An Extremal Inequality Motivated by Multiterminal Information Theoretic Problems

We prove a new extremal inequality, motivated by the vector Gaussian broadcast channel and the distributed source coding with a single quadratic distortion constraint problem. As a corollary, this inequality yields a generalization of the classical vector entropy-power inequality (EPI). As another corollary, this inequality sheds insight into maximizing differential entropy of a sum of jointly distributed random variables, generalizing a classical result of Cover and Zhang.