標題: A Complete MacWilliams Theorem for Convolutional Codes
作者: Lai, Ching-Yi
Hsieh, Min-Hsiu
Lu, Hsiao-feng
電機工程學系
Department of Electrical and Computer Engineering
公開日期: 1-Jan-2014
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.
URI: http://hdl.handle.net/11536/146806
ISSN: 2475-420X
期刊: 2014 IEEE INFORMATION THEORY WORKSHOP (ITW)
起始頁: 157
結束頁: 161
Appears in Collections:Conferences Paper