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 proceedingConference contributionScientificpeer-review

4 Citations (Scopus)
56 Downloads (Pure)


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 languageEnglish
Title of host publicationProceedings of the IEEE International Symposium on Information Theory, ISIT 2020
Number of pages6
ISBN (Electronic)9781728164328
Publication statusPublished - 2020
MoE publication typeA4 Article in a conference publication
EventIEEE International Symposium on Information Theory - Los Angeles, United States
Duration: 21 Jul 202026 Jul 2020

Publication series

NameIEEE International Symposium on Information Theory
ISSN (Print)2157-8095
ISSN (Electronic)2157-8117


ConferenceIEEE International Symposium on Information Theory
Abbreviated titleISIT
Country/TerritoryUnited States
CityLos Angeles


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


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