Graph-based Encoders and their Achievable Rates for Channels with Feedback

Oron Sabag, Bashar Huleihel, Haim H. Permuter

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

2 Scopus citations

Abstract

This paper investigates graph-based encoders for the unifilar finite-state channel (FSC) with feedback. A recent paper introduced the Q-graph as a tool for the recursive quantization of channel outputs on a directed graph. The Q- graph approach yielded single-letter lower and upper bounds on the feedback capacity of unifilar FSCs, termed here Q-LB and Q-UB, respectively. The current paper provides two computable optimization problems for the Q-LB and the Q-UB. The first, for the Q-LB, aims to find the graph-based encoder with the highest achievable rate. Specifically, for a structured cooperation between the encoder and the decoder, that is given by a particular Q-graph, the optimization problem maximizes the Q-LB over all input distributions. The resultant graph-based encoder from the optimization problem has a corresponding posterior matching scheme that achieves the Q-LB. The second optimization problem provides a formulation of the Q-UB as a convex optimization problem. Numerical results of the Q-LB and the Q-UB are presented for the Ising channel and a simplified version of a fading channel. The numerical results are then translated into analytical expressions for graph-based encoders and their achievable rates.

Original languageAmerican English
Title of host publication2018 IEEE International Symposium on Information Theory, ISIT 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1121-1125
Number of pages5
ISBN (Print)9781538647806
DOIs
StatePublished - 15 Aug 2018
Externally publishedYes
Event2018 IEEE International Symposium on Information Theory, ISIT 2018 - Vail, United States
Duration: 17 Jun 201822 Jun 2018

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2018-June
ISSN (Print)2157-8095

Conference

Conference2018 IEEE International Symposium on Information Theory, ISIT 2018
Country/TerritoryUnited States
CityVail
Period17/06/1822/06/18

Bibliographical note

Publisher Copyright:
© 2018 IEEE.

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