Polarization of the Rényi information dimension for single and multi terminal analog compression

Saeid Haghighatshoar, Emmanuel Abbe

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

8 Scopus citations

Abstract

This paper shows that the Rényi information dimension (RID) of an i.i.d. sequence of mixture random variables polarizes to the extremal values of 0 and 1 (fully discrete and continuous distributions) when transformed by an Hadamard matrix. This provides a natural counter-part over the reals of the entropy polarization phenomenon over finite fields. It is further shown that the polarization pattern of the RID is equivalent to the BEC polarization pattern, which admits a closed form expression. These results are used to construct universal and deterministic partial Hadamard matrices for analog to analog (A2A) compression of memoryless sources. In addition, a framework for the A2A compression of multi-terminal correlated sources is developed, providing a first counter-part of the Slepian-Wolf coding problem in the A2A setting.

Original languageEnglish (US)
Title of host publication2013 IEEE International Symposium on Information Theory, ISIT 2013
Pages779-783
Number of pages5
DOIs
StatePublished - Dec 19 2013
Event2013 IEEE International Symposium on Information Theory, ISIT 2013 - Istanbul, Turkey
Duration: Jul 7 2013Jul 12 2013

Publication series

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

Other

Other2013 IEEE International Symposium on Information Theory, ISIT 2013
CountryTurkey
CityIstanbul
Period7/7/137/12/13

All Science Journal Classification (ASJC) codes

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

Keywords

  • Analog compression
  • Compressed sensing
  • Distributed analog compression
  • Information preserving matrices
  • Polarization
  • Rényi information dimension

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  • Cite this

    Haghighatshoar, S., & Abbe, E. (2013). Polarization of the Rényi information dimension for single and multi terminal analog compression. In 2013 IEEE International Symposium on Information Theory, ISIT 2013 (pp. 779-783). [6620332] (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2013.6620332