An outer bound for the vector Gaussian CEO problem

We study the vector Gaussian CEO problem, and provide an outer bound for its rate-distortion region. 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 the properties of the Fisher information. Next, we address the tightness of our outer bound, and show that our outer bound does not provide the ratedistortion region in general. In particular, we provide a specific example where the rate-distortion region is strictly contained in our outer bound.