Optimal construction of extended short protograph LDPC codes

In order to design short quasi-cyclic low-density parity-check (QC-LDPC) codes with good performance and low complexity, an optimization code construction was proposed based on an extension of the protograph. Based on an optimized protograph, an efficient short QC-LDPC code was constructed by properly puncturing and expanding a check nodes in the protograph to a compound block code nodes, followed by enlarging the dimension of the sub-matrices of the code. Thus, a joint optimization algorithm, combined by the progressive edge growth (PEG) for the optimization of the extended base matrices and the QC improved approximated cycle extrinsic message degree (QC-IACE) for the circulant offset optimizations, was proposed to search the optimal offsets in the circulant permutation sub-matrices of the codeword, which helped to increase code performance by jointly improving and optimizing the stop set and trapping set of the code, as well as girths and cycle profiles. Simulation results indicate that the proposed codes have quite good performance of bit error rate, and compared with current excellent random LDPC code words, the proposed codes obtain almost the same performance. Therefore, the codes can possess low complexity and less latency of encoding and decoding due to their good properties of short code length. © 2016, Editorial Board of Journal of Huazhong University of Science and Technology. All right reserved.