English

MacWilliams Identities for Codes on Graphs

Information Theory 2009-08-04 v2 math.IT

Abstract

The MacWilliams identity for linear time-invariant convolutional codes that has recently been found by Gluesing-Luerssen and Schneider is proved concisely, and generalized to arbitrary group codes on graphs. A similar development yields a short, transparent proof of the dual sum-product update rule.

Cite

@article{arxiv.0903.4207,
  title  = {MacWilliams Identities for Codes on Graphs},
  author = {G. David Forney},
  journal= {arXiv preprint arXiv:0903.4207},
  year   = {2009}
}

Comments

5 pages, 2 figures; final version to be presented at IEEE Information Theory Workshop, Taormina, Sicily, Oct. 11-16, 2009

R2 v1 2026-06-21T12:44:04.221Z