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 /spl Psi//sub N/ that splits the received block into two halves in n different ways. First, about /spl radic/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/spl radic/N codewords obtained in all n trials. The algorithm can be applied to any linear code C and has complexity order of n/sup 3//spl radic/N. For any N/spl ges/q/sup n-k/, the decoding error probability P/sub N/ exceeds at most 1+q/sup n-k//N times the probability P/sub /spl Psi//(C) of maximum-likelihood decoding. For code rates R/spl ges/1/2, the complexity order q/sup n-k/2/ grows as square root of general trellis complexity q/sup min{n-k,k}/. When used on quantized additive white Gaussian noise (AWGN) channels, the algorithm /spl Psi//sub N/ can provide maximum-likelihood decoding for most binary linear codes even when N has an exponential order of q/sup n-k/.