On the Voronoi neighbor ratio for binary linear block codes

Soft-decision decoding of block codes is regarded as the geometrical problem of identifying the Voronoi region within which a given input vector lies. A measure, called the neighbor ratio, is proposed to characterize how many facets a Voronoi region has. Theory and algorithms are presented to determine the neighbor ratio for binary linear block codes and results are given for several types of codes. An asymptotic analysis for long codes reveals that the neighbor ratio depends on whether the code rate is less than 1/2 or not. For rates below this threshold, all pairs of codewords tend to share a Voronoi facet; for higher rates, a relatively small fraction of them do.