An Equivalent Expression for the Wyner-Ziv Source Coding Problem

We consider the coding problem for lossy source coding with side information at the decoder, which is known as the Wyner-Ziv source coding problem. The goal of the coding problem is to find the minimum rate such that the probability of exceeding a given distortion threshold is less than the desired level. We give an equivalent expression of the minimum rate by using the chromatic number and a notion of covering of a set. This allows us to analyze the coding problem in terms of graph coloring and covering.