Non-Asymptotic Fundamental Limits of Guessing Subject to Distortion

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Abstract

This paper investigates the problem of guessing subject to distortion, which was introduced by Arikan and Merhav. While the primary concern of the previous study was asymptotic analysis, our primary concern is non-asymptotic analysis. We prove non-asymptotic achievability and converse bounds of the moment of the number of guesses without side information (resp. with side information) by using a quantity based on the Rényi entropy (resp. the Arimoto-Rényi conditional entropy). Also, we introduce an error probability and show similar results. Further, from our bounds, we derive a single-letter characterization of the asymptotic exponent of guessing moment for a stationary memoryless source.

Original languageEnglish
Title of host publication2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages652-656
Number of pages5
ISBN (Electronic)9781538692912
DOIs
Publication statusPublished - 2019 Jul
Event2019 IEEE International Symposium on Information Theory, ISIT 2019 - Paris, France
Duration: 2019 Jul 72019 Jul 12

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2019-July
ISSN (Print)2157-8095

Conference

Conference2019 IEEE International Symposium on Information Theory, ISIT 2019
CountryFrance
CityParis
Period19/7/719/7/12

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ASJC Scopus subject areas

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

Cite this

Saito, S., & Matsushima, T. (2019). Non-Asymptotic Fundamental Limits of Guessing Subject to Distortion. In 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings (pp. 652-656). [8849434] (IEEE International Symposium on Information Theory - Proceedings; Vol. 2019-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2019.8849434