  We establish a new extremal inequality, which is further leveraged to give a
complete characterization of the rate region of the vector Gaussian CEO problem
with the trace distortion constraint. The proof of this extremal inequality
hinges on a careful analysis of the Karush-Kuhn-Tucker necessary conditions for
the non-convex optimization problem associated with the Berger-Tung scheme,
which enables us to integrate the perturbation argument by Wang and Chen with
the distortion projection method by Rahman and Wagner.
