On recursive decoding with sublinear complexity for Reed-Muller codes

Reed-Muller (RM) codes (m, r) of length 2^m are considered on a binary symmetric (BS) channel with high crossover error probability 1/2 -ε. For an arbitrarily small ε>0, new recursive decoding algorithms are designed that retrieve all information bits of RM codes of fixed order r with a vanishing error probability and sublinear complexity of order O(m^r+1). The algorithms utilize a vanishing fraction of the received symbols for both hard- and soft-decision decoding.