The Gaussian Scalar-Help-Vector Listening-Helper Source Coding Problem

A memoryless vector Gaussian source is encoded cooperatively by two parties: An encoder which forms its description upon observing the source and a helper which observes the encoder’s description and a scalar correlated side-information and then forms its description accordingly. First, we establish the optimality of the Gaussian law for the evaluation of the rate region. Then, we analyze the corresponding matrix optimization problem and derive a few properties of the optimal solution.