Cart (Loading....) | Create Account
Close category search window

Codes on Graphs: Duality and MacWilliams Identities

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

1 Author(s)
Forney, G.D., Jr. ; Lab. for Inf. & Decision Syst., Massachusetts Inst. of Technol., Cambridge, MA, USA

A conceptual framework involving partition functions of normal factor graphs is introduced, paralleling a similar recent development by Al-Bashabsheh and Mao. The partition functions of dual normal factor graphs are shown to be a Fourier transform pair, whether or not the graphs have cycles. The original normal graph duality theorem follows as a corollary. Within this framework, MacWilliams identities are found for various local and global weight generating functions of general group or linear codes on graphs; this generalizes and provides a concise proof of the MacWilliams identity for linear time-invariant convolutional codes that was recently found by Gluesing-Luerssen and Schneider. Further MacWilliams identities are developed for terminated convolutional codes, particularly for tail-biting codes, similar to those studied recently by Bocharova, Hug, Johannesson, and Kudryashov.

Published in:

Information Theory, IEEE Transactions on  (Volume:57 ,  Issue: 3 )

Date of Publication:

March 2011

Need Help?

IEEE Advancing Technology for Humanity About IEEE Xplore | Contact | Help | Terms of Use | Nondiscrimination Policy | Site Map | Privacy & Opting Out of Cookies

A not-for-profit organization, IEEE is the world's largest professional association for the advancement of technology.
© Copyright 2014 IEEE - All rights reserved. Use of this web site signifies your agreement to the terms and conditions.