Compressing neighbors in a Gauss-Markov tree

We consider a distributed rate-distortion problem in which the set of variables to be estimated and observed variables together form a Gauss-Markov tree, with mean-square error distortion constraints on each of the reproductions. Prior work has shown that a simple compression architecture that performs separate lossy quantization and Slepian-Wolf binning achieves the entire rate region for the problem of reproducing a single variable in the tree. We show that this architecture is sum-rate optimal for the problem of reproducing a pair of neighboring variables in the tree for the special case in which the observations are conditionally independent given the variables to be reproduced.