Design And Structured Construction Of Low-rate Protograph-based LDPC Codes

The key issue in communication system is how to realize reliable communication when the channel are not ideal. In order to meet the requirements, it is necessary to use channel coding techniques to improve transmission reliability. Channel coding technology in essence, is to transmit information together with some redundant bits, then at the receiving end, by using the redundant information to tell whether there’s an error in the information during the transmission process, and correct the corresponding information, so that to reach the purpose of reliable communication.The Shannon’s channel coding theory shows that under the condition of infinite length, code rate below the channel capacity and using the maximum likelihood decoding, one can achieve reliable transmission without error. Since then, various channel codes constantly showing up. LDPC is a kind of linear block codes, it has been proved to have the best performance among all the existenting channel encodes with capacity-approaching ability, however, when the code rate is low, the error performance of LDPC codes is worse than Turbo codes’ s under the same rate, thus, in order to remedy this disadvantage, the design and construction methods of low code rate LDPC codes were studied profoundly and systematically in this arctical by combining the advantages of protograph LDPC codes with the parallel concatenated structure, the main contents are as follows:Firstly, the concept of parallel concatenated structured protographs(PCSP) was proposed in this artical, by using the tool for theoretical analysis of protograph and characteristics of parallel concatenated structure, the criteria for the optimal design of PCSP was given, then a hierarchical design method for PCSP was proposed under the guidance of this criteria, then a PCSP code with rate 1/3 was designed through this method. Under the condition of BPSK modulation and AWGN channel, the theoretical BER curves of the designed PCSP code was given by using PEXIT algorithm. The Monte Carlo method was used to simulate the BER performance of the designed PCSP code, the results show that, at the BER 610?, the gap between the performance of the PCSP code and 1/3 rate Shannon limit is about 1.107dB; when the code length is 4096 bits, the gap between its BER performace and PCSP theoretical BER performances is only 0.4dB, the performance is comparable with Turbo codes under the same condition.Secondly, in order to make the designed PCSP code actual, an united expending algorithm for protograph was proposed in this article, namely Max Girth Circulant PEG(MG-CPEG) algorithm. The proposed algorithm divides the expending process into two steps, each step performs an expension using structured construction algorithms, which first step using the MG expanding algorithm, expansion factor is 4, eliminate the parallel edges in the protographs, and achieve the target girth, the second step adopted the adjustified Circulant PEG expanding algorithm to get the final parity check matrix, an arbitrary code length can be got by choosing different expansion factor. The girth histogram analysis and simulation results show that protograph LDPC codes expended by MG-CPEG algorithm possess a larger encoding gain compared to those expended by Circulant PEG algorithm. A structured generator matrix was constructed by using the Quasi-Cyclic feature of parity check matrix. Results show that, more than half of the p matrix in this generator matrix are sparse, so the PCSP code could reduce the encoding and decoding complexity enormously.Finally, in order to further improve the performance of serial message propagation decoding algorithm, Overlapped Shuffled-BP(OSBP) decoding algorithm and Overlapped Layerd-BP(OLBP) decoding algorithm were proposed here. Considering the later the update of node information, the higher reliability it could be, more than one sub-decoders are used to execute simultaneously, and every sub-decoder has different updating order from each other. Regarding each node, the most reliable messages are kept and used for the next iteration, thus a faster convergence can be provided. Both theoretical analysis and simulation results show that, compared with serial BP decoding algorithm, both OSBP and OLBP algorithms possess a better error performance as well as a higher convergence speed. Moreover, the proposed algorithm is effective for regular or irregular LDPC codes, and for the PCSP codes. Thus, the proposed algorithm can bring more coding gain and lower decoding latency in practical engineering applications.