Vector Gaussian two-terminal CEO problem under sum distortion

This paper characterizes the rate region of the vector Gaussian CEO problem with the trace distortion constraint. We develop a new analysis technique based on spectral decomposition of mean square error in Berger-Tung scheme. In order to prove the converse part of the rate distortion region, the perturbation method of Wang and Chen is utilized through combining with detailed analysis of Karush-Kuhn-Tucker necessary conditions of the non-convex optimization problem. Finally, we show that Berger-Tung inner bound can achieve the entire rate region of the vector Gaussian CEO problem with the trace distortion constraint, via deriving a novel extremal inequality.