Observability, controllability and local reducibility of linear codes on graphs

G. David Forney, Heide Gluesing-Luerssen

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

Abstract

This paper is concerned with the local reducibility properties of linear realizations of codes on finite graphs. Trimness and properness are dual properties of constraint codes. A linear realization is locally reducible if any constraint code is not both trim and proper. On a finite cycle-free graph, a linear realization is minimal if and only if every constraint code is both trim and proper. A linear realization is called observable if it is one-to-one, and controllable if all constraints are independent. Observability and controllability are dual properties. An unobservable or uncontrollable realization is locally reducible. A parity-check realization is uncontrollable if and only if it has redundant parity checks. A tail-biting trellis realization is uncontrollable if and only if its trajectories partition into disconnected subrealizations. General graphical realizations do not share this property.

Original languageEnglish
Title of host publication2012 IEEE International Symposium on Information Theory Proceedings, ISIT 2012
Pages641-645
Number of pages5
DOIs
StatePublished - 2012
Event2012 IEEE International Symposium on Information Theory, ISIT 2012 - Cambridge, MA, United States
Duration: Jul 1 2012Jul 6 2012

Publication series

NameIEEE International Symposium on Information Theory - Proceedings

Conference

Conference2012 IEEE International Symposium on Information Theory, ISIT 2012
Country/TerritoryUnited States
CityCambridge, MA
Period7/1/127/6/12

ASJC Scopus subject areas

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

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