Distributed Source Coding of Correlated Gaussian Sources

We consider the distributed source coding system of $L$ correlated Gaussian sources $Yi,i=1,2,...,L$ which are noisy observations of correlated Gaussian remote sources $Xk, k=1,2,...,K$. We assume that $Y^{L}={}{\rm t}(Y1,Y2,$ $..., YL)$ is an observation of the source vector $X^K={}{\rm t}(X1,X2,..., XK)$, having the form $Y^L=AXK+NL$, where $A$ is a $L\times K$ matrix and $N^L={}{\rm t}(N1,N2,...,NL)$ 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 $A=IL$, we study the multiterminal source coding problem where the decoder wishes to reconstruct the observation $Y^L=XL+NL$. 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.