An Outer Bound for the Vector Gaussian CEO Problem

TL;DR

This paper introduces a new outer bound for the rate-distortion region of the vector Gaussian CEO problem, improving upon previous bounds using Fisher information and de Bruijn identity, but not fully characterizing the region.

Contribution

It provides a novel outer bound for the vector Gaussian CEO problem's rate-distortion region, surpassing existing bounds through advanced information-theoretic techniques.

Findings

Our outer bound strictly improves existing bounds for all parameters.

The outer bound does not exactly characterize the rate-distortion region.

A specific example demonstrates the gap between the outer bound and the true region.

Abstract

We study the vector Gaussian CEO problem, where there are an arbitrary number of agents each having a noisy observation of a vector Gaussian source. The goal of the agents is to describe the source to a central unit, which wants to reconstruct the source within a given distortion. The rate-distortion region of the vector Gaussian CEO problem is unknown in general. Here, we provide an outer bound for the rate-distortion region of the vector Gaussian CEO problem. We obtain our outer bound by evaluating an outer bound for the multi-terminal source coding problem by means of a technique relying on the de Bruijn identity and the properties of the Fisher information. Next, we show that our outer bound strictly improves upon the existing outer bounds for all system parameters. We show this strict improvement by providing a specific example, and showing that there exists a gap between our outer bound and the existing outer bounds. Although our outer bound improves upon the existing outer bounds, we show that our outer bound does not provide the exact rate-distortion region in general. To this end, we provide an example and show that the rate-distortion region is strictly contained in our outer bound for this example.