loading page

Asymptotic Reverse Waterfilling Algorithm of NRDF for Certain Classes of Vector Gauss-Markov Processes
  • Photios A. Stavrou ,
  • Mikael Skoglund
Photios A. Stavrou
Author Profile
Mikael Skoglund
Author Profile


In this paper, we revisit the asymptotic reverse-waterfilling characterization of the nonanticipative rate distortion
function (NRDF) derived for a time-invariant multidimensional Gauss-Markov processes with mean-squared error (MSE) distortion in [1]. We show that for certain classes of time-invariant multidimensional Gauss-Markov processes, the specific characterization behaves as a reverse-waterfilling algorithm obtained in matrix form ensuring that the numerical approach of [1, Algorithm 1] is optimal. In addition, we give an equivalent characterization that utilizes the eigenvalues of the involved matrices reminiscent of the well-known reverse-waterfilling algorithm in information theory. For the latter, we also propose a novel numerical approach to solve the algorithm optimally. The efficacy of our proposed iterative scheme compared to similar existing schemes is demonstrated via experiments. Finally, we use our new results to derive an analytical solution of the asymptotic NRDF for a correlated time-invariant two-dimensional Gauss-Markov process.
Jun 2022Published in IEEE Transactions on Automatic Control volume 67 issue 6 on pages 3196-3203. 10.1109/TAC.2021.3099444