Near separability of optimal multiple description source codes

Abstract

In this paper, we first present new upper and lower bounds for the rate loss of multiple description source codes (MDSCs). For a two-description MDSC (2DSC), the rate loss of description i with distortion D_i is L_i = R_i $R(D_i ), i isin {1, 2}, where R_i is the rate of the ith description; the joint rate loss associated with decoding the two descriptions together to achieve central distortion D₀ is L ₀ = R₁ + R₂ - R(D₀). We show that given any memoryless source with variance sigma² and mean squared error distortion measure, for any optimal 2DSC, (a) 0 les L₀ les 0.8802 if D₀ les D₁ + D₂ - sigma²; (b) 0 les L₁, L₂ les 0.4401 if D₀ ges (1/D₁ + 1/D₂ - 1/sigma²)^-1; (c) 0 les L₁, L₂ les 0.3802 and R(max{D₁, D₂}) - 1 les L₀ les R(max{D₁, D₂}) + 0.3802 otherwise. We also present a tighter bound on the distance between the El Gamal-Cover inner bound and the achievable region. In addition, these new bounds, which are easy to compute, inspire new designs of low-complexity near-optimal 2DSC. In essence, we demonstrate that any optimal 2DSC can be nearly separated into a multi-resolution source code and a traditional single-resolution code, and the resulting rate penalty for each description is less than 0.6901 bit/sample for general sources and less than 0.5 bit/sample for successively refinable sources