Codes on Graphs: A Survey for Algebraists

  • Authors:
  • G. David Forney, Jr.

  • Affiliations:
  • -

  • Venue:
  • AAECC-13 Proceedings of the 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
  • Year:
  • 1999

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Abstract

There is intense current interest in the subject of "codes on graphs." Graphical models for codes arise from state realizations. Normal realizations may be assumed without loss of generality. A normal realization has a dual which necessarily generates the dual code. Conventional trellises and tail-biting realizations are inherently normal. Efficient realizations of Reed-Muller codes are presented. Low-density parity-check codes use generic parity-check realizations. Algebraic tools may improve such graph-based codes.