A Short Proof of Coding Theorems for Reed-Muller Codes Under a Mild Assumption
Information Theory
2025-04-24 v2 math.IT
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.
Cite
@article{arxiv.2504.14842,
title = {A Short Proof of Coding Theorems for Reed-Muller Codes Under a Mild Assumption},
author = {Xiao Ma},
journal= {arXiv preprint arXiv:2504.14842},
year = {2025}
}
Comments
12 pages, 1 figure