1High-Rate Analysis of Symmetric L-Channel Multiple Description Coding

Abstract—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 of the L descriptions ( < 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 redun-dancy 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 normal-ized 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. Index Terms—Multiple description coding, high-rate quantiza-tion, lattice quantizer. I