Capacity of Finite State Channels with Feedback: Algorithmic and Optimization Theoretic Properties

Andrea Grigorescu, Holger Boche, Rafael F. Schaefer, H. Vincent Poor

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

1 Scopus citations

Abstract

The capacity of finite state channels (FSCs) with feedback has been expressed by a limit of a sequence of multi-letter expressions. Despite many efforts, a closed-form single-letter capacity characterization remains unknown to date. In this paper, the feedback capacity is studied from a fundamental algorithmic point of view by addressing the question of whether or not the capacity can be algorithmically computed. To this aim, the concept of Turing machines is used, which provides fundamental performance limits of digital computers. It is shown that the feedback capacity of FSCs is not Banach-Mazur computable and therefore also not Borel-Turing computable. As a consequence, it is shown that either achievability or converse (or both) is not Banach-Mazur computable, which means that there are FSCs for which it is impossible to find computable tight upper and lower bounds. Furthermore, it is shown that the feedback capacity cannot be characterized as the maximization of a finite-letter formula of entropic quantities.

Original languageEnglish (US)
Title of host publication2022 IEEE International Symposium on Information Theory, ISIT 2022
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages498-503
Number of pages6
ISBN (Electronic)9781665421591
DOIs
StatePublished - 2022
Externally publishedYes
Event2022 IEEE International Symposium on Information Theory, ISIT 2022 - Espoo, Finland
Duration: Jun 26 2022Jul 1 2022

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2022-June
ISSN (Print)2157-8095

Conference

Conference2022 IEEE International Symposium on Information Theory, ISIT 2022
Country/TerritoryFinland
CityEspoo
Period6/26/227/1/22

All Science Journal Classification (ASJC) codes

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

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