2025/04/21 by Xiao Ma, Ma, Xiao
Computer Science · #Cellular Automata and Applications #Coding theory and cryptography #Error Correcting Code Techniques #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.2504.14842
openalex publication_date 2025/04/21 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28
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.