On the rate loss of multiple description source codes

The rate loss of a multiresolution source code (MRSC) describes the difference between the rate needed to achieve distortion D_i in resolution i and the rate-distortion function R(D_i). This paper generalizes the rate loss definition to multiple description source codes (MDSCs) and bounds the MDSC rate loss for arbitrary memoryless sources. For a two-description MDSC (2DSC), the rate loss of description i with distortion D_i is defined as L_i=R_i-R(D_i), i=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 measured either as L₀=R₁+R₂-R(D₀) or as L₁₂=L₁+L₂. We show that for any memoryless source with variance σ², there exists a 2DSC for that source with L₁≤1/2 or L₂≤1/2 and a) L₀≤1 if D₀≤D₁+D₂-σ², b) L₁₂≤1 if 1/D₀≤1/D₁+1/D₂-1/σ², c) L₀≤L_G0+1.5 and L₁₂≤L_G12+1 otherwise, where L_G0 and L_G12 are the joint rate losses of a Gaussian source with variance σ².