Optimizing Estimated Directed Information over Discrete Alphabets

Dor Tsur, Ziv Aharoni, Ziv Goldfeld, Haim H. Permuter

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

Abstract

Directed information (DI) is a fundamental measure for the study and analysis of sequential stochastic models. In particular, when optimized over the input distribution, it characterizes the capacity of general communication channels. However, existing optimization methods for discrete input alphabets assume full knowledge of the channel model, and are therefore not applicable when only samples are available. We derive a new method that overcomes this limitation and enables optimizing DI over unknown channels. To that end, we formulate the problem as a Markov decision process and leverage reinforcement learning techniques to optimize a deep generative model of the channel input probability mass function (PMF). Combining our optimizer with the DI neural estimator, we obtain an end-to-end estimation-optimization scheme which is applied for estimating the capacity of various discrete channels with memory. We provide empirical results that demonstrate the utility of the proposed framework and further show how to use the optimized PMF generator to obtain theoretical bounds on the feedback capacity for unifilar finite state channels.

Original languageEnglish
Title of host publication2022 IEEE International Symposium on Information Theory, ISIT 2022
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2898-2903
Number of pages6
ISBN (Electronic)9781665421591
DOIs
StatePublished - 2022
Event2022 IEEE International Symposium on Information Theory, ISIT 2022 - Espoo, Finland
Duration: 26 Jun 20221 Jul 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
Period26/06/221/07/22

Keywords

  • Analytical models
  • Atmospheric measurements
  • Optimization methods
  • Channel estimation
  • Reinforcement learning
  • Particle measurements
  • Markov processes

ASJC Scopus subject areas

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

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