Research On The Construction Of Parity Check Matrix Of Quasi-Cyclic Low-Density Parity-Check Codes

Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes are one kind of LDPC codes, whose performance can be near Shannon limit. And the construction of parity-check matrices are with quasi-cyclic style, so their encoding complexity and decoding complexity are low, which reduce the hardware requirement thus they are more practical than random ones.In this paper, we introduced the Theory of encoding and decoding, main factors that determine the performance of LDPC codes and three classes of methods to construct QC-LDPC codes. There are two way of the transformation of check matrix, one is to make the check matrix into a lower triangular form by Gaussian elimination method, the other is to make the check matrix into a similar structure of lower triangular by the replacement of rows and Columns. The decoding algorithm is mainly the domain BP algorithm and its simplified algorithm for theUMP BP-Based algorithms. The performance of LDPC was determined by its code distance and girth, the greater the Girth and distance between codes the better the performance of LDPC. QC-LDPC Codes are usually constructed based on finite geometry, combinatorial design and permutation matrix. This paper mainly based on the permutation matrix of QC-LDPC codes constructed.First, this paper improved the method of the construction of QC-LDPC based on PEG Algorithm. The girth of the QC-LDPC codes increased2. Construction step was that first of all the utilization of PEG algorithm to generate a base matrix, and then the unit circle permutation matrix to expand the base matrix, at the same time, the short loop of base matrix was eliminated This approach also has the advantages of the PEG algorithm and quasi-cyclic codes.Second, the base matrix with cyclic symmetry structure and6-girth is structured, and the6rings are distributed evenly in the check nodes and variable nodes. This method has the advantage of such a cycle permutation matrix unit easy to select the shift value, drawback is the8rings in the base matrix is complex, this paper constructs girth is equal to only8of the rules (3,6) code.Simulations show that the QC-LDPC constructed in this paper has as good error correcting performance as the LDPC codes generated by random construction. In addition, we focus on the distribution and structure of cycles, but not the girth of basic matrix. This design idea helps to construct the QC-LDPC with larger girth.