MacWilliams Identities for Terminated Convolutional Codes
Information Theory
2010-04-23 v3 math.IT
Abstract
Shearer and McEliece [1977] showed that there is no MacWilliams identity for the free distance spectra of orthogonal linear convolutional codes. We show that on the other hand there does exist a MacWilliams identity between the generating functions of the weight distributions per unit time of a linear convolutional code C and its orthogonal code C^\perp, and that this distribution is as useful as the free distance spectrum for estimating code performance. These observations are similar to those made recently by Bocharova, Hug, Johannesson and Kudryashov; however, we focus on terminating by tail-biting rather than by truncation.
Cite
@article{arxiv.1001.0723,
title = {MacWilliams Identities for Terminated Convolutional Codes},
author = {G. David Forney},
journal= {arXiv preprint arXiv:1001.0723},
year = {2010}
}
Comments
5 pages; accepted for 2010 IEEE International Symposium on Information Theory, Austin, TX, June 13-18