Ldpc Codes And Decoding Algorithms

Low-Density-Parity-Check-Codes is currently one of the pop research theses in communication field, it is the powerful competition in the 4th generation of mobile communication system. The decoding performance of LDPC is excellent and can be near the Shannon limit by iterative probability decoding algorithm. It has low complexity, the decoding algorithm is essentially parallel, so it is suitable to realize on hardware in parallel and reduce the decoding delay time. It can make certain that if the codes are decoded in the iterative decoding process and if the process can be finished in order to reduce iterative times, at the same time the decoding error can be detected. Bit error rate(BER) after decoding can be decreased arbitrarily along with the increase of Signal-to-Noise rate(SNR), and the error floor phenomenon can not occure. The complexity of encoding is high. Because the encoding process begins after receiving all needed signal bits, it brings certain delay time while the length of the codes is very long.This paper gives a systematic investigation of LDPC codes. First, the structures and some check matrix construction methods of LDPC codes are introduced; then several iterative Message Passing algorithms for LDPC codes are introduced, LDPC codes can be decoded with various decoding algorithms, such as Bit Flipping(BF) algorithm. Weighted BF(WBF) algorithm. Belief Propagation(BP) algorithm, Min-Sum algorithm. Normalized Min-Sum algorithm and iterative decoding algorithm based on reliability etc, the density evolution algorithm on a basis of BP algorithm for calculating noise threshold is also introduced; After that, it is discussed that how to solve the problem of its high encoding complexity, some encoding methods making use of the sparsity of parity check matrix are given, we have also designed two encoding methods in Verilog HDL language and their simulating waveforms are presented; Finally, some simulating results of BER performance of different length and rate for additive white Gaussian noise(AWGN) channels are presented, and an example is given to calculate the noise threshold by use of density evolution algorithm on a basis of BP algorithm, and it is compared with the simulating result. In addition, we have studied a kind of simplified Belief - Propagation decoding algorithm that used mathematic method by curve fitting to reduce iterative operations, so as to reduce decoding complexity.