Analysis of optimal dynamic rate shaping of Markov-1 sources

We discuss the behavior of the optimal solution to the dynamic rate shaping problem assuming an AR(1) source model. By analyzing the statistical and rate-distortion behavior of the different components of this minimization problem, the following key result is mathematically proven: "the set of optimal breakpoint values for any frame is invariant to the accumulated motion compensated shaping error from past frames and may be very reasonably approximated using the current frame shaping error alone".