Structural Properties of Nonanticipatory Epsilon Entropy of Multivariate Gaussian Sources

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.

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

DOI

10.1109/ISIT44484.2020.9174319

Citation

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 ., 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

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https://urn.fi/URN:NBN:fi:aalto-202010165872

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[article-cris] Sähkötekniikan korkeakoulu / ELEC

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Structural Properties of Nonanticipatory Epsilon Entropy of Multivariate Gaussian Sources

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