Rate-distortion functions for Gaussian Markov processes

The rate-distortion function with a mean square error distortion criterion is investigated for a class of Gaussian Markov sources. It is found that for rates greater than a certain minimum, the rate-distortion function is equivalent to that of an independent letter source. This minimum rate was found to be less than n bits per symbol, where n is the order of the Markov sequence. Comparisons between the rate-distortion function, and two quantizing systems are made.