On the Rate Distortion Function of Certain Sources with a Proportional Mean-Square Error Distortion Measure

TL;DR

This paper derives new bounds on the rate distortion function for certain non-Gaussian sources under a proportional-weighted MSE measure, analyzing how the rate distortion function grows with small distortions and comparing Gaussian and non-Gaussian sources.

Contribution

It introduces new bounds on the rate distortion function for non-Gaussian sources with proportional-weighted MSE and analyzes the growth of this function for small distortions.

Findings

Derived bounds on rate distortion function for non-Gaussian sources.

Showed the growth of rate distortion function for small distortions.

Compared rate distortion functions of Gaussian and non-Gaussian sources with the same statistics.

Abstract

New bounds on the rate distortion function of certain non-Gaussian sources, with a proportional-weighted mean-square error (MSE) distortion measure, are given. The growth, g, of the rate distortion function, as a result of changing from a non-weighted MSE distortion measure to a proportional-weighted distortion criterion is analyzed. It is shown that for a small distortion, d, the growth, g, and the difference between the rate distortion functions of a Gaussian memoryless source and a source with memory, both with the same marginal statistics and MSE distortion measure, share the same lower bound. Several examples and applications are also given.