A complete MacWilliams theorem for convolutional codes

Lai, CY; Hsieh, MH; Lu, HF

A complete MacWilliams theorem for convolutional codes

Lai, CY

Hsieh, MH

Lu, HF

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Publication Type:: Conference Proceeding
Citation:: 2014 IEEE Information Theory Workshop, ITW 2014, 2014, pp. 157 - 161
Issue Date:: 2014-01-01

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Field	Value	Language
dc.contributor.author	Lai, CY https://orcid.org/0000-0003-1970-8167	en_US
dc.contributor.author	Hsieh, MH https://orcid.org/0000-0002-3396-8427	en_US
dc.contributor.author	Lu, HF	en_US
dc.date.issued	2014-01-01	en_US
dc.identifier.citation	2014 IEEE Information Theory Workshop, ITW 2014, 2014, pp. 157 - 161	en_US
dc.identifier.isbn	9781479959990	en_US
dc.identifier.uri	http://hdl.handle.net/10453/43741
dc.description.abstract	© 2014 IEEE. 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.	en_US
dc.relation.ispartof	2014 IEEE Information Theory Workshop, ITW 2014	en_US
dc.relation.isbasedon	10.1109/ITW.2014.6970812	en_US
dc.title	A complete MacWilliams theorem for convolutional codes	en_US
dc.type	Conference Proceeding
utslib.for	080199 Artificial Intelligence and Image Processing not elsewhere classified	en_US
utslib.for	080203 Computational Logic and Formal Languages	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Strength - QSI - Centre for Quantum Software and Information
utslib.copyright.status	open_access
pubs.publication-status	Published	en_US

Abstract:

© 2014 IEEE. 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.

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http://hdl.handle.net/10453/43741