A Note on the Girth of (3, 19)-Regular Tanner's Quasi-Cyclic LDPC Codes

In this article, we study the cycle structure of (3, 19)-regular Tanner's quasi-cyclic (QC) LDPC codes with code length 19p , where p is a prime and p\equiv 1~(\bmod ~57) , and transform the conditions for the existence of cycles of lengths not more than 10 into polynomial equations in a 57...

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Veröffentlicht in:IEEE access 2021, Vol.9, p.28582-28590
Hauptverfasser: Zhou, Manjie, Zhu, Hai, Xu, Hengzhou, Zhang, Bo, Xie, Kaixuan
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Sprache:eng
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Zusammenfassung:In this article, we study the cycle structure of (3, 19)-regular Tanner's quasi-cyclic (QC) LDPC codes with code length 19p , where p is a prime and p\equiv 1~(\bmod ~57) , and transform the conditions for the existence of cycles of lengths not more than 10 into polynomial equations in a 57th root of unity of the prime field \mathbb {F}_{p} . By employing the Euclidean division algorithm to check whether these equations have solutions over the prime field \mathbb {F}_{p} , the girth values of (3, 19)-regular Tanner's QC-LDPC codes of code length 19p are determined. In order to show the good performance of this class of QC-LDPC codes, numerical results are also provided.
ISSN:2169-3536
2169-3536
DOI:10.1109/ACCESS.2021.3058732