Asymmetric Multilevel Diversity Coding and Asymmetric Gaussian Multiple Descriptions

Abstract

We consider the asymmetric multilevel diversity (A-MLD) coding problem, where a set of $2^K-1$ information sources, ordered in a decreasing level of importance, is encoded into $K$ messages (or descriptions). There are $2^K-1$ decoders, each of which has access to a non-empty 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 small, which results in an approximate characterization of the asymmetric Gaussian three description rate region.