Research On Low Error Floor LDPC Codes Based On Optimizing Error-Prone Substructures

As a research hotspot in the field of channel coding,Low-Density Parity-Check(LDPC)Codes have the advantages of strong agility,excellent error correction performance,and low complexities of encoding and decoding arithmetic.However,the error floor problem of LDPC codes restricts its further development and application.In this thesis,from the perspective of codes construction methods,the method of eliminating error floor through optimizing error-prone substructures in LDPC codes is deeply studied.The main research work is as follows:1.Aiming at error-prone substructures such as short cycles and cycles with low connectivity in LDPC codes,a construction method of LDPC codes based on girth constraint and extrinsic message degree(EMD)is proposed.The PGAE-LDPC(3024,1512)code with the code rate of 0.5 and the PGAE-LDPC(1200,800)code with the code rate of 0.67 are constructed by the proposed method.The simulation results show that at the bit error rate of 10-6,compared with the PEG-ACE-LDPC(3024,1512)code constructed by the progressive edge growth(PEG)algorithm and the approximate cycle extrinsic message degree(ACE)algorithm,the PEG-LDPC(3024,1512)code constructed by the PEG algorithm,and the PEG-GA-LDPC(3024,1512)code constructed by the PEG algorithm and girth constraints,the coding gain of the PGAE-LDPC(3024,1512)code has increased by approximately 0.04 d B,0.22 d B,and 0.20 d B,respectively.At the bit error rate of 10-6,compared with the PEG-ACE-LDPC(1200,800)code and the PEG-LDPC(1200,800)code,the coding gain of the PGAE-LDPC(1200,800)code has increased by approximately 0.09 d B and 0.77 d B,respectively.As the bit error rate decreases,the coding gain is increased,and at the same time,there is no obvious error floor phenomenon in the two codes.2.In order to reduce the computation when constructing the check matrix,and eliminate the cycles with low connectivity in the check matrix at the same time,a construction method of Quasi-Cyclic Low-Density Parity-Check(QC-LDPC)codes based on arithmetic progression(AP)and EMD is proposed.The PEAP-QC-LDPC(1200,600)code with the code rate of 0.5 is constructed by the proposed method.The simulation results show that at the bit error rate of 10-6,comparedwith the PEG-AP-QC-LDPC(1200,600)code constructed by the PEG algorithm and AP,the CC-QC-LDPC(1200,600)code constructed by controlling cycles,and the AP-QC-LDPC(1200,600)code constructed by AP,the coding gain of the PEAP-QC-LDPC(1200,600)code has increased by approximately 0.18 d B,0.44 d B,and0.51 d B,respectively.In addition,there is no error floor phenomenon in the PEAP-QC-LDPC(1200,600)code.3.Aiming at the elementary trapping sets in LDPC codes,according to the expansion relationship between the elementary trapping sets,an improved algorithm for eliminating elementary trapping sets is proposed to reduce the number of small elementary trapping sets in the check matrix.A construction method of QC-LDPC codes based on the improved algorithm and AP is proposed.The PTAP-QC-LDPC(1200,600)code with the code rate of 0.5 is constructed.The simulation results show that at the bit error rate of 10-6,compared with the IEEE 802.16QC-LDPC(1200,600)code constructed by the IEEE 802.16 standard method,the PEG-AP-QC-LDPC(1200,600)code,the CC-QC-LDPC(1200,600)code and the AP-QC-LDPC(1200,600)code,the coding gain of the PTAP-QC-LDPC(1200,600)code has increased by approximately 0.08 d B,0.31 d B,0.57 d B,and 0.64 d B;at the bit error rate of 10-7,the coding gain of the PTAP-QC-LDPC(1200,600)code is improved by about 0.24 d B over the IEEE 802.16 QC-LDPC(1200,600)code.As the bit error rate decreases,the coding gain is increased,and there is no obvious error floor phenomenon in the PTAP-QC-LDPC(1200,600)code.