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:在本文中,对Gray-Wyner有损源编码系统的速率失真理论进行了研究。对于联合高斯分布源的情况,我们在二次失真约束下建立了速率失真函数的表达式。利用所提出的速率失真函数,可以方便地计算速率失真区域上的任何角点。我们以Wyner的公共信息为例,并提供了一种通用且简单的方法来解决此问题。通过分析速率失真函数,本文还介绍了每个层上的速率以及辅助随机变量和源的协方差矩阵。