Multiple description Delta-Sigma quantization with individual and central receivers

In this work we present a practical scheme for L-channel symmetric Multiple Description coding when one is only interested in receiving either a single description or all L descriptions. This scheme is based on oversampling and dithered Delta-Sigma quantization and is an extension of a scheme previously presented by Østergaard and Zamir. The oversampling process creates L redundant representations of the source, while the delta-sigma quantization with feedback-loop enables trading-off side distortion (receiving one description) for central distortion (receiving all the descriptions). We prove that the proposed scheme is asymptotically optimal (at large lattice quantizer dimension and high noise-shaping filter order) at any resolution for a Gaussian source and MSE fidelity criterion. In order to prove this optimality result we give an explicit expression for the rate-distortion function, which was previously known as a non explicit optimization problem.