Asymptotic Reverse-Waterfilling Characterization of Nonanticipative Rate Distortion Function of Vector-Valued Gauss-Markov Processes with MSE Distortion
Date
2018Author
Stavrou, Photios A.Charalambous, Themistoklis
Charalambous, Charalambos D.
Loyka, Sergey
Skoglund, Mikael
ISBN
978-1-5386-1395-5Publisher
IEEEPlace of publication
Miami Beach, FLSource
2018 IEEE Conference on Decision and Control (CDC)Pages
14-20Google Scholar check
Metadata
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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.