coding gain of 12 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.


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

