  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. Jointly Gaussian descriptions are optimal in achieving the
limiting rates. The key component of the solution is a novel
information-theoretic inequality that is used to lower bound the achievable
multiple description rates.
