Distributed Source Coding of Correlated Gaussian Sources

We consider the distributed source coding system of L correlated Gaussian sources Yl, l = 1, 2, · · · , L which are noisy observations of correlated Gaussian remote sources Xk, k = 1, 2, · · · ,K. We assume that Y L = (Y1, Y2, · · · , YL) is an observation of the source vector X = (X1, X2, · · · , XK), having the form Y L = AX+N, where A is a L×K matrix and N = (N1, N2, · · · , NL) is a vector of L independent Gaussian random variables also independent of X . In this system L correlated Gaussian observations are separately compressed by L encoders and sent to the information processing center. We study the remote source coding problem where the decoder at the center attempts to reconstruct the remote source X . We consider three distortion criteria based on the covariance matrix of the estimation error on X . For each of those three criteria we derive explicit inner and outer bounds of the rate distortion region. Next, in the case of K = L and A = IL, we study the multiterminal source coding problem where the decoder wishes to reconstruct the observation Y L = X + N. To investigate this problem we shall establish a result which provides a strong connection between the remote source coding problem and the multiterminal source coding problem. Using this result, we drive several new partial solutions to the multiterminal source coding problem.