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

Research output: Contribution to journal › Article › peer-review

12 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

Access to Document

10.1109/TIT.2020.2992388

Cite this

@article{065e3bc62e4e446f9e3cb1476b2d52bb,

title = "Metric Mean Dimension and Analog Compression",

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 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.",

keywords = "analog signals, information dimension, lossless compression, metric mean dimension",

author = "Yonatan Gutman and Adam {\'S}piewak",

note = "Publisher Copyright: {\textcopyright} 1963-2012 IEEE.",

year = "2020",

month = nov,

doi = "10.1109/TIT.2020.2992388",

language = "אנגלית",

volume = "66",

pages = "6977--6998",

journal = "IEEE Transactions on Information Theory",

issn = "0018-9448",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "11",

}

TY - JOUR

T1 - Metric Mean Dimension and Analog Compression

AU - Gutman, Yonatan

AU - Śpiewak, Adam

PY - 2020/11

Y1 - 2020/11

N2 - 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.

AB - 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.

KW - analog signals

KW - information dimension

KW - lossless compression

KW - metric mean dimension

UR - https://www.scopus.com/pages/publications/85094679300

U2 - 10.1109/TIT.2020.2992388

DO - 10.1109/TIT.2020.2992388

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85094679300

SN - 0018-9448

VL - 66

SP - 6977

EP - 6998

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 11

M1 - 9086002

ER -

Metric Mean Dimension and Analog Compression

Abstract

Bibliographical note

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this