New Uniform Bounds for Almost Lossless Analog Compression

Yonatan Gutman; Adam Śpiewak

doi:10.1109/ISIT.2019.8849340

New Uniform Bounds for Almost Lossless Analog Compression

Yonatan Gutman, Adam Śpiewak

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

5 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 mathcal{S} \subset {[ {0,1} ]{\mathbb{Z}}} 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.

Original language	English
Title of host publication	2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1702-1706
Number of pages	5
ISBN (Electronic)	9781538692912
DOIs	https://doi.org/10.1109/ISIT.2019.8849340
State	Published - Jul 2019
Externally published	Yes
Event	2019 IEEE International Symposium on Information Theory, ISIT 2019 - Paris, France Duration: 7 Jul 2019 → 12 Jul 2019

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2019-July
ISSN (Print)	2157-8095

Conference

Conference	2019 IEEE International Symposium on Information Theory, ISIT 2019
Country/Territory	France
City	Paris
Period	7/07/19 → 12/07/19

Bibliographical note

Publisher Copyright:
© 2019 IEEE.

Funding

Y.G was partially supported by the National Science Center (Poland) Grant 2013/08/A/ST1/00275. Y.G and A.S were partially supported by the National Science Center (Poland) grant 2016/22/E/ST1/00448. We are grateful to Amos Lapidoth, Neri Merhav and Erwin Riegler for helpful discussions. Y.G was partially supported by the National Science Center (Poland) Grant 2013/08/A/ST1/00275. Y.G and A.S´ were partially supported by the National Science Center (Poland) grant 2016/22/E/ST1/00448.

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

Access to Document

10.1109/ISIT.2019.8849340

Cite this

Gutman, Y., & Śpiewak, A. (2019). New Uniform Bounds for Almost Lossless Analog Compression. In 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings (pp. 1702-1706). Article 8849340 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2019-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2019.8849340

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abstract = "Wu and Verd{\'u} 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 mathcal\{S\} \textbackslash{}subset \{[ \{0,1\} ]\{\textbackslash{}mathbb\{Z\}\}\} 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.",

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Gutman, Y & Śpiewak, A 2019, New Uniform Bounds for Almost Lossless Analog Compression. in 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings., 8849340, IEEE International Symposium on Information Theory - Proceedings, vol. 2019-July, Institute of Electrical and Electronics Engineers Inc., pp. 1702-1706, 2019 IEEE International Symposium on Information Theory, ISIT 2019, Paris, France, 7/07/19. https://doi.org/10.1109/ISIT.2019.8849340

New Uniform Bounds for Almost Lossless Analog Compression. / Gutman, Yonatan; Śpiewak, Adam.
2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2019. p. 1702-1706 8849340 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2019-July).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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New Uniform Bounds for Almost Lossless Analog Compression

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