The Degree of Suboptimality of Sending a Lossy Version of the Innovations Process in Gauss-Markov Rate-Distortion

In critical distortion range, the MSE rate-distortion function of time-discrete stationary Gaussian first-order autoregressive source is equal to that of related time-discrete i.i.d. Gaussian source. For 0 < D les D_c it is necessary to provide additional information of non-negligible positive rate in order to obtain a D-admissible code for the original source via the R-D coding of the innovations process and additional post-processing at the decoder. In this scenario, we provide an explicit expression of additional description rate about the original source to find the degree of suboptimality of sending a lossy version of the innovations process in Gauss-Markov rate-distortion. It is shown that additional description rate is monotone increasing on alpha isin [0,1) and is constant on all critical distortion range