Rate distortion region for distributed source coding of correlated Gaussian remote sources

We consider the separate source coding problem of L correlated Gaussian observations Y_i, i=1, 2,hellip, L. We consider the case that Y_i, i=1, 2,hellip, L satisfy Y_i=X_i+N_i, i=1, 2,hellip, L where X_i, i=1, 2,hellip, L are L correlated Gaussian random variables and N_i, i=1, 2,hellipL are independent additive Gaussian noises also independent of X_i, i=1, 2,hellip, L. On this coding system the determination problem of the rate distortion region remains open. In our previous works, we derived explicit outer and inner bounds of the rate distortion region and sufficient condition for the inner and outer bounds to match. In this paper we derive a stronger sufficient condition for those two bounds to match.