Codes on Graphs: Duality and MacWilliams Identities
Name
Forney-Codes on Graphs.pdf
Size
317.08 KB
Format
Adobe PDF
Checksum (MD5)
93af7223e017136974f26db3e05b649f
Author(s)
Forney, G. David, Jr.
Date Issued
February 2011
Journal
IEEE Transactions on Information Theory
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Forney, G. David. “Codes on Graphs: Duality and MacWilliams Identities.” IEEE Transactions on Information Theory 57.3 (2011): 1382–1397.
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1109/tit.2011.2104994
