The Sum Rate of Vector Gaussian Multiple Description Coding with Tree-Structured Covariance Distortion Constraints

TL;DR

This paper derives a tight lower bound and complete sum-rate characterization for vector Gaussian multiple description coding with tree-structured distortion constraints, extending classical results with new Markov tree auxiliary variables.

Contribution

It introduces a generalized converse argument and an achievable scheme for the vector Gaussian case with tree-structured distortions, providing a full sum-rate characterization.

Findings

Established a single-letter lower bound on sum rate.

Achieved the lower bound with an extended El Gamal-Cover scheme.

Provided a complete sum-rate characterization for the problem.

Abstract

A single-letter lower bound on the sum rate of multiple description coding with tree-structured distortion constraints is established by generalizing Ozarow's celebrated converse argument through the introduction of auxiliary random variables that form a Markov tree. For the quadratic vector Gaussian case, this lower bound is shown to be achievable by an extended version of the El Gamal-Cover scheme, yielding a complete sum-rate characterization.