A Short Note on the Girth of Tanner (5,13)-Regular QC-LDPC Codes
Hengzhou Xu, Hai Jiang Zhu, Xiaoxiao Miao, Mengmeng Xu, Zhen Luo, Huaan Li · 2021 17th International Conference on Computational Intelligence and Security (CIS) · 2021
This paper studies the girth of Tanner (5,13)-regular QC-LDPC codes. We present the conditions for the existence of cycles of lengths less than 12 in Tanner (5,13)-regular QC-LDPC codes of length${13p}$where${p}$is a prime of the form${65i+1}$, and transfer these conditions into the equations in a 65th root of unity of the prime field${\mathbb{F}_p}$. By checking the existence of solutions for these equations over${\mathbb{F}_p}$, we derive the girth distribution of Tanner (5,13)-regualr QC-LDPC codes.