A companding approximation for the statistical divergence of quantized data

Asymptotic analysis using companding approximations has proven to be a very useful technique for the performance analysis and design of minimum-distortion data quantizers. However, when quantized data is to be used for inferential (e.g., detection or estimation) purposes, the use of distortion-based performance criteria is inappropriate since the measures of quality in such problems are usually based on quantities such as error probability or mean-square estimation error. In this paper we use companding approximations to derive asymptotic criteria for the evaluation of quantizer performance and the design of optimum quantizers based on statistical measures of divergence at the output of the quantizer. Several applications of these results to signal detection and parameter estimation are considered.