On the Rate Region of the Vector Gaussian One-Helper Distributed Source-Coding Problem

In this paper we consider the rate region of the vector Gaussian one-helper distributed source coding problem. In particular, we derive optimality conditions under which a weighted sum rate is minimum by using a contradiction-based argument. When the sources are specified to be scalar, the optimality conditions can always be constructed for any weighted sum rate. In the derivation of the optimality conditions, we introduce a new concept of "source enhancement", which can be viewed as a dual to the well known "channel enhancement" technique. In particular, source enhancement refers to the operation of increasing the covariance matrix of a Gaussian source in a partial ordering sense. This new technique makes the derivation of the optimality conditions straightforward.