On the rate distortion region of Gaussian multiterminal source coding

We consider the distributed source coding system of L correlated Gaussian sources Y_i, i = 1,2, ⋯, L. We assume that Y^L = ^t(Y₁, Y₂, ⋯, Y_L) is an observation of the remote source vector X^L = ^t(X₁, X₂, ⋯, X_L), having the form Y ^L = X^K + N^L, where N^L = ^t(N₁, N₂, ···, N_L) is a vector of L independent Gaussian random variables also independent of X^L. In this system L correlated Gaussian observations are separately compressed by L encoders and sent to the information processing center. In this paper, we study the multiterminal source coding problem where the decoder wishes to reconstruct the observation Y^L = X^L +N^L. We consider three distortion criteria based on the covariance matrix of the estimation error on Y^L. For each of those three criteria we derive explicit inner and outer bounds of the rate distortion region.