The Construction Design Of A Class Of QC-LDPC Codes

In the past two decades,LDPC codes have gradually become the focus of attention due to its close proximity to the Shannon limit.It was found that the sparsity of the calibration matrix gives a good advantage in decoding complexity and error level.Therefore,it has been widely used in optical fiber communication,audio broadcasting,mobile communication and other fields.In this paper,two construction methods of the quasi-cyclic LDPC(QC-LDPC)codes are presented,the code rate calculation formula of the QC-LDPC code is given,and their performance is analyzed by computer simulation.Firstly,in this paper,we study an algebraic construction method of QC-LDPC code.L.Chen proposed a construction method of QC-LDPC code in 1994.The construction step is to construct the basis matrix which satisfies the RD constraint,and then expand the basis matrix into the low density parity matrix that the girth is at least 6.In terms of the structure of the basis matrix,they give two constructional methods based on the addition method group and the multiplication method group.We improve and popularize the construction methods based on these two methods,and put forward two new basic matrix construction methods.The first construction method is based on the structure of multiplicative group accompanying set.The basis matrix is based on the method group and its accompanying set,and it satisfies the RD constraint.Its elements are linear combinations of the representative elements of the accompanying set.The second is based on the condition Ω We call set U,V in finite field satisfy condition Ω that means,for the set U,V,(u’,v’),(u,v)∈U×X,if uv = u’v’,then u =u,v＝v.Then,we improve the calculation method of the code rate of the QC-LDPC code based on additive group structure,and apply it to the QC-LDPC code constructed by the two new construction methods.In this paper,the rank of the parity matrix is converted into the rank of the equivalent block diagonal matrix.First of all,we transform the parity check matrix into the equivalent block diagonal matrix.Secondly,we consider the block rank of the block diagonal matrix.By using the parity characteristics of the number of combinations in the Yang Hui triangle,we get the expression of the rank of each check matrix respectively.Finally,we adopt the bit flipping decoding method,and simulate the QC-LDPC codes by MATLAB.The result shows that,on the basis of the threshold of 3 and with 20 iteration,when the error rate is lower 10’5,the construction method based on the multiplicative set is lower,and the error rate of the constructed method based on Ω is better than that based of multiplication coset.These three methods are applicable to the four-bit inversion method.And the simulation results are consistent with the cascade characteristics of the bit flip decoding method,so both the QC-LDPC codes constructed by the method proposed by us and by L.Chen all have better decoding performance when the SNR is high.