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

Low Density Parity-Check (LDPC) Codes is a very advanced channel coding technology,which has the error correction performance approximating Shannon Limits. Nonbinary QC-LDPC code is a subclass of LDPC code, it not only has excellent decoding performances which nonbinary LDPC code possesses, but also only needs less storage space for its quasi circulation structure,and also because of its introducing accumulate registers and reducing encoding complexity, it has high practical value.This paper briefly introduces the basic theory of channel coding and its development and evolution,and also generally expounds the representation,classification and general constr-uction method of LDPC code, besides these,this paper also introduces the related theory of QC-LDPC code in detail.This paper mainly studies how to design the check-up matrix of QC-LDPC code with flexible and excellent performance. The results can roughly be divided into the following two parts:Firstly, we expound the structured construction method of nonbinary QC-LDPC code systemically.The circulation or quasi circulation structure is one of the great strengths of structured check-up matrix, which make its hardware realization very simply and promote the practical process of LDPC code greatly. This paper introduces several kinds of general structured methods.We can ensure that the girth of the matrix H is at least six by elaborately choosing the elements of matrix W. Finally,we also put forward a kind of structured construction method whose girth is at least eight, which greatly improving the decoding performance. The simulation results show that the performance of the structured nonbinary QC-LDPC with large girth constructed by our method is very close to or even exceeds the nonbinary LDPC code generated by random way.Secondly, we come up with the construction method of nonbinary QC-LDPC based on PEG. Because of its superior decoding performance, PEG algorithm is very popular in the construction of binary LDPC code’s check-matrix H.The construction of nonbinary QC-LDPC code based on PEG raised by this paper plans to set those excellent characteristics such as PEG algorithm, quasi circulation structure and nonbinary into a body,which makes the nonbinary QC-LDPC code constructed by this method have all these excellent characteristics. The simulation results show that the performance of the nonbinary QC-LDPC constructed by this method indeed has superior performance. In Rayleigh channel, the decoding performance of the nonbinary QC-LDPC code constructed by this method is nearly same with the nonbinary LDPC code generated by random way. In gaussian channel, the decoding performance of the nonbinary QC-LDPC constructed by this method is also better than the nonbinary QC-LDPC constructed by general structured method.Therefore,it has a quite broad application prospect.