An Outer Bound for the Multi-Terminal Rate-Distortion Region

TL;DR

This paper introduces a new outer bound for the multi-terminal rate-distortion region that improves upon previous bounds by leveraging single-letter mutual information expressions, despite the complexity of n-letter constraints.

Contribution

It proposes a tighter outer bound for the multi-terminal rate-distortion region and simplifies the computation by using single-letter mutual information conditions.

Findings

The new outer bound is tighter than previous bounds.

The outer bound involves n-letter Markov chain constraints.

A simplified single-letter outer bound is derived.

Abstract

The multi-terminal rate-distortion problem has been studied extensively. Notably, among these, Tung and Housewright have provided the best known inner and outer bounds for the rate region under certain distortion constraints. In this paper, we first propose an outer bound for the rate region, and show that it is tighter than the outer bound of Tung and Housewright. Our outer bound involves some $n$-letter Markov chain constraints, which cause computational difficulties. We utilize a necessary condition for the Markov chain constraints to obtain another outer bound, which is represented in terms of some single-letter mutual information expressions evaluated over probability distributions that satisfy some single-letter conditions.