Metric Mean Dimension and Analog Compression

Yonatan Gutman; Adam Śpiewak

doi:10.1109/TIT.2020.2992388

Metric Mean Dimension and Analog Compression

Yonatan Gutman, Adam Śpiewak

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9 Scopus citations

Abstract

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.

Original language	English
Article number	9086002
Pages (from-to)	6977-6998
Number of pages	22
Journal	IEEE Transactions on Information Theory
Volume	66
Issue number	11
DOIs	https://doi.org/10.1109/TIT.2020.2992388
State	Published - Nov 2020
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 1963-2012 IEEE.

Funding

Manuscript received July 2, 2019; revised April 17, 2020; accepted April 25, 2020. Date of publication May 4, 2020; date of current version October 21, 2020. The work of Yonatan Gutman was supported in part by the National Science Center, Poland, under Grant 2013/08/A/ST1/00275 and Grant 2016/22/E/ST1/00448. The work of Adam S´piewak was supported by the National Science Center, Poland, under Grant 2016/22/E/ST1/00448. This article was presented in part at the 2019 IEEE International Symposium on Information Theory. (Corresponding author: Yonatan Gutman.) Yonatan Gutman is with the Institute of Mathematics, Polish Academy of Sciences, 00-656 Warszawa, Poland (e-mail: [email protected]).

Funders	Funder number
National Science Center	2013/08/A/ST1/00275, 2016/22/E/ST1/00448

Keywords

analog signals
information dimension
lossless compression
metric mean dimension

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10.1109/TIT.2020.2992388

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Metric Mean Dimension and Analog Compression

Abstract

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Keywords

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