On the vector Gaussian L-terminal CEO problem

We derive an outer bound of the rate region of the vector Gaussian L-terminal CEO problem by establishing a lower bound on each supporting hyperplane of the rate region. To this end we prove a new extremal inequality by exploiting the connection between differential entropy and Fisher information as well as some fundamental estimation-theoretic inequalities. It is shown that the outer bound matches the Berger-Tung inner bound in the high-resolution regime.