On the MacWilliams Identity for Classical and Quantum Convolutional Codes

doi:10.1109/TCOMM.2016.2585641

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	On the MacWilliams Identity for Classical and Quantum Convolutional Codes
	Lai, Ching-Yi 1; Hsieh, Min-Hsiu 1,2; Lu, Hsiao-Feng 3
	2016-08-01
发表期刊	IEEE TRANSACTIONS ON COMMUNICATIONS
ISSN	0090-6778
卷号	64 期号:8 页码:3148-3159
摘要	The weight generating functions associated with convolutional codes (CCs) are based on state space realizations or the weight adjacency matrices (WAMs). The MacWilliams identity for CCs on the WAMs was first established by Gluesing-Luerssen and Schneider in the case of minimal encoders, and generalized by Forney. We consider this problem in the viewpoint of constraint codes and obtain a simple and direct proof of this MacWilliams identity in the case of minimal encoders. For our purpose, we choose a different representation for the exact weight generating function (EWGF) of a block code, by defining it as a linear combination of orthonormal vectors in Dirac bra-ket notation. This representation provides great flexibility so that general split weight generating functions and their MacWilliams identities can be easily obtained from the MacWilliams identity for EWGFs. As a result, we also obtain the MacWilliams identity for the input-parity WAMs of a systematic convolutional code and its dual. Finally, paralleling the development of the classical case, we establish the MacWilliams identity for quantum CCs.
关键词	Convolutional codes Fourier transforms Hamming weight MacWilliams identity
DOI	10.1109/TCOMM.2016.2585641
语种	英语
资助项目	Australian Research Council (ARC)[DP120103776] ; UTS Chancellors postdoctoral research fellowship ; UTS Early Career Researcher Grants Scheme ; ARC Future Fellowship[FT140100574] ; Taiwan Ministry of Science and Technology[MOST 103-2221-E-009-043-MY3]
WOS研究方向	Engineering ; Telecommunications
WOS类目	Engineering, Electrical & Electronic ; Telecommunications
WOS记录号	WOS:000384312200002
出版者	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/23631
专题	中国科学院数学与系统科学研究院
通讯作者	Lai, Ching-Yi
作者单位	1.Univ Technol Sydney, Ctr Quantum Computat & Intelligent Syst, Fac Engn & Informat Technol, Ultimo, NSW 2007, Australia 2.Chinese Acad Sci, UTS Acad Math & Syst Sci AMSS, Joint Res Lab Quantum Computat & Quantum Informat, AMSS, Beijing 100190, Peoples R China 3.Natl Chiao Tung Univ, Dept Elect & Comp Engn, Hsinchu 300, Taiwan
推荐引用方式 GB/T 7714	Lai, Ching-Yi,Hsieh, Min-Hsiu,Lu, Hsiao-Feng. On the MacWilliams Identity for Classical and Quantum Convolutional Codes[J]. IEEE TRANSACTIONS ON COMMUNICATIONS,2016,64(8):3148-3159.
APA	Lai, Ching-Yi,Hsieh, Min-Hsiu,&Lu, Hsiao-Feng.(2016).On the MacWilliams Identity for Classical and Quantum Convolutional Codes.IEEE TRANSACTIONS ON COMMUNICATIONS,64(8),3148-3159.
MLA	Lai, Ching-Yi,et al."On the MacWilliams Identity for Classical and Quantum Convolutional Codes".IEEE TRANSACTIONS ON COMMUNICATIONS 64.8(2016):3148-3159.