Construction of Type-II QC LDPC Codes Based on Perfect Cyclic Difference Set

Quasi-cyclic (QC) Low-density parity-check (LDPC) codes are constructed from combination of weight-0 (null matrix) and Weight-2 (W2) Circulant matrix (CM), which can be seen as a special case of the general type-II QC LDPC codes. The shift matrix of the codes is built on the basis of one integer sequence, called perfect Cyclic difference set (CDS), which guarantees the girth of the code at least six. Simulation results show that the codes can perform well in comparison with a variety of other LDPC codes. They have excellent error floor and decoding convergence characteristics.