A complete MacWilliams theorem for convolutional codes

Ching-Yi Lai, Min Hsiu Hsieh, Francis Lu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

In this paper, we prove a MacWilliams identity for the weight adjacency matrices based on the constraint codes of a convolutional code (CC) and its dual. Our result improves upon a recent result by Gluesing-Luerssen and Schneider, where the requirement of a minimal encoder is assumed. We can also establish the MacWilliams identity for the input-parity weight adjacency matrices of a systematic CC and its dual. Most importantly, we show that a type of Hamming weight enumeration functions of all codewords of a CC can be derived from the weight adjacency matrix, which thus provides a connection between these two very different notions of weight enumeration functions in the convolutional code literature. Finally, the relations between various enumeration functions of a CC and its dual are summarized in a diagram. This explains why no MacWilliams identity exists for the free-distance enumerators.

Original languageEnglish
Title of host publication2014 IEEE Information Theory Workshop, ITW 2014
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages157-161
Number of pages5
ISBN (Electronic)9781479959990
DOIs
StatePublished - 1 Dec 2014
Event2014 IEEE Information Theory Workshop, ITW 2014 - Hobart, Australia
Duration: 2 Nov 20145 Nov 2014

Publication series

Name2014 IEEE Information Theory Workshop, ITW 2014

Conference

Conference2014 IEEE Information Theory Workshop, ITW 2014
CountryAustralia
CityHobart
Period2/11/145/11/14

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    Lai, C-Y., Hsieh, M. H., & Lu, F. (2014). A complete MacWilliams theorem for convolutional codes. In 2014 IEEE Information Theory Workshop, ITW 2014 (pp. 157-161). [6970812] (2014 IEEE Information Theory Workshop, ITW 2014). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ITW.2014.6970812