Structure Optimization Of QC-LDPC Codes And Application In Distributed Source Compression

Channel coding that have performance close to the Shannon limit has been an important focus of concern. One of them with excellent performance is Low density parity check (LDPC) codes, but its complex structure in coding and decoding hinders its application in most of fields. Quasi cyclic low-density parity check (QC-LDPC) code with a simple coding and decoding structure is a special LDPC code, which can be efficiently implemented using simple shift registers with complexity linearly. These provide a broad prospect for the application of QC-LDPC codes. However, Short cycles in the Tanner graphs of QC-LDPC codes prevent the sum-product decoding algorithm from converging. Therefore, researching accurately and effectively compute the short cycles in the Tanner graph, reducing its impact on the decoding performance and constructing QC-LDPC code with infinitely approach the Shannon limit have become a research hotspot in recent years.In this paper, we firstly studied the theory and relation technology of LDPC code, and then we conduct our research centering on the studying of short cycle and construction algorithm of the QC-LDPC code and propose a statistic algorithm of short cycle and a construction algorithm for QC-LDPC codes. And then, in order to test the performance of QC-LDPC code constructed by the proposed construction algorithm, it is used to correct the error codes that occur in the optical communication system. Finally, we further research the problem of data compression and joint iterative decoding algorithm application, and propose a data compression algorithm and a joint iterative decoding algorithm. The main content and innovation of this paper are as follows.1. A statistic algorithm for short cycle of QC-LDPC codes based on the full expansion of tree structure of base matrix is proposed. A several special cycles are studied in this paper. According to the study, we can precisely count up the number of the arbitrary cycle. At the same time, compared with other algorithms, the algorithm further reveals the inherent relationship of the cycle between the base matrix and parity check matrix, which play a positive role to predict the performance and correct some flows occurred in the construction procedure of QC-LDPC code.2. A construction algorithm with optimizing the shift value of circulant permutation for QC-LDPC codes is proposed. The algorithm firstly ensure the largest cycle of the base matrix; and then according to the inherent relationship of the cycle between the base matrix and parity check matrix, we calculate the set of the shift value of circulant permutation in base matrix; finally this set are optimized by the algorithm, which not only reduce the number of short cycle and maximize the girth, but also improve the performance of the QC-LDPC code. Finally, A solution to correct the error of fiber-based optical parametric amplifier for40Gb/s NRZ-DPSK signal transmission system employing QC-LDPC codes is proposed. Accordint to research the error caused by the fiber and the system itself, we finally correct these errors by QC-LDPC code, so as to improve the system performance and coding gain.3. A data compression algorithm based on distributed source coding (DSC) is proposed to reduce the volume of wirelessly transmitted data. According to the correlation among sources, the sensor data are compressed by the parity-based tactics using QC-LDPC code. When the compressed data received on the terminal, the data punctured on encoder are predicted using the Kalman filter. The prediction data also know as side information. To correctly perform the joint source-channel decoding, a full codeword is constructed by integrating the side information with the received data. Ultimately, the algorithm not only compress the sensor data, but also recover the source data accurately.4. A joint iterative source-channel decoding algorithm is propose to improve the tranditonal joint source-channel decoding. The algorithm consist of two stage iterative decoding, i.e. local and global iteration decoding.A global iteration decoding are added to the local iteration decoding to further exchange the additive information between the local iteration decoding, which can update the decoding information of a new round of local iteration decoding. The algorithm can not only improve the performance of traditional joint decoding, but also get higher coding gain.The research results of this dissertation have been published/accepted as papers in different journals and conferences.