On the Structure of the Capacity Formula for General Finite State Channels with Applications

Publikation: Beitrag in Buch/Konferenzbericht/Sammelband/GutachtenBeitrag in KonferenzbandBeigetragenBegutachtung

Beitragende

  • Holger Boche - , Technische Universität München (Autor:in)
  • Rafael F. Schaefer - , Technische Universität Berlin (Autor:in)
  • H. Vincent Poor - , Princeton University (Autor:in)

Abstract

Finite state channels (FSCs) model discrete channels with memory where the channel output depends on the channel input and the actual channel state. The capacity of general FSCs has been established as the limit of a sequence of multi-letter expressions; a corresponding finite-letter characterization is not known to date. In this paper, it is shown that it is indeed not possible to find such a finite-letter entropic characterization for FSCs whose input, output, and state alphabets satisfy |X| ≥ 2, |Y| ≥2, and |S| ≥2. Further, the algorithmic computability of the capacity of FSCs is studied. To account for this, the concept of a Turing machine is adopted as it provides fundamental performance limits for today's digital computers. It is shown that the capacity of a FSC is not Banach-Mazur computable and therewith not Turing computable for |X| ≥ 2, |Y| ≥ 2, |S| ≥ 2.

Details

OriginalspracheEnglisch
Titel2019 IEEE Information Theory Workshop, ITW 2019
Herausgeber (Verlag)Institute of Electrical and Electronics Engineers Inc.
ISBN (elektronisch)978-1-5386-6900-6
PublikationsstatusVeröffentlicht - Aug. 2019
Peer-Review-StatusJa
Extern publiziertJa

Konferenz

Titel2019 IEEE Information Theory Workshop, ITW 2019
Dauer25 - 28 August 2019
StadtVisby
LandSchweden

Externe IDs

ORCID /0000-0002-1702-9075/work/165878263