Sequential Decoding of High-Rate Reed-Muller Codes

Abstract

A soft-input sequential decoder for Reed-Muller (RM) codes of length $2^{m}$ and order $m-3$ is proposed. The considered algorithm sequentially processes different permuted versions of the received vector using a decoder of an extended Hamming code, with permutations being selected on-the-fly from the RM codes' automorphism group based on soft information from a channel. It is shown that the proposed algorithm outperforms the recursive list decoder with similar computational complexity and achieves near maximum-likelihood decoding performance with reasonable computational complexity for RM codes of length 512 and 1024.