Vector Gaussian multiple description with two levels of receivers

The problem of L multiple descriptions of a stationary and ergodic Gaussian source with two levels of receivers is investigated. Each of the first-level receivers receive (an arbitrary subset) k of the L descriptions, (k < L). The second-level receiver receives all L descriptions. All the receivers, both at the first level and the second level, reconstruct the source using the subset of descriptions they receive. The corresponding reconstructions are subject to quadratic distortion constraints. Our main result is the derivation of an outer bound on the sum rate of the descriptions so that the distortion constraints are met. We show that an analog-digital separation architecture involving joint Gaussian vector quantizers and a binning scheme meets this outer bound with equality for several scenarios. These scenarios include the case when the distortion constraints are symmetric and the case for general distortion constraints with k = 2 and L = 3.