Rate-distortion dimension of stochastic processes

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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 languageEnglish (US)
Title of host publicationProceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages5
ISBN (Electronic)9781509018062
StatePublished - Aug 10 2016
Event2016 IEEE International Symposium on Information Theory, ISIT 2016 - Barcelona, Spain
Duration: Jul 10 2016Jul 15 2016

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8095


Other2016 IEEE International Symposium on Information Theory, ISIT 2016


  • Compressed Sensing
  • Information Dimension
  • Rate-Distortion Dimension

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics


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