Distributed source coding of correlated Gaussian observations

We consider a distributed source coding problem of L correlated Gaussian observations Y_i, i = 1, 2,hellip, L. We consider the case where Y_i, i = 1, 2,hellip, L satisfy Y_i = X_i + N_i, i = 1, 2,hellip, L. Here X_i, i = 1, 2,hellip, L are L correlated Gaussian random variables and N_i, i = 1, 2,hellip, L are independent additive Gaussian noises also independent of X_i, i = 1, 2,hellip, L. The estimation error on the L correlated sources are measured by the distortion covariance matrix. The rate distortion region is defined by a set of all rate vectors for which the estimation error is upper bounded by an arbitrarily prescribed covariance matrix in the meaning of positive semi definite. In this paper we derive explicit outer and inner bounds of the rate distortion region. Our result may provide a useful tool to study two other open problems on this Gaussian distributed source coding system.