A de Bruijn identity for discrete random variables

Oliver Johnson, Saikat Guha

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

3 Scopus citations

Abstract

We discuss properties of the 'beamsplitter addition' operation, which provides a non-standard scaled convolution of random variables supported on the non-negative integers. We give a simple expression for the action of beamsplitter addition using generating functions. We use this to give a self-contained and purely classical proof of a heat equation and de Bruijn identity, satisfied when one of the variables is geometric.

Original languageEnglish (US)
Title of host publication2017 IEEE International Symposium on Information Theory, ISIT 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages898-902
Number of pages5
ISBN (Electronic)9781509040964
DOIs
StatePublished - Aug 9 2017
Event2017 IEEE International Symposium on Information Theory, ISIT 2017 - Aachen, Germany
Duration: Jun 25 2017Jun 30 2017

Publication series

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

Other

Other2017 IEEE International Symposium on Information Theory, ISIT 2017
CountryGermany
CityAachen
Period6/25/176/30/17

ASJC Scopus subject areas

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

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  • Cite this

    Johnson, O., & Guha, S. (2017). A de Bruijn identity for discrete random variables. In 2017 IEEE International Symposium on Information Theory, ISIT 2017 (pp. 898-902). [8006658] (IEEE International Symposium on Information Theory - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2017.8006658