On Thresholding Quantizer Design for Mutual Information Maximization: Optimal Structures and Algorithms

Abstract

Consider a channel having the discrete input X that is corrupted by a continuous noise to produce the continuous-valued output U. A thresholding quantizer is then used to quantize the continuous-valued output U to the final discrete output V . One wants to design a thresholding quantizer that maximizes the mutual information between the input and the final quantized output I(X; V ). In this paper, the structure of optimal thresholding quantizer is established that finally results in two efficient algorithms having the time complexities O(NM + K log <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> (NM)) for finding the local optimal quantizer and O(K M log(NM)) for finding the global optimal quantizer where N, M, K are the size of input X, received output U and quantized output V , respectively. Both theoretical and numerical results are provided to verify our contributions.