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(Y₁, Y₂,...,Y_L) is an observation of the source vector X^K = t(X₁, X₂, . . . , X_K), having the form Y^L = AX^K+N^L, where A is a L×K matrix and N^L = t(N₁, N₂, ... , 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.