Structured non-binary LDPC codes with large girth

An LDPC code is called ultra-sparse if its parity-check matrix has uniform column weight 2. A class of non-binary ultra-sparse quasi-cyclic LDPC (UQ-LDPC) codes with girth 12 is constructed. These codes have simple structures and very fast encoding. With iterative decoding based on the belief propagation algorithm, simulation results show that the non-binary UQ-LDPC codes significantly outperform the non-binary ultra-sparse random LDPC codes with the same parameters in certain cases.