On Mutual Information-Based Optimal Quantizer Design


DÜLEK B.

IEEE COMMUNICATIONS LETTERS, vol.26, no.5, pp.1008-1011, 2022 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 26 Issue: 5
  • Publication Date: 2022
  • Doi Number: 10.1109/lcomm.2022.3153457
  • Journal Name: IEEE COMMUNICATIONS LETTERS
  • Journal Indexes: Science Citation Index Expanded, Scopus, PASCAL, Aerospace Database, Communication Abstracts, Compendex, INSPEC, Metadex, Civil Engineering Abstracts
  • Page Numbers: pp.1008-1011
  • Keywords: Quantization (signal), Mutual information, Probability distribution, Random variables, Distortion measurement, Distortion, Standards, Channel quantization, mutual information maximization, convex analysis

Abstract

The problem of optimal quantizer design that maximizes the mutual information between the input and the quantized output of a communication channel is considered. It is shown that an optimal quantizer exists which employs convex polytopes as its decision regions in the Euclidean space of likelihood ratios. This complements the previous results in the literature by presenting a new and intuitive proof, establishing a unified treatment of the most general case, extending the solution to continuous-input channels, and providing a characterization for the form of optimal decision rule based on likelihood ratios, whereas the previous results are expressed in terms of the posterior probabilities and depend on the channel input distribution. The result is corroborated with an analytical example employing the transmission of a spherically symmetric random vector source over an additive white Gaussian noise channel.