Rate distortion of stationary and nonstationary vector gauaaian sources

Rate distortion of certain vector Gaussian sources is addressed. To evaluate rate distortion of a stationary vector Gaussian source and a vector AR Gaussian source, limiting eigenvalue distribution of block Toeplitz matrices is used. To evaluate rate distortion of a vector AR Gaussian source with time varying coefficients, where time variation is described by a stationary, ergodic vector process, random ergodic operator theory is used. To solve this last problem, the limiting eigenvalue distribution of a sequence of matrices of increasing order describing the AR source, is shown to exist. Sufficient conditions are given for each of the three cases for which source coding theorems hold