Voronoi regions for binary linear block codes

The Voronoi regions of a block code govern many aspects of the code’s performance on a Gaussian channel, and they are fundamental instruments in, for example, error probability analysis and soft decision decoding. This paper presents an efficient method to find the boundaries of the Voronoi regions for an arbitrary binary linear block code. Two theoretical results together lead to the Voronoi regions. First, it is shown that the question of Voronoi neighborship can be reduced into testing a simpler relation, called Gabriel neighborship. Second, a fast method to recognize Gabriel neighbors is proposed. These results are finally employed to describe the Voronoi regions for the Golay codes and several BCH codes, including Hamming codes.