Sort-and-match algorithm for soft-decision decoding

Let a q-ary linear (n, k) code C be used over a memoryless channel. We design a decoding algorithm Ψ_N that splits the received block into two halves in n different ways. First, about √N error patterns are found on either half. Then the left- and right-hand lists are sorted out and matched to form codewords. Finally, the most probable codeword is chosen among at most n√N codewords obtained in all n trials. The algorithm can be applied to any linear code C and has complexity order of n³√N. For any N⩾q^n-k, the decoding error probability P_N exceeds at most 1+q^n-k/N times the probability P_Ψ (C) of maximum-likelihood decoding. For code rates R⩾1/2, the complexity order q^n-k/2 grows as square root of general trellis complexity q^min{n-k,k}. When used on quantized additive white Gaussian noise (AWGN) channels, the algorithm Ψ_N can provide maximum-likelihood decoding for most binary linear codes even when N has an exponential order of q^n-k