Separate Source Coding of Correlated Gaussian Remote Sources

We consider the separate source coding problem of correlated Gaussian observations . We consider the case that satisfy where are correlated Gaussian random variables and are independent additive Gaussian noises also independent of . On this coding system the determination problem of the rate distortion region remains open. In our previous work, we derived explicit outer and inner bounds of the rate distortion region. In this paper we show that when Gaussian correlated sources satisfy some condition, the outer bound coincides with the inner bound.