Column Weight Two and Three LDPC Codes with High Rates and Large Girths

In this paper, the concept of the broken diagonal pair in the chess-like square board is used to define some well-structured block designs whose incidence matrices can be considered as the parity-check matrices of some high rate cycle codes with girth 12. Interestingly, the constructed regular cycle codes with row-weights t, 3 ≤ t ≤ 20, t 6= 7, 15, 16, have the best lengths among the known regular girth-12 cycle codes. In addition, the proposed cycle codes can be easily extended to some high rate column weight-3 LDPC codes with girth 6. Simulation results show that the constructed column weight 3 QC LDPC codes remarkably outperform QC LDPC codes based on Steiner triple systems and integer lattices.