Symmetric Vector Gaussian Multiple Description with Two Levels of Receivers

L symmetric multiple descriptions of a vector Gaussian source with two levels of receivers is investigated, where the first level receiver can receive any k descriptions (k<L) and the second level receiver can receive all descriptions. Both receivers need to reconstruct the vector Gaussian source subject to covariance distortion measure constraints, in a positive semidefinite ordering. The symmetric rate is characterized. Jointly Gaussian descriptions are shown to be optimal in achieving the symmetric rate. It is also shown that one layer of jointly Gaussian description is sufficient to achieve the optimal symmetric rate for two levels of receivers.