Generalized Gaussian Multiterminal Source Coding: The Symmetric Case

Consider a generalized multiterminal source coding system, where ( l m ) encoders, each observing a distinct sizem subset of l (l ≥ 2) zero-mean unit-variance symmetrically correlated Gaussian sources with correlation coefficient ρ, 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 ratedistortion 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 ρ = 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 ρ ≤ 0 and for distortions below an explicit positive threshold (depending on m) when ρ > 0. Moreover, when ρ > 0, the minimum achievable rate of generalized multiterminal source coding subject to an arbitrary positive distortion constraint d is shown to be within a finite gap (depending on m and d) from its centralized counterpart in the large l limit except for possibly the critical distortion d = 1− ρ.