On Coding And Decoding Of Low-Density Parity-Check Codes: Theory And Implementation

Low-Density Parity-Check (LDPC) codes are a class of capacity approaching error-correcting codes. For long code lengths, LDPC codes can even outperform Turbo codes. Due to the advantages of LDPC codes, such as lower complexity of decoding and lower error floor, 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.Through taking part in the project: the implementation of LDPC encoder and decoder, I have understood the theories of LDPC codes. Those are main contents in this paper. The implementation of LDPC encoder, the choice of LDPC decoding methods and the method of synchronization are presented. Those contents are useful for the implementation of LDPC.Based on the structure of LDPC in IEEE802.16e, a combined serial and parallel encoding scheme is presented. Shift register is used in the encoder without storing the check matrix of LDPC, which is simply. The implementation characteristics of sum-product algorithm and turbo-decoding message-passing algorithm are discussed. Progressive edge growth algorithm is an important method of constructing a check matrix randomly. In this article, PEG is used to construct a check matrix without ascertain girth. Through analyzing the time complexity and simulation, an effective implementation method are proposed, which are fit for the original algorithm. When decoding, the data must be synchronized. Here,'m'sequence is used before the frame. Local'm'sequence correlates with information from the channel which is not hard decided (namely soft correlation). Then compare the correlation value with threshold, which can decide whether information is synchronized. When the probability sum of false synchronization and missed synchronization is minimized, the threshold will be decided. The simulation is given too. Besides above contents, an example is given to explain the theory of sum-product algorithm. The theory of density evolution is described too.