Symmetric Generalized Gaussian Multiterminal Source Coding

Consider a generalized multiterminal source coding system, where (l m) encoders, each observing a distinct size-m subset of l (l >= 2) zero-mean unit-variance symmetrically correlated Gaussian sources with correlation coefficient rho, compress their observations in such a way that a joint decoder can reconstruct the sources within a prescribed mean squared error distortion based on the compressed data. The optimal rate-distortion performance of this system was previously known only for the two extreme cases m = l (the centralized case) and m = 1 (the distributed case), and except when rho = 0, the centralized system can achieve strictly lower compression rates than the distributed system under all non-trivial distortion constraints. Somewhat surprisingly, it is established in the present paper that the optimal rate-distortion performance of the afore-described generalized multiterminal source coding system with m >= 2 coincides with that of the centralized system for all distortions when rho <= 0 and for distortions below an explicit positive threshold (depending on m) when rho > 0.