| Low-Density Parity-Check (LDPC) codes are a class of capacity approaching good error-correcting codes. By using linear time complexity belief propagation iterative decoding algorithm, LDPC codes can get near Shannon limit decoding performance with almost all errors detectable. Due to the advantages of LDPC codes, their applications in reliable communications have received great interests and have become one of most attractive field in channel coding community. Now, the application of LDPC has been put on the agenda.Based on the existing knowledge of LDPC codes, this dissertation mainly focus on searching good LDPC codes and finding small stopping sets of LDPC codes. Some results are obtained and summarized as follows:1.The coding and decoding ideas of low-density parity-check codes on graphs are systematically summarized. The message-passing decoding algorithm is analyzed at priority. Two main factors, the girth and stopping sets, which impact the decoding performance of LDPC codes, are analyzed in detail.2.Two kinds of constructing good LDPC codes algorithms based on heuristic search and girth conditioning are analyzed intensively. By numerical simulations experiences of two algorithms, the codes generated with construction algorithm based on girth conditioning for LDPC codes have larger average girth and better decoding performance; the simulations results also show that the codes with larger average girth have better connectivity and lower error floor.3.The fast and simple algorithm to find small stopping set in bipartite graph and codewords with small Hamming weight of LDPC codes is given. Asymptotic bounds for the frame error rates over binary erasure channel and over the AWGN channel with stopping set size distribution and with the Hamming weight distribution found by the algorithm are calculated. Simulations show that asymptotic bounds can be used to predict the frame error rates for a transmission over binary erasure channel for a low erasure probability. |
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