To cut down the hardware implementation cost this paper presents an efficient method to construct large girth Quasi-Cyclic low density parity check (QC-LDPC) codes. The row groups are paired two times the row weight, which has the complexity as compared to the connection of individual columns and rows. The complexity of directing within groups estimates on the transposition employed to connect rows and columns between groups. The newly obtained codes are incorporated with diversity techniques and are employed as a forward error correction codes to cater for some anti-jamming (AJ) competences in the presence of partial band noise jamming (PBNJ). The robustness of two girth-twelve QC-LDPC codes is evidenced by comparing it with randomly constructed LDPC codes and QC-LDPC codes proposed in [14].