Abstract
A soft-input sequential decoder for Reed-Muller (RM) codes of length <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$2^{m}$</tex> and order <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$m-3$</tex> 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.
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