A bound on the rate of a system for encoding an unknown Gaussian autoregressive source

To obtain the rate distortion function of an autoregressive (AR) source when the source parameters are fixed but unknown, it is common simply to insert the estimated parameters into the known-spectrum rate distortion expressions. This approach, although asymptotically correct, ignores any error in estimating the parameters, ignores distortion incurred by the need to encode the parameters for transmission to the receiver, and does not include a component for the side information. We derive a lower bound to the rate distortion performance of a relatively general system for encoding an unknown Gaussian AR source with respect to the mean-squared error (MSE) fidelity criterion. Asymptotically in the estimator frame length n and in the encoder blocklength N, the lower bound equals the usual Gaussian rate distortion function for small distortions