Column Weight Two and Three LDPC Codes with High Rates and Large Girths
Gholami, Mohammad · Raeisi, Ghaffar
Original · EN
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. The structure of the proposed parity-check matrices significantly reduces the complexity of encoding and decoding. Interestingly, the constructed regular cycle codes with row-weights t, 3≤ t ≤ 20, t≠ 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 codes achieve excellent performances, specially the constructed column weight 3 LDPC codes outperform LDPC codes based on Steiner triple systems (STS).
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