Vector Gaussian multiple description with individual and central receivers

L multiple descriptions of a vector Gaussian source for individual and central receivers are investigated. The sum rate of the descriptions with covariance distortion measure constraints, in a positive semidefinite ordering, is exactly characterized. For two descriptions, the entire rate region is characterized. The key component of the solution is a novel information-theoretic inequality that is used to lower-bound the achievable multiple description rates. Jointly Gaussian descriptions are optimal in achieving the limiting rates. We also show the robustness of this description scheme: The distortions achieved are no larger when used to describe any non-Gaussian source with the same covariance matrix.