A New Sufficient Condition for Sum-Rate Tightness in Quadratic Gaussian Multiterminal Source Coding

This paper considers the quadratic Gaussian multiterminal (MT) source coding problem and provides a new sufficient condition for the Berger-Tung (BT) sum-rate bound to be tight. The converse proof utilizes a set of virtual remote sources given which the observed sources are block independent with a maximum block size of 2. The given MT source coding problem is then related to a set of two-terminal problems with matrix-distortion constraints, for which a new lower bound on the sum-rate is given. By formulating a convex optimization problem over all distortion matrices, a sufficient condition is derived for the optimal BT scheme to satisfy the subgradient-based Karush-Kuhn-Tucker condition. The subset of the quadratic Gaussian MT problem satisfying our new sufficient condition subsumes all previously known tight cases, and our proof technique opens a new direction for more general partial solutions.