Approximating the rate-distortion region of the distributed source coding for three jointly Gaussian tree-structured sources

The rate-distortion region for the distributed source coding of the three jointly-Gaussian tree-structured sources with the quadratic distortion measure, is characterized within a constant gap. As a simplified counterpart of the Gaussian problem, we first investigate the rate region of a three binary-expanded sources where each pair of the sources have a certain number of the most-significant bits in common, and the central decoder needs to reconstruct each source with a target resolution. Motivated by the result of binary-expansion model, we prove that the achievable region of the quantize-and-binning scheme and the outer-bound of the cooperative scheme has a bounded gap of 2.4771 bits.