Math @ Duke

Publications [#326795] of Henry Pfister
Papers Published
 Kudekar, S; Kumar, S; Mondelli, M; Pfister, HD; Sasoǧlu, E; Urbanke, RL, Reedmuller codes achieve capacity on erasure channels,
Ieee Transactions on Information Theory, vol. 63 no. 7
(July, 2017),
pp. 42984316, Institute of Electrical and Electronics Engineers (IEEE) [doi]
(last updated on 2019/07/22)
Abstract: © 2017 IEEE. We introduce a new approach to proving that a sequence of deterministic linear codes achieves capacity on an erasure channel under maximum a posteriori decoding. Rather than relying on the precise structure of the codes, our method exploits code symmetry. In particular, the technique applies to any sequence of linear codes where the blocklengths are strictly increasing, the code rates converge, and the permutation group of each code is doubly transitive. In other words, we show that symmetry alone implies nearoptimal performance. An important consequence of this result is that a sequence of ReedMuller codes with increasing blocklength and converging rate achieves capacity. This possibility has been suggested previously in the literature but it has only been proven for cases where the limiting code rate is 0 or 1. Moreover, these results extend naturally to all affineinvariant codes and, thus, to extended primitive narrowsense BCH codes. This also resolves, in the affirmative, the existence question for capacityachieving sequences of binary cyclic codes. The primary tools used in the proof are the sharp threshold property for symmetric monotone Boolean functions and the area theorem for extrinsic information transfer functions.


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