Vector Gaussian hypothesis testing and lossy one-helper problem

We study the vector Gaussian versions of two problems: hypothesis testing under a communication constraint and the lossy one-helper problem. In the hypothesis testing problem, a test against independence is considered when a vector Gaussian source is available at the detector which receives a message about another vector Gaussian source at a specified rate. Two equivalent characterizations of the optimal type 2 error exponent are given when the type 1 error is at most a fixed constant. The first characterization is based on enhancement technique introduced by Weingarten et. al. and the other is transform-based. The transform-based characterization directly yields a water pouring interpretation, and establishes successive refinability. For the lossy one-helper problem, we determine a portion of the boundary of the rate region.