On the girth of Tanner (۳,۷) quasi-cyclic LDPC codes

‎‎S‎. ‎Kim et al‎. ‎have been analyzed the girth of some algebraically‎ ‎structured quasi-cyclic (QC) low-density parity-check (LDPC)‎ ‎codes‎, ‎i.e‎. ‎Tanner (۳,۵) of length ۵p‎, ‎where p is a prime of‎ ‎the form ۱۵m+۱‎. ‎In this paper‎, ‎by extension this method to‎ ‎Tanner (۳,۷) codes of length ۷p‎, ‎where p is a prime of the‎ ‎form ۲۱m‎+ ‎۱‎, ‎the girth values of Tanner (۳,۷) codes will be‎ ‎derived‎. ‎As an advantage‎, ‎the rate of Tanner (۳,۷) codes is‎ ‎about ۰.۱۷ more than the rate of Tanner (۳,۵) codes‎.

Keywords:

LDPC codes , Tanner graph , Girth