Multiple Description Coding with Many Channels

An achievable region for the $L$ channel multiple description coding problem is presented. This region generalizes previous two-channel results of El Gamal and Cover and of Zhang and Berger. It further generalizes three channel results of Gray and Wyner and of Zhang and Berger. The region is shown to be the best possible for successive refinement on trees. A new outer bound on the rate distortion region for memoryless Gaussian sources with mean squared error distortion is also derived. The achievable region meets this outer bound for certain symmetric cases.