Girth Analysis of Tanner (5,11) Quasi-Cyclic LDPC Codes
Hengzhou Xu, Hai Jiang Zhu, Mengmeng Xu, Bo Zhang, Sifeng Zhu · 2018
Motivated by the works on the girth of Tanner (3,5), (3,7), (3,11), and (5,7) quasi-cyclic (QC) LDPC codes, we in this paper study the girth of Tanner (5,11) QC-LDPC codes. We first analyze the cycles of Tanner (5,11) QC-LDPC codes, and obtain the conditions for the existence of cycles of length less than 12 in Tanner (5,11) QC-LDPC codes of length 11p where p is a prime number and p =1 (mod 55). Notice that the condition is represented by the polynomial equations in a 55th root of unity of the prime field Fp. By checking the existence of solutions for these equations over Fp, the girths of Tanner (5,11) QC-LDPC codes are obtained.