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

Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes as one kind of LDPC codes,that not only has the equally performance of the near Shannon Limit, but also has the higher practical value than the randomly generated LDPC codes, thanks to the quasi circulation structure of the check matrix, the less requires of storage space, and can introduce accumulate registers to reduce encoding complexity.This paper introduced the basic principle of encoding and decoding of the LDCP codes,and combined with QC-LDPC code’s own quasi circulation structure characteristics, introduced rapid encoding method which is suitable for it. For the main factors, to affect the LDPC code performance, including codes length, codes rate, mininum distance and the girth,this paper also gave the actual analysis. Eventually we concentrated the methods to constructe the QC-LDPC codes with good performance on the methods of constructing QC-LDPC codes with large girth.The mainly researches of this article is designing a quick, flexible and excellent performance QC-LDPC codes structure schemes,and the main achievements are divided into two aspects:On the one hand,the randomly construction of QC-LDPC cods based on permutation matrixs. When the circular displacement matrix dimension is small, this paper proposed one kind of correction algorithm based on cycles-searching, that greatly improved the success rate of one-time construction of the QC-LDPC codes with no short cycles happen; but when the circular displacement matrix dimension is large, this paper proposed a method using rows relations algorithm in replacing of the cycles-searching algorithm, saved a lot of time cost, and also achieved the purpose of breaking short cycles. The performance of our codes are closed to,or even better than the codes with randomly construction methods.On the other hand, this paper used algebraic structures to constructe the QC-LDPC codes with large girth successly. This paper used the vector position relations based on the circulation group theory to constructe the basic QC-LDPC codes, has reached the purpose of eliminating all the4cycles. Additional properly bits delete method further enlarge the girth.At last,we proposed a structure by using short component to restore long codes based on the Chinese remainder theorem,not only can setup the code rate flexiblely, but also can keep the previous large girth.Using this algebraic method to constructe the QC-LDPC codes, the girth can reach10, and simulation performance are closed to randomly generated LDPC codes.