A complete MacWilliams theorem for convolutional codes

Ching-Yi Lai, Min Hsiu Hsieh, Francis Lu

研究成果: Conference contribution同行評審

1 引文 斯高帕斯(Scopus)

摘要

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.

原文English
主出版物標題2014 IEEE Information Theory Workshop, ITW 2014
發行者Institute of Electrical and Electronics Engineers Inc.
頁面157-161
頁數5
ISBN(電子)9781479959990
DOIs
出版狀態Published - 1 12月 2014
事件2014 IEEE Information Theory Workshop, ITW 2014 - Hobart, Australia
持續時間: 2 11月 20145 11月 2014

出版系列

名字2014 IEEE Information Theory Workshop, ITW 2014

Conference

Conference2014 IEEE Information Theory Workshop, ITW 2014
國家/地區Australia
城市Hobart
期間2/11/145/11/14

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