Joint encoding-decoding construction of LDPC codes with reduced complexity

LDPC codes are now one of intensely studied areas in coding due to their near Shannon limit performance and parallel decoding architecture. Because the LDPC codes parity-check matrices are defined in terms of sparse random graphs, the implementation of the decoding and encoding is of high complexity. A new design methodology of LDPC codes, which are constructed by the cyclic shift matrices, is proposed in order to reduce the decoding complexity under the Sum-Product algorithm. Meanwhile,the encoding problem of LDPC codes is also considered, then a simplified encoding structure is given. A new procedure of removing the short loops from the bipartite graph is demonstrated according to the construction scheme of our LDPC codes. Performance comparisons between our codes and random constructed LDPC codes on BER, loop distributions and minimum distance estimation are given by extensive simulations and numerical analysis.