Explicit constructions for type-1 QC-LDPC codes with girth at least ten

From Sidon sequence over Z_P, two classes of type-1 (J = 3;L) QC-LDPC codes are explicitly proposed with block length L²P and with girth at least ten. For the first method, any Sidon sequence over Z_P (P odd) with cardinality no smaller than L (L odd) corresponds to a class of type-1 (3, L) QC-LDPC codes with girth at least ten. For the second one, any Sidon sequence over Z_P (P prime) with cardinality no smaller than L (L arbitrary) corresponds to a class of type-1 (3, L) QC-LDPC codes with girth at least ten. Compared with the method from 3-D lattices, which can also generate type-1 QC-LDPC codes with girth at least ten, the main advantage of the new methods is that the construction process is much simpler, and L is not necessarily a prime integer. Simulation results show that the new type-1 QC-LDPC codes outperform the girth-8 QC-LDPC codes constructed by Sidon sequence or the earliest sequence, and perform almost as well as Bocharova´s shortest girth-12 QC-LDPC codes.