Vector Gaussian Multiterminal Source Coding

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. We then derive a lower bound on each supporting hyperplane of the rate region of the direct vector Gaussian \(L\) -terminal source coding problem by coupling it with the CEO problem through a limiting argument. The tightness of this lower bound in the high-resolution regime and the weak-dependence regime is also proved.