The Structural Design Of Several Types Of QC-LDPC Codes

With the rapid development of information technology,the requirement of information transmission is higher and higher,which promotes the research of modern coding theory.As a kind of excellent codes with approaching Shannon limit properties,the low-density parity-check(LDPC)codes have been the research focus of channel coding in twenty years,plays an irreplaceable role in many fields.LDPC code is a kind of special linear block code,its parity check matrix has sparseness,and thus has excellent decoding performance.Its research direction includes the construction of parity check matrix,the optimization of codec algorithm and performance analysis.The quasi-cyclic parity(QC-LDPC)code is an important class of LDPC codes,the parity check matrix is quasi cyclic,without consuming large amounts of storage space,lower decoding complexity,therefore,it is important for channel coding research.This paper gives two kinds of QC-LDPC check matrix construction.The first method was derived from vandermonde matrix,firstly we construct mother matrix which is based on a given sequence,and construct QC-LDPC codes with the girth of 6 by circulant permutation matrix.Then we reduce the matrix elements in power processing,obtain the code length of the parity check matrix is more flexible,while removing a length of six ring.Finally,a step-by-step minimum algorithm is given to ensure that the order of the expansion matrix is small.Meanwhile,the results are also compared with those given by Fossorier in 2004.When the number of rows is 2 and the number of rows and columns are all 3,the shift matrix is smaller,the number of rows is 3,the number of columns is 7 or 8,the two are the same.In the case of smaller parent matrices,the order of the expansion matrix obtained by our proposed algorithm is close to that of Fossorier's computer exhaustive search.The second class is based on the study of Euclidean geometry(EG)LDPC codes,which provides a novel method for improving the parity matrix.The existence condition of the ring with length of 6 is combined with the European geometry.Two EG-LDPC codes with a length of at least 8 are given on the basis of avoiding the connection of the three points in the European geometry,there are(6,9,2,3)code and(8,12,2,4)code.Then,a non-existent condition of a ring with a length of 8 is combined with the European geometry.We give(8,12,2,3)code with the girth at least 10 of the EG-LDPC code in the case of the four points are terminated in the European geometry and the fixed row weight and the column weight are less than 4.Finally,the QC-LDPC codes are obtained by extending the permutation matrix.Compared with the existing researches on EG-LDPC,this method provides a simple and effective method for constructing high girth check matrix.Finally,the QC-LDPC code constructed by the first-class step-by-step minimum algorithm and the QC-LDPC code with the second type of circumference are simulated by the bit flip algorithm.The simulation results show that the two kinds of QC-LDPC codes have good decoding performance.