Research On The Decoding Simulation Of Non-Binary LDPC Codes

Low density parity check (LDPC) codes were first proposed in the 1960s by Gallager. A LDPC code is a linear block code with a very sparse check matrix. Since 1990's the research results of LDPC codes have shown excellent performance near the Shannon limit. Compared with binary LDPC codes, non-binary LDPC codes in GF(q), which were first proposed by Davey and MacKay in 1998, have better error correction performance.First,this dissertation introduces basic theories,such as the Tanner graph representation of LDPC codes and the encoding and decoding principles of binary and non-binary LDPC codes, Various construction methods of LDPC codes, such as Gallager construction method, MacKay construction method and Progressive Edge-Growth(PEG) construction method, are introduced shortly, followed by the construction methods of non-binary LDPC codes, and various encoding algorithms of LDPC codes, such as direct encoding method, LU coding and some iterative coding, are also introduced.Next, this paper introduces the Belief Propagation Algorithm (BP) decoding algorithm and Log-likelihood ratio Belief Propagation Algorithm (LLR BP) decoding algorithm of binary LDPC codes. After the LDPC codes were encoded by LU decomposition method, a variety of length and rate of the LDPC code were simulated by C language.at the end the sparse matrixs were stored by using cross-linked list, the speed of operation was greatly improved by using the cross-linked. The simulation results show that binary LDPC codes have the excellent performance.Finally, based on the realization of a binary LDPC decoding algorithm,non-binary LDPC codes'decoding were studied.Fast Fourier Transform-Belief Propagation Algorithm (FFT-BP) decoding algorithm, Log-likelihood ratio-Belief Propagation Algorithm (LOG-BP) decoding algorithm and the MAX Log-likelihood ratio Belief Propagation Algorithm (MAX-LOG-BP) algorithm of non-binary LDPC codes were mainly introduced. Check matrixs of non-binary LDPC codes were received by using elements of GF(q) replacing the check matrixs's elements of the binary LDPC codes randomly, then a variety of length and GF(q) of the LDPC code were simulated by C language.From the simulation results show that the higher the order of GF(q), the more superior of the LDPC codes performance, non-binary LDPC codes have a more excellent performance than binary LDPC.