  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 version of the
El Gamal-Cover scheme, yielding a complete sum-rate characterization.
