Research On Low-Complexity Decoding And Rate Compatibility Of LDPC Codes

Since low-density parity-check(LDPC)codes can achieve the performance near Shannon's limit conbined with iterative decoding,they have been drawn more and more attentions.Iterative decoding has excellent performance,but the computational and storage complexities are still the obstacles for its applications.As LDPC codes are applied in time-varying channels,such as wireless communication and underwater acoustic communication,the design of rate-compatible LDPC codes is another challenge.In this paper,the low-complexity decoding and rate adaptability of LDPC codes are mainly investigated.It has achieved important results as follows:Firstly,low-complexity decoding of binary LDPC codes is researched based on bit flipping(BF)algorithm.The factors that affect the performance of bit flipping(BF)and its improved algorithms(BF-based)are systematically analyzed.Then the RIMWBF and MGDBF algorithms are presented by modified the IMWBF and GDBF algorithms.Simulation results show that the presented algorithms can get better performance than the original algorithm effectively,especially for the MGDBF algorithm,which has 1.5 dB performance gain compared with GDBF algorithm.Secondly,low-complexity decoding of binary LDPC codes is researched based on brief propagation(BP)algorithm.The practical serial scheduling scheme is designed for the regular and irregular LDPC codes.The schedules designed by the proposed scheme are fixed and they can effectively improve the convergence rate of the BP decoding algorithms.For the BP-based normalized min-sum(NMS)decoding algorithm,each module of the decoder is designed and then the NMS decoder is implemented in Field Programmable Gate Array(FPGA)for LDPC code with length 16384.Thirdly,the low-complexity decoding of non-binary LDPC codes is studied from the perspective of bit-wise decoding.Based on the extended binary representation,the hard-decision and soft-decision algorithms for bit-wise decoding of non-binary LDPC codes are presented by modified the GDBF and MS algorithms of binary LDPC codes.Simulation results show that the modifed GDBF and MS algorithms can effectively work as it in binary LDPC decoding with the complexity of linear increasing with the order of GF(q).Fourthly,an efficient puncturing algorithm is proposed by minimizing the recovery-error probability of the punctured nodes.The algorithm can guarantee the recovery speed and prevent the punctured nodes from forming the short loops by considering the iterations for recovering the puntured nodes and the distances between the puntured nodes.Simulation results show that the proposed algorithm can achieve better performance than the popular Grouping/Sorting algorithm.Fifthly,under the assumption that the LDPC codes are decoded with serial schedule,an efficient punturing algorithm is proposed for irregular LDPC codes.Combining the design of the serial schedule with the selection of the punctured nodes,all the punctured nodes can be recovered after the first iteration in the proposed algorithm.In addition,the proposed algorithm also takes the varible-node degree and ACE metrics into account,whose effect is to reduce the adverse effects of punctured nodes on the LDPC code structure.Simulation results show that the proposed puncturing algorithm based on serial scheduling can effectively improve the convergence speed of punctured LDPC code and improve their performance.The proposed puncturing algorithm,which can produce good punctured LDPC codes with high code rate and excellent performance,is a very efficient alogorithm for rate compatibility.