Research On Quasi-cyclic Expansion Algorithm For Protograph LDPC Codes

Low Density Parity Check (LDPC) codes have achieved performance close to the channel capacity with low decoding complexity, so more and more attention is paid to them in recent years. Protograph LDPC codes proposed by Jet Propulsion Laboratory which have better performance, such as low coding complexity, fast encoding and decoding and good BER performance, based on former study. Protograph LDPC codes have become coding scheme for use in deep space communications in standards of Consultative Committee for Space Data Systems (CCSDS) and Digital Video Broadcasting-Satellite 2 (DVB-S2). As known to all, the protograph LDPC quasi-cyclic expansion (PQCE) algorithm influences the property of constructed protograph LDPC codes and the hardware implementation complexity of codec. However, there are still some problems remaining to be solved, so the research on this algorithm is of great significance. The main contributions in this thesis are illustrated as follows:(1) In this thesis, the development history, research significance and status are introduced. Then the basic theory of protograph LDPC codes, theory of encoding and decoding, and protograph EXIT are elaborated in detail.(2) The existing PQCE algorithms may be with a low convergence rate, or construct check matrixs with many short cycles. Aimming at this problem, PEG-PH-PQCE algorithm is presented in this thesis. Base matrix is acquired by PEG parallel edges elimination expansion algorithm during the first-step expansion of protograph. The second-step expansion is completed by PH quasi-cyclic expansion algorithm, in which the initial index matrix is acquired by PEG quasi-cyclic expansion algorithm, and then Hill Climbing algorithm is used to get a check matrix with good property by optimizing the initial index matrix. Simulation results show that the new algorithm could diminish the number of short cycles with a high convergence rate.(3) The connectivity of cycles in protograph LDPC codes constructed by the existing PQCE algorithms is low. Aiming at this issue, PE-IPEG-PQCE algorithm is presented in this thesis. In the first-step expansion, PEG algorithm is used to get the initial base matrixs and edge swapping is utilizing to optimize the cycle distribution in the initial base matrixs. IPEG quasi-cyclic expansion algorithm is used to the second-step expansion to get the check matrix with good connectivity, in which the number of the new short cycles and ACE is used as a criterion to expanding tree. Simulation results show that the presented algorithm decreases the number of short cycles, increases the connectivity between cycles and then improves the code error property.