Indirect and Direct Gaussian Distributed Source Coding Problems - Oohama, Yasutada (IEEE transactions on information theory, 2014)
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.