Computing the Rate-Distortion Function of Gray-Wyner System

TL;DR

This paper derives the rate-distortion function for the Gray-Wyner lossy source coding system with Gaussian sources and quadratic distortion, enabling easier calculation of the rate-distortion region and related parameters.

Contribution

It provides a closed-form expression for the rate-distortion function of Gaussian sources in the Gray-Wyner system, facilitating analysis of the entire rate-distortion region.

Findings

Explicit rate-distortion function for Gaussian sources

Method to compute corner points of the rate-distortion region

Analysis of auxiliary variables and source covariance matrices

Abstract

In this paper, the rate-distortion theory of the Gray-Wyner lossy source coding system is investigated. For the case of jointly Gaussian distributed sources, we establish an expression for the rate-distortion function under the constraint of quadratic distortion. Using the proposed rate-distortion function, any corner point on the rate-distortion region can be conveniently calculated. We take Wyner's common information as an example and provide a general and simple method to solve this problem. Through the analysis of the rate-distortion function, the rate on each layer and covariance matrix of auxiliary random variables and the sources are also presented in this paper.