High-Rate Analysis of Symmetric L-Channel Multiple Description Coding

This paper studies the tight rate-distortion bound for L-channel symmetric multiple-description coding of a scalar Gaussian source with two levels of receivers. Each of the first-level receivers obtains κ of the L descriptions (κ <; L). The second-level receiver obtains all L descriptions. We find that if the central distortion (corresponding to the second-level receiver) is much smaller than the side distortion (corresponding to the first-level receivers), the product of a function of the side distortions and the central distortion is asymptotically independent of the redundancy between the descriptions. Using this property, we analyze the asymptotic behavior of a practical multiple-description lattice vector quantizer (MDLVQ). Our analysis includes the treatment of the MDLVQ system from a new geometric viewpoint, which results in an expression for the side distortions using the normalized second moment of a sphere of higher dimensionality than the quantization space. The expression of the distortion product derived from the lower bound is then applied as a criterion to assess the performance loss of the considered MDLVQ system. In principle, the efficiency of other practical MD systems can also be evaluated using the derived distortion product.