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 N that splits the received block into two halves in n different ways. First, about p N error patterns are found on either half. Then the leftand right-hand lists are sorted out and matched to form codewords. Finally, the most probable codeword is chosen among at most n p N codewords obtained in all n trials. The algorithm can be applied to any linear code C and has complexity order of n p N: For any N q , the decoding error probability PN exceeds at most 1 + q =N times the probability P (C) of maximum-likelihood decoding. For code rates R 1=2, the complexity order q k)=2 grows as square root of general trellis complexity q . When used on quantized additive white Gaussian noise (AWGN) channels, algorithm N can provide maximum-likelihood decoding for most binary linear codes even when N has exponential order of q .