On the Rate Loss of Multiple Sources Codes in the Wyner–Ziv Setting

Abstract

In this paper, we consider the rate loss and achievable region of multiple sources codes (also named multiterminal source codes) in the Wyner-Ziv setting (WZ-MSC), in which two stationary memoryless sources (X, Y) are compressed separately from each other at respective rates R1 and R2, and the joint decoder, having access to the side information S which is correlated with sources (X, Y), reconstructs X and Y with distortion D1 and D2, respectively. We define the rate loss L1 = R1 RX|Y,S(D1), L2 = R2 RY|X,S(D2), and L0 = R1 - R2 - RX,Y|S(D1,D2). For general real-valued stationary memoryless sources and mean squared error distortion measure, we show that the rate loss can be bounded by Li ≤ Ki + 1,i = 1,2, and L0 ≤ 1, where K1 = RX,Y|S(D1, D2) - RY|S(D2) RX|Y,S(D1) and K2 = RX,Y|S(D1,D2) - RX|S(D1) RY|X,S(D2). When the sources and side information have a jointly Gaussian distribution, we give upper bounds of K1 and K2 by a function of conditional correlation coefficient ρXY|S. For a special case when there is no side information, our result tightens Feng's rate loss bounds. Using our upper bounds of the rate loss, we give good approximations of the achievable region.