Explicit Constructions for Type-1 QC-LDPC Codes With Girth 12

Given any J × J (J > 3) square matrix over Z
_P
such that the differences of any two row vectors contain each element in Z
_P
at most once, a class of (3, L)-regular quasicyclic low-density parity-check codes is explicitly constructed with lengths P J L
²
and girth 12, where L is any integer satisfying 3 <; L ≤ J. Simulation results show that the new codes perform very well for moderate rates and lengths.