On the Generalized Gaussian CEO Problem.

This paper considers a distributed source coding (DSC) problem where L encoders observe noisy linear combinations of K correlated remote Gaussian sources, and separately transmit the compressed observations to the decoder to reconstruct the remote sources subject to a sum-distortion constraint. This DSC problem is referred to as the generalized Gaussian CEO problem since it can be viewed as a generalization of the quadratic Gaussian CEO problem where the number of remote source K=1. First, we provide a new outer region obtained using the entropy power inequality and an equivalent argument (in the sense of having the same rate-distortion region and Berger–Tung inner region) among a certain class of generalized Gaussian CEO problems. We then give two sufficient conditions for our new outer region to match the inner region achieved by Berger–Tung schemes, where the second matching condition implies that in the low-distortion regime, the Berger–Tung inner rate region is always tight, while in the high-distortion regime, the same region is tight if a certain condition holds. The sum-rate part of the outer region is also studied and shown to meet the Berger–Tung sum-rate upper bound under a certain condition, which is obtained using the Karush–Kuhn–Tucker conditions of the underlying convex semidefinite optimization problem, and is in general weaker than the aforesaid two for rate region tightness. [ABSTRACT FROM PUBLISHER]