Approximating the Gaussian multiple description rate region under symmetric distortion constraints

We consider multiple description coding for the Gaussian source with K descriptions under the symmetric mean squared error distortion constraints. Inner and outer bounds for the achievable rate region are derived and carefully tailored, such that they can be compared conveniently. The inner bound is based on a generalization of the multilayer scheme previously proposed by Puri et al., through a more flexible binning method. The resulting achievable region has the same geometric structure as the rate region of the lossless multilevel diversity coding problem, which reveals a strong connection between them. The outer bound is derived by combining the bounding technique for the sum rate in our earlier work, together with the alpha-resolution method introduced by Yeung and Zhang. Comparison between the inner and outer bounds shows that the gap in between is upper bounded by some constants. Particularly for the three description problem, the bounds can be written explicitly, and both the inner and outer bounds can be represented by ten planes with matching normal directions, between which the pairwise difference is small.