Research On The Construction Methods Of QC-LDPC Codes Based On The Sequence Algorithm

Low-Density Parity-Check?LDPC?codes have been paid the widespread attention by scholars because of their error correction performance approaching the Shannon limit.Currently,the common structured LDPC codes are Quasi-Cyclic?QC?-LDPC codes.Their quasi-cyclic and low-density characteristics make their implementation complexity low.Therefore,they own unlimited development potential.Compared with other construction methods of QC-LDPC codes,the mathematical basis of the sequence algorithm is relatively easy.If it is applied to the construction methods of the codes,the constructed codes generally possess well error correction performance.Therefore,the research on the methods has become a hot spot.After reviewing a large amount of documents,it was found that in the current construction process of QC-LDPC codes,there are the problems that the selection of the code rate is not flexible enough,the encoding complexity is high,and the error correction performance is not good enough caused by the short cycles and other factors.Aiming at the above problems,the construction methods of QC-LDPC codes based on the sequence algorithm are studied in this thesis.The primary contents of the research are shown as follows:1.Aiming at the problem that the selection of the code rate is not flexible enough,a new method of constructing regular QC-LDPC codes based on Fibonacci-Lucas?FL?sequence is proposed,which can construct QC-LDPC codes with flexible code rate.It can flexibly set the number of rows and columns of the base matrices,and then obtain regular QC-LDPC codes by extending the base matrices and encoding.In addition,it is theoretically confirmed that the constructed check matrices have the girth of at least 8.The simulation results reflect that in the case of the bit error rate?BER?of 10^-6 and the code rate of 0.5,the coding gain of the FL-QC-LDPC?3138,1569?code constructed by the method is larger than those of the DY-QC-LDPC?3138,1569?code based on the da yan?DY?sequence and the other compared codes.In the case of the code rate of 0.67 and the BER of 10^-5,the FL-QC-LDPC?5229,3486?code constructed by the method is also superior to the Mackay-LDPC?5229,3486?code and the other compared codes.Therefore,it has better error correction performance,and its coding complexity is comparable to those of the several compared QC-LDPC codes.2.In order to cope with the problem that the encoding complexity is high,a new method of constructing irregular QC-LDPC codes based on arithmetic progression?AP?is proposed in this thesis,which can construct the codes that could be quickly encoded.The check matrices constructed by the method have the novel quasi-double diagonal structure,and no existence of four-cycles and six-cycles.In addition,the encoding complexity and the fast encoding algorithm of the constructed codes are analyzed in detail.The simulation results show that in the case of the code rate of 0.5 and the BER of 10^-6,the coding gain of the AP-QC-LDPC?3110,1555?code constructed by the method is respectively about 0.37dB,0.54dB and 0.65dB more than those of the LCW-QC-LDPC?3110,1555?code with large column weight?LCW?and low encoding complexity,the classical Mackay-LDPC?3110,1555?code and the GCD-QC-LDPC?3110,1555?code based on greatest common divisor?GCD?algorithm.Therefore,the codes constructed by the method not only have lower encoding complexity,but also have better error correction performance.3.In order to cope with the problem that the error correction performance is not good enough caused by the short cycles and other factors,combined with arithmetic progression and masking?APM?technique,a new construction method of large girth and irregular QC-LDPC codes is put forward in this thesis.The check matrices constructed through the method not only have the characteristic of large girth,but also have the characteristic of good degree distribution.The simulation results reflect that in the same case of the code rate of 0.5 and the BER of 10^-5,the coding gain of the APM-QC-LDPC?5110,2555?code constructed by the method is respectively about 0.03dB,0.33dB and 0.4dB more than those of the classical PEG-LDPC?5110,2555?code,the M-QC-LDPC?5112,2556?code based on masking?M?technology and the DY-QC-LDPC?5106,2553?code.And it has equivalent encoding complexity with the compared QC-LDPC codes.In addition,the codes constructed by the method,compared with the codes constructed by the first and second methods proposed in this thesis,can improve the error correction performance,and possess more excellent error correction performance.