Remote Vector Gaussian Source Coding with Decoder Side Information Under Mutual Information and Distortion Constraints

Let $\mbi{X}, \mbi{Y}, \mbi{Z}$ be zero-mean, jointly Gaussian random vectors of dimensions $n_{x}$, $n_{y}$, and $n_{z}$, respectively. Let ${\cal P}$ be the set of random variables $W$ such that $W\leftrightarrow \mbi{Y} \leftrightarrow (\mbi{X,Z})$ is a Markov string. We consider the following optimization problem: $$\min _{W\in {\cal P}} I(\mbi{Y};W\vert \mbi{Z})$$ subject to one of the following two possible constraints: 1) $I(\mbi{X};W\ver…