1. Asymptotic Reverse-Waterfilling Characterization of Nonanticipative Rate Distortion Function of Vector-Valued Gauss-Markov Processes with MSE Distortion
- Author
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Stavrou, Photios A., Charalambous, Themistoklis, Charalambous, Charalambos D., Loyka, Sergey, Skoglund, Mikael, KTH Royal Institute of Technology, Department of Electrical Engineering and Automation, University of Cyprus, University of Ottawa, Aalto-yliopisto, Aalto University, Charalambous, Charalambos D. [0000-0002-2168-0231], and Charalambous, Themistoklis [0000-0003-4800-6738]
- Subjects
0209 industrial biotechnology ,Optimization problem ,Markov process ,02 engineering and technology ,resource description framework ,Upper and lower bounds ,symbols.namesake ,020901 industrial engineering & automation ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,Entropy (information theory) ,Symmetric matrix ,Parametric statistics ,Mathematics ,Computer Science::Information Theory ,Distortion function ,ta213 ,ta111 ,020206 networking & telecommunications ,Algebraic equation ,symmetric matrices ,symbols ,RNA ,rate-distortion ,distortion ,entropy ,optimization - Abstract
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. 14 20
- Published
- 2019