Sequential decoding of high-rate Reed-Muller codes

01/27/2021

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by   Mikhail Kamenev, et al.

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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.