We consider irregular quasi-cyclic low-density parity-check (LDPC) codes derived from difference families. The resulting codes can be encoded with low complexity and perform well when iteratively decoded with the sum-product algorithm.
Based on the optical orthogonal codes, a method for constructing irregular LDPC (low-density parity check) codes was presented. These LDPC codes are quasi-cyclic codes and can be encoded with low complexity with a linear relationship to code length. These codes have Tanner graphs free of 4-cycles. They perform well with the sum-product iterative decoding. Compared with random codes and regular LDPC codes based on the optical orthogonal codes with similar parameters, they have decoding performance gains respectively about 0.3 and 0.15 dB when bit error rate is 10~(-5).