Lifting method for quasi-cyclic low-density parity-check codes based on approximated cycle extrinsic message degree in optical communication systems

Abstract

Quasi-cyclic low-density parity-check (QC-LDPC) codes with low-complexity hardware implementation and excellent performance have become a hot research topic in many optical communication systems. To meet the different requirements of code lengths in optical communication systems, lifting methods which remove all the short cycles equally are usually used to construct long QC-LDPC codes of larger lengths by lifting short QC-LDPC codes. A lifting method is proposed, which considers both length and connectivity of short cycles. The proposed lifting method reduces the complexity of calculating the approximated cycle extrinsic message degree -related metrics and improves connectivity of the Tanner graph. The numerical results prove that, by employing our proposed lifting method, the lifted long QC-LDPC codes have better bit error rate performance compared with the lifted codes employing the traditional lifting method.