MacWilliams Identities for Codes on Graphs
arXiv:0903.4207
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.
5 pages, 2 figures; final version to be presented at IEEE Information Theory Workshop, Taormina, Sicily, Oct. 11-16, 2009