  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.
