Regular Quasi-cyclic LDPC Codes with Girth 6 from Prime Fields

The short paper proposes a method for constructing regular quasi-cyclic (QC) LDPC codes based on circulant permutation matrices via simple prime field operations. The main advantage is that regular QC LDPC codes with a variety of block lengths and rates can be easily constructed which have no cycles of length four or less. Simulation results show that within only a maximum of ten decoding iterations of sum-product algorithm(SPA) the constructed regular codes of high rates have no error floor down to the bit-error rate of 10 -7 .