On the construction of low-density parity-check codes with girth 10

In this letter, construction of a class of (3,k)(3,k) LDPC codes is presented. The proposed codes are constructed in 2-D lattices; by selection of slope-sets in the lattices, general triangles and quadrangles are removed, which leads to the corresponding codes to have girth no less than 10. By column and row permutation, the check matrix could be introduced to quasi-cyclic structure, which leads to encoding efficient, and the experiment shows that the codes have large minimum distance, and the bit error rate performance over AWGN channels is excellent.