Near Optimality of Composite Multiple Description Source Codes

Abstract

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 D is defined as L_i = R_i - R(D_i), i Є {1,2}, where R_{i} 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 D_0 is measured as L_0 = R_1 + R_2 - R(D_0). Consider an arbitrary memoryless source with variance 0^2 and let the distortion measure be the mean squared error distortion measure. It is shown that for any optimal 2DSC, (a)0 ≤ L_0 ≤ 0.8802 and ≤ 0 L_1, L_2 ≤ 0.3802 if D_0 ≤ D_1 + D_2 - σ^2; (b) 0 ≤ L_1, L_2 ≤ 0.4401 if D_0 ≥ (1/D_1 + 1/D_2 - 1/σ^2)^(-1); (c) 0 ≤ L_1, L_2 ≤ 0.3802 and R(max {D_1, D_2) - 1 ≤ L_0 ≤ R(max {D_1, D_2}) + 0.3802 for all other D_0. 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 packets. Finally, Gaussian sources are analyzed in detail to verify these bounds and examine their tightness.

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