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On the Girth of Tanner (5,7) Quasi-Cyclic LDPC Codes

On the Girth of Tanner(5,7) Quasi-Cyclic LDPC Codes

作     者:Hengzhou Xu Baoming Bai Dan Feng Cheng Sun 

作者机构:State Key Laboratory of Integrated Services NetworksXidian UniversityXi’an 710071China 

出 版 物:《Journal of Harbin Institute of Technology(New Series)》 (哈尔滨工业大学学报(英文版))

年 卷 期:2017年第24卷第6期

页      面:80-89页

学科分类:0810[工学-信息与通信工程] 08[工学] 0805[工学-材料科学与工程(可授工学、理学学位)] 081002[工学-信号与信息处理] 0812[工学-计算机科学与技术(可授工学、理学学位)] 

基  金:Sponsored by the National Natural Science Foundation of China(Grant Nos.61372074 and 91438101) the National High Technology Research and Development Program of China(Grant No.2015AA01A709) 

主  题:LDPC codes quasi-cyclic Tanner graph girth 

摘      要:The girth plays an important role in the design of LDPC codes. In order to determine the girth of Tanner(5,7) quasi-cyclic( QC) LDPC codes with length 7p for p being a prime with the form 35 m + 1,the cycles of lengths 4,6,8,and 10 are analyzed. Then these cycles are classified into sixteen categories,each of which can be expressed as an ordered block sequence,or a certain type. It is also shown that the existence of these cycles is equal to polynomial equations over Fpwho has a 35th unit root. We check if these polynomial equations have a 35th unit root and obtain the girth values of Tanner(5,7) QC LDPC codes.

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