Low-complexity quantization of discrete memoryless channels

Abstract

A quantizer design algorithm for discrete memory-less channels with non-binary inputs is given, when the objective is to maximize the mutual information between the channel input and quantizer output. The algorithm is the means algorithm, where the conventional Euclidean distance metric is replaced by the Kullback-Leibler divergence. When the channel input is non-binary, KL means algorithm has a significant complexity advantage over the currently best-known alternative, called greedy combining. While the KL means algorithm is suboptimal, it produces quantizer designs which have higher mutual information than greedy combining, particularly when the number of quantizer outputs is small, as shown by numerical evaluations.