Improved Construction of Low-Density Parity-Check Codes Based on Lattices

In this paper we construct a class of LDPC codes with girth 10 based on 2-D lattices. The parity check matrix is an incident matrix of lines and points in the lattices. By selection of slope sets, general triangles and quadrangles are removed in the lattices which leads to the corresponding codes have girth no less than 10. The codes are regular, whose column weight is 3. The generated check matrix have quasi-cyclic structure, and the codes show excellent bit error rate(BER) performance over A WGN channels.