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An achievable region for the L-channel multiple description coding problem is presented. This region generalizes two-channel results of El Gamal and Cover (1982) and of Zhang and Berger (1987). It further generalizes three-channel results of Gray and Wyner (1974) and of Zhang and Berger. A source that is successively refinable on chains is shown to be successively refinable on trees. A new outer bound on the rate-distortion (RD) region for memoryless Gaussian sources with mean squared error distortion is also derived. The achievable region meets this outer bound for certain symmetric cases.