Generalized Statistics Framework for Rate Distortion Theory

TL;DR

This paper extends rate distortion theory using Tsallis nonextensive statistics, deriving variational principles and numerical schemes that improve modeling in lossy compression scenarios.

Contribution

It introduces a generalized statistics framework for rate distortion theory based on Tsallis entropy, with new variational principles and evaluation algorithms.

Findings

Numerical schemes effectively evaluate the nonextensive RD function.

Generalized models demonstrate improved performance in simulations.

The framework applies for different values of the nonextensivity parameter q.

Abstract

Variational principles for the rate distortion (RD) theory in lossy compression are formulated within the ambit of the generalized nonextensive statistics of Tsallis, for values of the nonextensivity parameter satisfying $ 0 < q < 1 $ and $ q > 1 $. Alternating minimization numerical schemes to evaluate the nonextensive RD function, are derived. Numerical simulations demonstrate the efficacy of generalized statistics RD models.