Near Optimality of Composite Multiple Description Source Codes

In this paper, new upper and lower bounds are first presented for the rate loss of multiple description source codes (MDSCs). For a two-description MDSC (2DSC), the rate loss of description i with distortion Di is defined as Li=Ri-R(Di), i ∈ {1,2}, where Ri is the rate of the ith description and R(D) is the rate-distortion function for the given source; the joint rate loss associated with decoding the two descriptions together to achieve central distortion D₀ is measured as L₀=R₁+R₂-R(D₀). Consider an arbitrary memoryless source with variance σ² and let the distortion measure be the mean squared error distortion measure. It is shown that for any optimal 2DSC, (a)0 ≤ L₀ ≤ 0.8802 and 0 ≤ L₁,L₂ ≤ 0.3802 if D₀ ≤ D₁+D₂-σ² ; (b) 0 ≤ L₁, L₂ ≤ 0.4401 if D₀ ≥ (1/D₁+1/D₂-1/σ²)^-1; (c) 0 ≤ L₁,L₂ ≤ 0.3802 and R(max{D₁,D₂})-1 ≤ L₀ ≤ R(max{D₁,D₂})+0.3802 for all other D₀ . A tighter bound on the distance between the El Gamal-Cover inner bound and the achievable region is also presented. Inspired by these new bounds, a low-complexity composite 2DSC design first developed by Lastras-Montaño and Castelli is extended and the resulting code is shown to be near-optimal for all memoryless sources and all distortions. These results are also extended to MDSCs with an arbitrary number of packet- - s. Finally, Gaussian sources are analyzed in detail to verify these bounds and examine their tightness.