Structural Properties of Nonanticipatory Epsilon Entropy of Multivariate Gaussian Sources

Charalambos D. Charalambous; Themistoklis Charalambous; Christos Kourtellaris; Jan H. Van Schuppen

doi:10.1109/ISIT44484.2020.9174319

Structural Properties of Nonanticipatory Epsilon Entropy of Multivariate Gaussian Sources

Charalambos D. Charalambous
, Themistoklis Charalambous
, Christos Kourtellaris
, Jan H. Van Schuppen

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

8 Citations (Scopus)

174 Downloads (Pure)

Abstract

The complete characterization of the Gorbunov and Pinsker [1], [2] nonanticipatory epsilon entropy of multivariate Gauss-Markov sources with square-error fidelity is derived, which remained an open problem since 1974. Specifically, it is shown that the optimal matrices of the stochastic realization of the optimal test channel or reproduction distribution, admit spectral representations with respect to the same unitary matrices, and that the optimal reproduction process is generated, subject to pre-processing and post-processing by memoryless parallel additive Gaussian noise channels. The derivations and analyses are new and bring out several properties of such optimization problems over the space of conditional distributions and their realizations.

Original language	English
Title of host publication	Proceedings of the IEEE International Symposium on Information Theory, ISIT 2020
Publisher	IEEE
Pages	2867-2872
Number of pages	6
ISBN (Electronic)	9781728164328
DOIs	https://doi.org/10.1109/ISIT44484.2020.9174319
Publication status	Published - 2020
MoE publication type	A4 Conference publication
Event	IEEE International Symposium on Information Theory - Los Angeles, United States Duration: 21 Jul 2020 → 26 Jul 2020

Publication series

Name	IEEE International Symposium on Information Theory
Publisher	IEEE
ISSN (Print)	2157-8095
ISSN (Electronic)	2157-8117

Conference

Conference	IEEE International Symposium on Information Theory
Abbreviated title	ISIT
Country/Territory	United States
City	Los Angeles
Period	21/07/2020 → 26/07/2020

Funding

ACKNOWLEDGEMENTS This work was co-funded by the European Regional Development Fund and the Republic of Cyprus through the Research and Innovation Foundation (Project: EXCELLENCE/1216/0365). The work of T. Charalambous was supported by the Academy of Finland under Grant 317726.

Keywords

Entropy
Gaussian channels
Gaussian noise
Markov processes
Matrix algebra
Spectral analysis
Stochastic programming

Access to Document

10.1109/ISIT44484.2020.9174319

ELEC_Charalambous_etal_Structural-Properties-of-Nonanticipatory_ISIT2020_authoracceptedmanuscriptAccepted author manuscript, 1.24 MB

Cite this

Charalambous, C. D., Charalambous, T., Kourtellaris, C., & Van Schuppen, J. H. (2020). Structural Properties of Nonanticipatory Epsilon Entropy of Multivariate Gaussian Sources. In Proceedings of the IEEE International Symposium on Information Theory, ISIT 2020 (pp. 2867-2872). Article 9174319 (IEEE International Symposium on Information Theory). IEEE. https://doi.org/10.1109/ISIT44484.2020.9174319

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title = "Structural Properties of Nonanticipatory Epsilon Entropy of Multivariate Gaussian Sources",

abstract = "The complete characterization of the Gorbunov and Pinsker [1], [2] nonanticipatory epsilon entropy of multivariate Gauss-Markov sources with square-error fidelity is derived, which remained an open problem since 1974. Specifically, it is shown that the optimal matrices of the stochastic realization of the optimal test channel or reproduction distribution, admit spectral representations with respect to the same unitary matrices, and that the optimal reproduction process is generated, subject to pre-processing and post-processing by memoryless parallel additive Gaussian noise channels. The derivations and analyses are new and bring out several properties of such optimization problems over the space of conditional distributions and their realizations.",

keywords = "Entropy, Gaussian channels, Gaussian noise, Markov processes, Matrix algebra, Spectral analysis, Stochastic programming",

author = "Charalambous, \{Charalambos D.\} and Themistoklis Charalambous and Christos Kourtellaris and \{Van Schuppen\}, \{Jan H.\}",

year = "2020",

doi = "10.1109/ISIT44484.2020.9174319",

language = "English",

series = "IEEE International Symposium on Information Theory",

publisher = "IEEE",

pages = "2867--2872",

booktitle = "Proceedings of the IEEE International Symposium on Information Theory, ISIT 2020",

address = "United States",

note = "IEEE International Symposium on Information Theory, ISIT ; Conference date: 21-07-2020 Through 26-07-2020",

}

Charalambous, CD, Charalambous, T, Kourtellaris, C & Van Schuppen, JH 2020, Structural Properties of Nonanticipatory Epsilon Entropy of Multivariate Gaussian Sources. in Proceedings of the IEEE International Symposium on Information Theory, ISIT 2020., 9174319, IEEE International Symposium on Information Theory, IEEE, pp. 2867-2872, IEEE International Symposium on Information Theory, Los Angeles, California, United States, 21/07/2020. https://doi.org/10.1109/ISIT44484.2020.9174319

Structural Properties of Nonanticipatory Epsilon Entropy of Multivariate Gaussian Sources. / Charalambous, Charalambos D.; Charalambous, Themistoklis; Kourtellaris, Christos et al.
Proceedings of the IEEE International Symposium on Information Theory, ISIT 2020. IEEE, 2020. p. 2867-2872 9174319 (IEEE International Symposium on Information Theory).

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

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T1 - Structural Properties of Nonanticipatory Epsilon Entropy of Multivariate Gaussian Sources

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AU - Van Schuppen, Jan H.

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AB - The complete characterization of the Gorbunov and Pinsker [1], [2] nonanticipatory epsilon entropy of multivariate Gauss-Markov sources with square-error fidelity is derived, which remained an open problem since 1974. Specifically, it is shown that the optimal matrices of the stochastic realization of the optimal test channel or reproduction distribution, admit spectral representations with respect to the same unitary matrices, and that the optimal reproduction process is generated, subject to pre-processing and post-processing by memoryless parallel additive Gaussian noise channels. The derivations and analyses are new and bring out several properties of such optimization problems over the space of conditional distributions and their realizations.

KW - Entropy

KW - Gaussian channels

KW - Gaussian noise

KW - Markov processes

KW - Matrix algebra

KW - Spectral analysis

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ER -

Structural Properties of Nonanticipatory Epsilon Entropy of Multivariate Gaussian Sources

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-: Co-design of control and communication systems for wireless networked control systems

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Structural Properties of Nonanticipatory Epsilon Entropy of Multivariate Gaussian Sources

Abstract

Publication series

Conference

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Keywords

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-: Co-design of control and communication systems for wireless networked control systems

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