Suboptimal decoding of linear codes: partition technique

Abstract

General symmetric channels are introduced, and near-maximum-likelihood decoding in these channels is studied. First, we define a class of suboptimal decoding algorithms based on an incomplete search through the code trellis. It is proved that the decoding error probability of suboptimal decoding is bounded above for any q-ary code of length n and code rate r by twice the error probability of its maximum-likelihood decoding and tends to the latter as n grows. Second, we design a suboptimal trellis-like algorithm, which reduces the known decoding complexity of the order of q/sup n min (r,1-r)/ operations to that of q/sup nr(i-r)/ operations for all cyclic codes and virtually all long linear codes. We also consider the corresponding bounds for concatenated codes. An important corollary is that this suboptimal decoding can provide complexity below the lower bounds on trellis complexity at a negligible expense in terms of decoding error probability.