A Novel Method for the Design of Piecewise Linear Compressor Function based on the First Derivate Approximation of Optimal Compressor Function in the Case of Gaussian Source

Abstract

This paper proposes a novel method for the design of a piecewise linear optimal compressor function for the Gaussian source. It is well known that by using the inverse optimal compressor function in the case of Gaussian probability density function, it is not possible to derive closed-form expressions for the decision thresholds and representation levels of a quantizer. Accordingly, the method we propose implies some approximations contributing to a simple design solution of the piecewise uniform quantizer, as well as to the closed-form expression for its distortion computation. Our quantizer assumes an equidistant support region division into segments. For the proposed quantizer, we study the influence of the chosen segment number on the signal to quantization noise ratio as well as on the design complexity. Based on this analysis, we decided on the conditions under which the proposed quantizer is the most suitable solution for practical implementation.