Research On LDPC Codes Based On Permutation Polynomials

With the rapid development of mobile communication technology, especially 3G,4G technology's rapid development, channel coding which is a key technology of physical layer has become a hot research topic. Since 1996 Low-density Parity-check (LDPC) Codes have been rediscovered. Because of it close to the Shannon limit error correction performance and lower decoding complexity, all these make LDPC Codes become a hot research in Channel coding field, and adopted by various standards. In this thesis, we research LDPC Codes which are based on permutation polynomials, then select the LDPC Codes without small cycles by means of short cycle detection algorithm, and get LDPC Codes with Superior error-correction performance.Firstly, the thesis introduces the basic principles of LDPC Codes, which including the definition of LDPC Codes and Tanner graph; various construction methods of LDPC Codes, such as Gallager construction method, MacKay construction method etc; various coding algorithms of LDPC Codes, such as Gaussian elimination, coding algorithm based on lower triangular; and also LDPC Codes' soft decision BP decoding algorithm and LLR BP decoding algorithm.Secondly, the thesis elaborates the structure and recursive coding method of LDPC Codes provided by IEEE 802.16e. Using the standard provided encoding method, BP decoding algorithm and C language for simulation. From the simulation results of various code length and rate, we can see the excellent performance of IEEE 802.16e LDPCThirdly, the thesis researches the short cycle detection algorithm of the LDPC Codes. First, we introduces the detection algorithm based on check matrix and the detection algorithm based on permutations which proposed by Jun Fan etc. Then, combining some analysts of the detection algorithm which proposed by Jun Fan etc. an improved algorithm for short cycle detection has been proposed. The thesis simulates two algorithms, and the related results show that the improved algorithm can detect more number of 6,8,10 cycles.Finally, the thesis researches the LDPC Codes Constructed by permutation polynomials. First, we introduced the basic concepts of permutation polynomials and determine conditions of permutation polynomials. Oscar Y. Takeshita first constructed LDPC Codes using 2-order polynomial permutation. The thesis construct LDPC Codes extended to m-order permutation polynomials. Then, we using the improved cycle detection algorithm remove LDPC codes which exist small cycles, choose superior error-correction performance LDPC Codes. From the simulation analysis of LDPC Codes constructed by 2-order,3-order and 4-order permutation polynomials we selected, we can see that LDPC Codes constructed by permutation polynomials have slightly better performance compare with MacKay LDPC Codes and slightly worse performance than IEEE 802.16e LDPC Codes.