On the Rate Loss of Multiterminal Source Codes

In this paper, we study the rate loss and achievable region of the multiterminal source code (MTSC), which is the code designed for a system comprising two independent encoders and joint decoder: encoders 1 and 2 describe sources X and Y using rates R₁ and R₂ , respectively, and the joint decoder reconstructs X with distortion D₁ and reconstructs Y with distortion D₂. The rate loss of an MTSC is defined as L₁ = R ₁ $R_X|Y(D₁), L₂ = R₂ - R_X|Y(D₂), and L₀ = R₁ + R₂ - R_XY(D₁, D₂), where R_XY(D₁, D₂) is the joint rate-distortion function of (X,Y), and R_X|Y(D₁) and R_Y|X(D₂) are two conditional rate-distortion functions. We first show that for general real-valued memoryless sources and mean squared error distortion measure, the rate loss has an intrinsic connection with K₁ = R_XY(D₁, D₂) $R_Y(D₂) - R_X|Y(D₁ ) and K₂ = R_XY(D₁, D₂) - R_X(D₁) - R_Y|X(D₂). We then study two common types of sources, jointly Gaussian sources and remote sources, in more details and bound K₁ and K₂ from above by small universal constants, which leads to small universal upper bounds on the rate loss and therefore good approximations of the achievable region