Indirect and Direct Gaussian Distributed Source Coding Problems

We consider the distributed source coding system of L correlated Gaussian sources Y-l, l = 1, 2, . . . , L, which are noisy observations of correlated Gaussian remote sources X-k, k = 1, 2, . . . , K. We assume that Y-L = (t)(Y-1, Y-2 , . . . , Y-L) is an observation of the source vector X-K = (t)(X-1, X-2 , . . . , X-K), having the form Y-L = AX(K) + N-L, where A is a LxK matrix and N-L = (t)(N-1, N-2, . . . , N-L) is a vector of L-independent Gaussian random variables also independent of X-K. 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-K. We consider three distortion criteria based on the covariance matrix of the estimation error on X-K. 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 = I-L, we study the multiterminal source coding problem, where the decoder wishes to reconstruct the observation Y-L = X-L + N-L. To investigate this problem, we shall establish a result that provides a strong connection between the remote source coding problem and multiterminal source coding problem. Using this result, we derive several new partial solutions to the multiterminal source coding problem.