  In this work, the rate region of the vector Gaussian multiple description
problem with individual and central quadratic distortion constraints is
studied. In particular, an outer bound to the rate region of the L-description
problem is derived. The bound is obtained by lower bounding a weighted sum rate
for each supporting hyperplane of the rate region. The key idea is to introduce
at most L-1 auxiliary random variables and further impose upon the variables a
Markov structure according to the ordering of the description weights. This
makes it possible to greatly simplify the derivation of the outer bound. In the
scalar Gaussian case, the complete rate region is fully characterized by
showing that the outer bound is tight. In this case, the optimal weighted sum
rate for each supporting hyperplane is obtained by solving a single
maximization problem. This contrasts with existing results, which require
solving a min-max optimization problem.
