Near separability of optimal multiple description source codes

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