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

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 R_X|Y,S(D₁), L₂ = R₂ R_Y|X,S(D₂), and L₀ = R₁ - R₂ - R_X,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 L_i ≤ K_i + 1,i = 1,2, and L₀ ≤ 1, where K₁ = R_X,Y|S(D₁, D₂) - R_Y|S(D₂) R_X|Y,S(D₁) and K₂ = R_X,Y|S(D₁,D₂) - R_X|S(D₁) R_Y|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 ρ_XY|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.