Asymmetric Multilevel Diversity Coding and Asymmetric Gaussian Multiple Descriptions

TL;DR

This paper characterizes the rate region for asymmetric multilevel diversity coding with three descriptions and extends insights to approximate the rate region for asymmetric Gaussian multiple descriptions, highlighting the need for network coding strategies.

Contribution

It provides the first single-letter characterization for the 3-description asymmetric multilevel diversity coding problem and develops bounds for the Gaussian multiple description problem.

Findings

Achieved a single-letter rate region characterization for 3-description A-MLD.

Developed inner and outer bounds for the asymmetric Gaussian MD problem.

Found the bounds are close, enabling an approximate rate region description.

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.