The Construction Method Of QC-LDPC Code Based On Jacobsthal Sequence And The Performance Improvement Of Large Girth Length

Low Density Parity Check Codes(LDPC)are a class of linear block Codes with sparse Check matrix,which have excellent performance close to Shannon's limit,and have obvious advantages of parallel decoding,decoding error detection and Low decoding complexity.By the international mobile communication standards organization 3GPP,identified as the fifth generation of mobile communication technology enhanced mobile broadband scenario(5G eMBB)data channel short code and long code coding scheme.Quasi Cyslice-Low Density Parity Check Codes(QC-LDPC)is a common structural LDPC code.Its checksum matrix has the advantages of standard structure and simple mathematical expression,simple function implementation and Low storage consumption.It realizes the combination of decoding speed and decoding complexity.The information bits in the check matrix structure of QC-LDPC codes are usually determined and constructed by sequence.In general,the quasi-cyclic code type constructed by using sequence has good error correction performance.The common structural sequence includes arithmetic sequence,Fibonacci sequence,large derivative sequence,Hoey sequence and Lucas sequence.However,in the practical application,the QC-LDPC code constructed by using the sequence has many problems,such as the rate selection is not flexible enough,the coding complexity is high,the error correction performance is not improved enough and so on.The Jacobsthal sequence combination background has profound significance and is widely used in real life.In this paper,the excellent combinatorial properties of Jacobsthal sequence are applied to the construction of the basis matrix of QC-LDPC codes.QC-LDPC codes based on Jacobsthal sequence(JACO-QC-LDPC)are innovatively constructed by using the basis matrix construction method of double diagonal structure and mask modification technique.The simulation results show that the modified JACO-QC-LDPC code can flexibly select the code rate and code word length to achieve fast coding,and its Net Coding Gain(NCG)is increased by about 0.1 dB,0dB,0.1 dB,0.1 dB,respectively.The overall performance is good,and it has better error basis and coding performance.Then,this paper designs a JACO-QC-LDPC code after eliminating the short loop by using the ergodic elimination method.The simulation results show that the NCG of the JACO-QC-LDPC code after eliminating the short loop is increased by about 0.1 dB,0dB,0.1 dB and 0.1 dB,respectively,which further improves the coding performance and reduces the error probability.Finally,by modifying the cyclic permutation matrix coefficient of QC-LDPC code,this paper designs a short loop elimination algorithm,and constructs a large girth JACO-QC-LDPC code with better performance.The large girth JACO-QCLDPC code constructed by this algorithm has a faster decoding convergence speed,and its NCG is increased by about 0.3dB,0.2dB and 0.1dB,respectively,which further improves the compilation performance of JACO-QC-LDPC code and reduces the bit error rate.Compared with other coding schemes,the coding performance of JACO-QC-LDPC code has been continuously optimized and improved,with faster iterative decoding convergence speed and less decoding interference.Especially in the waterfall area,its coding performance is more excellent and has a good application prospect.