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