A Note on the Girth of (3, 19)-Regular Tanner’s Quasi-Cyclic LDPC Codes
Manjie Zhou, Hai Jiang Zhu, Hengzhou Xu, Bo Zhang, Kaixuan Xie · IEEE Access · 2021
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.