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Metric mean dimension and analog compression

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posted on 11.08.2020, 14:16 by Yonatan Gutman, Adam Śpiewak
Wu and Verdú developed a theory of almost lossless analog compression, where one imposes various regularity conditions on the compressor and the decompressor with the input signal being modelled by a (typically infinite-entropy) stationary stochastic process. In this work we consider all stationary stochastic processes with trajectories in a prescribed set of (bi-)infinite sequences and find uniform lower and upper bounds for certain compression rates in terms of metric mean dimension and mean box dimension. An essential tool is the recent Lindenstrauss-Tsukamoto variational principle expressing metric mean dimension in terms of rate-distortion functions. We obtain also lower bounds on compression rates for a fixed stationary process in terms of the rate-distortion dimension rates and study several examples.

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Invariant measures, entropy and other growth parameters in the classical and non-classical dynamical systems

National Science Center

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Interrelations between ergodic theory and topological dynamics

National Science Center

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Email Address of Submitting Author

a.spiewak@mimuw.edu.pl

ORCID of Submitting Author

https://orcid.org/0000-0002-5012-0428

Submitting Author's Institution

University of Warsaw

Submitting Author's Country

Poland

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