A New Data Processing Inequality and Its Applications in Distributed Source and Channel Coding

TL;DR

This paper introduces a new data processing inequality based on spectrum analysis to derive necessary conditions for distributed source and channel coding problems involving correlated sources.

Contribution

It proposes a novel spectrum-based data processing inequality and applies it to derive single-letter necessary conditions for distributed coding scenarios.

Findings

New necessary conditions for multi-terminal rate-distortion region

Necessary conditions for multiple access channel with correlated sources

Spectrum analysis-based data processing inequality

Abstract

In the distributed coding of correlated sources, the problem of characterizing the joint probability distribution of a pair of random variables satisfying an n-letter Markov chain arises. The exact solution of this problem is intractable. In this paper, we seek a single-letter necessary condition for this n-letter Markov chain. To this end, we propose a new data processing inequality on a new measure of correlation by means of spectrum analysis. Based on this new data processing inequality, we provide a single-letter necessary condition for the required joint probability distribution. We apply our results to two specific examples involving the distributed coding of correlated sources: multi-terminal rate-distortion region and multiple access channel with correlated sources, and propose new necessary conditions for these two problems.