Computing the Rate-Distortion Function of Gray-Wyner System

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. At last, an iterative algorithm is proposed to calculate the numerical value of the rate-distortion function for general sources. Convergence of the proposed iterative algorithm and the projection plane of rate-distortion regions are described by numerical simulations.