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

Abstract

Given any $J\times J\,\,(J>3)$ square matrix over $\textbf {Z}_{P}$ such that the differences of any two row vectors contain each element in $\textbf {Z}_{P}$ at most once, a class of $(3,L)$ -regular quasi-cyclic low-density parity-check codes is explicitly constructed with lengths $PJL^{2}$ and girth 12, where $L$ is any integer satisfying $3 . Simulation results show that the new codes perform very well for moderate rates and lengths.