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.

翻译：本文研究了Gray-Wyner有损信源编码系统的率失真理论。针对联合高斯分布信源，我们建立了二次失真约束下的率失真函数表达式。利用所提出的率失真函数，可以方便地计算率失真区域上的任意角点。以Wyner公共信息为例，我们提供了一种通用且简洁的方法来解决该问题。通过对率失真函数的分析，本文还给出了各层的速率以及辅助随机变量与信源之间的协方差矩阵。