  We consider the distributed source coding system for $L$ correlated Gaussian
observations $Y_i, i=1,2, ..., L$. Let $X_i,i=1,2, ..., L$ be $L$ correlated
Gaussian random variables and $N_i,$ $i=1,2,... L$ be independent additive
Gaussian noises also independent of $X_i, i=1,2,..., L$. We consider the case
where for each $i=1,2,..., L$, $Y_i$ is a noisy observation of $X_i$, that is,
$Y_i=X_i+N_i$. On this coding system the determination problem of the rate
distortion region remains open. In this paper, we derive explicit outer and
inner bounds of the rate distortion region. We further find an explicit
sufficient condition for those two to match. We also study the sum rate part of
the rate distortion region when the correlation has some symmetrical property
and derive a new lower bound of the sum rate part. We derive a sufficient
condition for this lower bound to be tight. The derived sufficient condition
depends only on the correlation property of the sources and their observations.
