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

作　　者：Hengzhou Xu Baoming Bai Dan Feng Cheng Sun 

机构地区：[1]State Key Laboratory of Integrated Services Networks,Xidian University,Xi’an 710071,China

出　　处：《Journal of Harbin Institute of Technology(New Series)》2017年第6期80-89,共10页哈尔滨工业大学学报（英文版）

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)

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.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.

关 键 词：LDPC CODES quasi-cyclic Tanner GRAPH GIRTH 

分 类 号：TN911[电子电信—通信与信息系统]