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 L×K 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.