The Sum Rate of Vector Gaussian Multiple Description Coding With Tree-Structured Covariance Distortion Constraints

A single-letter lower bound on the sum rate of multiple description coding with tree-structured distortion constraints is established by generalizing Ozarow's celebrated converse argument through the introduction of auxiliary random variables that form a Markov tree. For the quadratic vector Gaussian case, this lower bound is shown to be achievable by an extended El Gamal-Cover scheme, yielding a complete characterization of the minimum sum rate.