Asymmetric multilevel diversity coding and asymmetric Gaussian multiple descriptions

Authors:
Soheil Mohajer;Chao Tian;Suhas N. Diggavi
Affiliations:
School of Computer and Communication Sciences, Ecole Polytechnique Federale de Lausanne, Switzerland;AT&T Labs-Research, Florham Park, NJ and School of Computer and Communication Sciences, Ecole Polytechnique Federale de Lausanne, Switzerland;Department of Electrical Engineering, University of California, Los Angeles, CA and School of Computer and Communication Sciences, Ecole Poly technique Federale de Lausanne, Switzerland
Venue:
IEEE Transactions on Information Theory
Year:
2010

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Abstract

We consider the asymmetric multilevel diversity (A-MLD) coding problem, where a set of 2K - 1 information sources, ordered in a decreasing level of importance, is encoded into K messages (or descriptions). There are 2K -1 decoders, each of which has access to a nonempty subset of the encoded messages. Each decoder is required to reproduce the information sources up to a certain importance level depending on the combination of descriptions available to it. We obtain a single letter characterization of the achievable rate region for the 3-description problem. In contrast to symmetric multilevel diversity coding, source-separation coding is not sufficient in the asymmetric case, and ideas akin to network coding need to be used strategically. Based on the intuitions gained in treating the A-MLD problem, we derive inner and outer bounds for the rate region of the asymmetric Gaussian multiple description (MD) problem with three descriptions. Both the inner and outer bounds have a similar geometric structure to the rate region template of the A-MLD coding problem, and, moreover, we show that the gap between them is constant, which results in an approximate characterization of the asymmetric Gaussian three description rate region.