An Outer Bound for the Vector Gaussian CEO Problem

We study the vector Gaussian CEO problem, where there are 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 multiterminal source coding problem by means of a technique relying on the de Bruijn identity and properties of the Fisher information. Next, we investigate the tightness of our outer bound. Although our outer bound is tight for certain cases, 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.