Block coding for stationary Gaussian sources with memory under a square-error fidelity criterion

In this paper, we present a new version of the source coding theorem for the block coding of stationary Gaussian sources with memory under a square-error distortion criterion. For both time-discrete and time-continuous Gaussian sources, the average square-error distortion of the optimum block source code of rate R > R(D) is shown to decrease at least exponentially in block-length to D, where R(D) is the square-error criterion rate distortion function of the stationary Gaussian source with memory. In both cases, the exponent of convergence of average distortion is explicitly derived