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Asymptotic Reverse-Waterfilling Characterization of Nonanticipative Rate Distortion Function of Vector-Valued Gauss-Markov Processes with MSE Distortion
- Source :
- 2018 IEEE Conference on Decision and Control (CDC), CDC
- Publication Year :
- 2019
-
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
- 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
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- 2018 IEEE Conference on Decision and Control (CDC), CDC
- Accession number :
- edsair.doi.dedup.....0fe2ccaa9991ddfad263e2f970fa1111