A Short Proof of Coding Theorems for Reed-Muller Codes Under a Mild Assumption

Xiao Ma

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arXiv · 2504.14842

A Short Proof of Coding Theorems for Reed-Muller Codes Under a Mild Assumption

Xiao Ma

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Abstract

In this paper, by treating Reed-Muller (RM) codes as a special class of low-density parity-check (LDPC) codes and assuming that sub-blocks of the parity-check matrix are randomly interleaved to each other as Gallager's codes, we present a short proof that RM codes are entropy-achieving as source coding for Bernoulli sources and capacity-achieving as channel coding for binary memoryless symmetric (BMS) channels, also known as memoryless binary-input output-symmetric (BIOS) channels, in terms of bit error rate (BER) under maximum-likelihood (ML) decoding.

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Xiao Ma. 2025-04-21. A Short Proof of Coding Theorems for Reed-Muller Codes Under a Mild Assumption. https://arxiv.org/abs/2504.14842

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