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

TL;DR

This paper demonstrates that the Combinatorial Message Sharing (CMS) scheme outperforms the Venkataramani-Kramer-Goyal (VKG) scheme in the quadratic Gaussian multiple descriptions problem for all channels with three or more descriptions, extending the achievable region.

Contribution

It proves that CMS strictly extends VKG for the L-channel quadratic Gaussian MD problem, even when 2-description regions coincide, and achieves the complete rate-distortion region in new asymmetric scenarios.

Findings

CMS outperforms VKG for L≥3 channels.

CMS achieves the complete rate-distortion region in certain asymmetric cases.

CMS strictly extends the VKG region despite EC region completeness for 2-descriptions.

Abstract

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