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Asymptotic Reverse Waterfilling Algorithm of NRDF for Certain Classes of Vector Gauss-Markov Processes
KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Information Science and Engineering.ORCID iD: 0000-0003-0989-1682
KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Information Science and Engineering.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

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 \cite{stavrou:2018cdc}. We show that for certain classes of time-invariant multidimensional Gauss-Markov processes, the specific characterization behaves as a reverse-waterfilling algorithm obtained in {\it matrix form} ensuring that the numerical approach of \cite[Algorithm 1]{stavrou:2018cdc} is optimal. In addition, we give an equivalent characterization that utilizes the {\it 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.

Keywords [en]
reverse-waterfilling, commuting matrices, simultaneous diagonalization, orthogonal matrices
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Applied and Computational Mathematics, Optimization and Systems Theory; Mathematics; Electrical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-271245OAI: oai:DiVA.org:kth-271245DiVA, id: diva2:1416345
Projects
KAW Foundation and the Swedish Foundation for Strategic Research
Note

QC 20200324

Available from: 2020-03-23 Created: 2020-03-23 Last updated: 2020-03-24Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • ieee
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  • vancouver
  • Other style
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Language
  • de-DE
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  • en-US
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  • nn-NB
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  • Other locale
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Output format
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