Bounding the Rate Region of Vector Gaussian Multiple Descriptions with Individual and Central Receivers

TL;DR

This paper derives an outer bound for the rate region of the vector Gaussian multiple description problem with individual and central distortion constraints, simplifying the analysis by using auxiliary variables and Markov structures, and fully characterizes the scalar case.

Contribution

It introduces a simplified outer bound for the vector Gaussian multiple description rate region using auxiliary variables and Markov structures, and fully characterizes the scalar case.

Findings

Derived an outer bound for the vector Gaussian case.

Proved tightness of the bound in the scalar case.

Simplified the optimization for the scalar case.

Abstract

In this work, the rate region of the vector Gaussian multiple description problem with individual and central quadratic distortion constraints is studied. In particular, an outer bound to the rate region of the L-description problem is derived. The bound is obtained by lower bounding a weighted sum rate for each supporting hyperplane of the rate region. The key idea is to introduce at most L-1 auxiliary random variables and further impose upon the variables a Markov structure according to the ordering of the description weights. This makes it possible to greatly simplify the derivation of the outer bound. In the scalar Gaussian case, the complete rate region is fully characterized by showing that the outer bound is tight. In this case, the optimal weighted sum rate for each supporting hyperplane is obtained by solving a single maximization problem. This contrasts with existing results, which require solving a min-max optimization problem.