The Construction And Optimization Of The Non-binary QC-LDPC Codes

Low density parity check codes was first proposed by Gallager in1962, but wasignored for the high encoding and decoding complexity and the hardware limits. BinaryLDPC codes was rediscovered by Mackay and Neal with the introduction of turbo codes in1993.Research shows that Binary LDPC code has better performance when the code is verylarge, but LDPC codes does not have outstanding performance for short and middle lengthLDPC codes. Nonbinary LDPC code has better performance than binary codes, especiallyfor the short and middle length codes, but it has a high encoding and decoding complexity.So we try to construct nonbinary QC-LDPC codes, to lower the encoding and decodingcomplexity using the designability of quasi cyclic codes.In this article, we use the traditional construction of QC-LDPC codes. First, constructa small matrix. Second use permutation matrix to replace the nonzero value of the smallmatrix and use null matrix to replace the zero value of it. And then, we can obtain the checkmatrix of LDPC codes. We focus on how to obtain the circulant shift value and constructthe permutation matrix over GF(q).In our work, we proposed a circulant shift value search algorithm on the basis ofcondition that the cycle satisfy when it exist. Using this search algorithm, we can obtain theshift value of the matrix and the size of permutation matrix to obtain QC-LDPC codes withtarget girth. According to the characteristics of the Galois field, we construct a matrix thatmeets the shift characteristics of Quasi Cyclic codes. Through the above process, we canobtain the check matrix of nonbinary QC-LDPC codes, then obtain the codes.Research shows that the codes which is constructed using our method have the betterperformance of nonbinary and structural of QC-LDPC codes, achieving our goal.