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This paper focuses on the problem of $L-$channel quadratic Gaussian multipledescription (MD) coding. We recently introduced a new encoding scheme in [1]for general $L-$channel MD problem, based on a technique called `CombinatorialMessage Sharing' (CMS), where every subset of the descriptions shares adistinct common message. The new achievable region subsumes the most well knownregion for the general problem, due to Venkataramani, Kramer and Goyal (VKG)[2]. Moreover, we showed in [3] that the new scheme provides a strictimprovement of the achievable region for any source and distortion measures forwhich some 2-description subset is such that the Zhang and Berger (ZB) schemeachieves points outside the El-Gamal and Cover (EC) region. In this paper, weshow a more surprising result: CMS outperforms VKG for a general class ofsources and distortion measures, which includes scenarios where for all2-description subsets, the ZB and EC regions coincide. In particular, we showthat CMS strictly extends VKG region, for the $L$-channel quadratic Gaussian MDproblem for all $L\geq3$, despite the fact that the EC region is complete forthe corresponding 2-descriptions problem. Using the encoding principlesderived, we show that the CMS scheme achieves the complete rate-distortionregion for several asymmetric cross-sections of the $L-$channel quadraticGaussian MD problem, which have not been considered earlier.

On the Role of Common Codewords in Quadratic Gaussian Multiple Descriptions Coding