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

Low-density Parity-check(LDPC) codes were originally introduced by Gallage in his doctoral thesis. LDPC codes are linear block codes, their bit error rate(BER) performance approaches to Shannon Limit when BP algorithm is employed to decode. Since discovery of LDPC codes, there has been renewed interest in LDPC codes. Quaci-cyclic(QC) LDPC codes are special assembles with simple structure and linear encoding complexity which reduce the hardware requirement, thus they are more practical than random ones.In this paper, we focus on the research of construction of quasi-cyclic LDPC code. Having studied some proposed construction of QC-LDPC codes, we improved their construction method and constructed two classes of regular QC-LDPC codes and a class of irregular ones. Firstly, we construct the circulant matrixs with correlation function and column split those matrixs in order to simplify the design and optimize the performance. The column splitting breaks up many short cycles and improves the performance of QC codes. According to the simulation, we find this kind of QC codes performs well and it owns simpler design method.Secondly,we consider a construction method of regular QC codes based on circulant matrix. In this method, the core matrix is designed according to CO-BIBD. And the number of circulant shifting is surposed to design in terms of short cyclic structure condition. This is a very simple and flexible method and various code length and code rate can be obtained through this method. The small structured modulation of this code makes it easier to practice the encoding and need less storage spaces. This class of QC codes shows good performance according to the simulation.Irregular LDPC codes show better performance than regular codes. So we preposed an algebraic construction method of irregular QC codes based on circulant matrix. The H(d) matrix is design according to the design method of regular QC codes, and unites with the matrix H(p), which quotes from Fujita's thesis. The construction method of irregular codes is very simple to practice. Also, the obtained irregular QC codes are easy to encode and storage. The simulation result also proves the good performance of them.