The Duality Upper Bound for Unifilar Finite-State Channels with Feedback

Oron Sabag, Haim H. Permuter

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

The capacity of finite-state channels (FSCs) with feedback is considered. We derive a simple upper bound on the feedback capacity. The upper bound is based on an extension of the known duality upper bound on mutual information to the case of directed information. The upper bound is a function of test distributions on the channel outputs ensemble. We show that if the test distribution is structured on a Q-graph, and the FSC is unifilar, the upper bound can be formulated as a Markov decision process (MDP). The resulted MDP has finite states, actions and disturbances and, therefore, can be solved analytically with standard MDP tools. We illustrate the simplicity of computing the bounds for the dicode erasure and the Ising channels. The resulted upper bounds are tight and their derivation serves as an alternative and simple converse proof. The developed methodology is capable of solving channels with large alphabets of the channel states, inputs and outputs.
Original languageEnglish
Title of host publicationInternational Zurich Seminar on Information and Communication (IZS 2020). Proceedings
EditorsAmos Lapidoth, Stefan M. Moser
Place of PublicationZurich
PublisherETH Zurich
Pages68 - 72
DOIs
StatePublished - 26 Feb 2020
EventInternational Zurich Seminar on Information and Communication 2020 - Zurich, Switzerland
Duration: 26 Feb 202028 Feb 2020
https://www.izs.ethz.ch/2020/

Conference

ConferenceInternational Zurich Seminar on Information and Communication 2020
Abbreviated titleIZS 2020
Country/TerritorySwitzerland
CityZurich
Period26/02/2028/02/20
Internet address

Bibliographical note

International Zurich Seminar on Information and Communication (IZS 2020); Conference Location: Zurich, Switzerland; Conference Date: February 26–28, 2020

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