Rate-distortion dimension of stochastic processes

Farideh Ebrahim Rezagah; Shirin Jalali; Elza Erkip; H. Vincent Poor

doi:10.1109/ISIT.2016.7541665

Rate-distortion dimension of stochastic processes

Farideh Ebrahim Rezagah, Shirin Jalali, Elza Erkip, H. Vincent Poor

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

3 Scopus citations

Abstract

The rate-distortion dimension (RDD) of an analog stationary process is studied as a measure of complexity that captures the amount of information contained in the process. It is shown that the RDD of a process, defined as two times the asymptotic ratio of its rate-distortion function R(D) to log 1/D as the distortion D approaches zero, is equal to its information dimension (ID). This generalizes an earlier result by Kawabata and Dembo and provides an operational approach to evaluate the ID of a process, which previously was shown to be closely related to the effective dimension of the underlying process and also to the fundamental limits of compressed sensing. The relation between RDD and ID is illustrated for a piecewise constant process.

Original language	English (US)
Title of host publication	Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2079-2083
Number of pages	5
ISBN (Electronic)	9781509018062
DOIs	https://doi.org/10.1109/ISIT.2016.7541665
State	Published - Aug 10 2016
Event	2016 IEEE International Symposium on Information Theory, ISIT 2016 - Barcelona, Spain Duration: Jul 10 2016 → Jul 15 2016

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2016-August
ISSN (Print)	2157-8095

Other

Other	2016 IEEE International Symposium on Information Theory, ISIT 2016
Country/Territory	Spain
City	Barcelona
Period	7/10/16 → 7/15/16

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Information Systems
Modeling and Simulation
Applied Mathematics

Keywords

Compressed Sensing
Information Dimension
Rate-Distortion Dimension

Access to Document

10.1109/ISIT.2016.7541665

Cite this

Rezagah, F. E., Jalali, S., Erkip, E., & Poor, H. V. (2016). Rate-distortion dimension of stochastic processes. In Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory (pp. 2079-2083). Article 7541665 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2016-August). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2016.7541665

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Rezagah, FE, Jalali, S, Erkip, E & Poor, HV 2016, Rate-distortion dimension of stochastic processes. in Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory., 7541665, IEEE International Symposium on Information Theory - Proceedings, vol. 2016-August, Institute of Electrical and Electronics Engineers Inc., pp. 2079-2083, 2016 IEEE International Symposium on Information Theory, ISIT 2016, Barcelona, Spain, 7/10/16. https://doi.org/10.1109/ISIT.2016.7541665

Rate-distortion dimension of stochastic processes. / Rezagah, Farideh Ebrahim; Jalali, Shirin; Erkip, Elza et al.
Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory. Institute of Electrical and Electronics Engineers Inc., 2016. p. 2079-2083 7541665 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2016-August).

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

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N2 - The rate-distortion dimension (RDD) of an analog stationary process is studied as a measure of complexity that captures the amount of information contained in the process. It is shown that the RDD of a process, defined as two times the asymptotic ratio of its rate-distortion function R(D) to log 1/D as the distortion D approaches zero, is equal to its information dimension (ID). This generalizes an earlier result by Kawabata and Dembo and provides an operational approach to evaluate the ID of a process, which previously was shown to be closely related to the effective dimension of the underlying process and also to the fundamental limits of compressed sensing. The relation between RDD and ID is illustrated for a piecewise constant process.

AB - The rate-distortion dimension (RDD) of an analog stationary process is studied as a measure of complexity that captures the amount of information contained in the process. It is shown that the RDD of a process, defined as two times the asymptotic ratio of its rate-distortion function R(D) to log 1/D as the distortion D approaches zero, is equal to its information dimension (ID). This generalizes an earlier result by Kawabata and Dembo and provides an operational approach to evaluate the ID of a process, which previously was shown to be closely related to the effective dimension of the underlying process and also to the fundamental limits of compressed sensing. The relation between RDD and ID is illustrated for a piecewise constant process.

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Rate-distortion dimension of stochastic processes

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