Combinatorial design-based quasi-cyclic LDPC codes with girth eight

This paper presents a novel regular Quasi-Cyclic(QC) Low Density Parity Check(LDPC) codes with columnweight three and girth at least eight. These are designed on the basis of combinatorial design in which subsets applied for the construction of circulant matrices are determined by a particular subset. Considering the nonexistence of cycles four and six in the structure of the parity check matrix, a bound for their minimum weight is proposed. The simulations conducted confirm that without applying a masking technique, the newly implemented codes have a performance similar to or better than other well-known codes. This is evident in the waterfall region,while their error floor at very low Bit Error Rate(BER) is expected.