Reed-Muller Codes Achieve Capacity on Erasure Channels

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...

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Bibliographic Details
Published in:	IEEE transactions on information theory Vol. 63; no. 7; pp. 4298 - 4316
Main Authors:	Kudekar, Shrinivas, Kumar, Santhosh, Mondelli, Marco, Pfister, Henry D., Sasoglu, Eren, Urbanke, Rüdiger L.
Format:	Journal Article
Language:	English
Published:	New York IEEE 01.07.2017 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Affine-invariant codes BCH codes Binary codes Boolean algebra Boolean functions capacity-achieving codes Codes Computers Convergence Decoding Electronic mail erasure channels EXIT functions Information transfer Linear codes MAP decoding monotone Boolean functions Parity check codes Permutations quadratic-residue codes Reed-Muller codes Symmetry Transfer functions
ISSN:	0018-9448, 1557-9654
Online Access:	Get full text
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