Research On The Construction Of Good Quasi-Cyclic LDPC Codes

Low Density Parity Check (LDPC) code is widely interested by the scholars researching on the channel coding for its near Shannon limit performance and relatively simple decoding structure. Currently, the high encoding complexity of a LDPC code is the main bottleneck for its practical applications. A quasi-cyclic LDPC (QC-LDPC) code is a class of LDPC codes with low encoding complexity. A QC-LDPC code has a good performance not only because of its low encoding complexity, low storage requirements, but also its approximate the same error-rate as the randomly constructed LDPC code under the same signal to noise ratio (SNR). Therefore, a QC-LDPC code is a very promising LDPC code for practical applications. This paper has conducted some systematic research on the QC-LDPC codes.The main research contributions are as follows:1) It gives a detailed discussion about the degree distribution and ensemble of a LDPC code. The dissertation pointes out that although, it is difficult to directly construct a good LDPC code, it is relatively easy to achieve a very good overall performance of a single LDPC code based on the distributions of the average overall performance. Therefore, the first step to construct a good code is to look for a good ensemble.2) It discusses the loop lengths and the methods of controlling the loop lengths in QC-LDPC. It gives a necessary and sufficient condition for the 2l length loop. The parity check matrix has been extended which has at least the same girth as the original matrix. Also we propose a detail method for controlling loop lengths.3) It proposes a new type of of QC-LDPC code having lower triangular partiy check matrix which leads to good error-rate performance and fast encoding. Based on the approximate lower triangular structure of QC-LDPC code using an improvement on the Seho-Myung's methods, it not only can meet the arbitrary rate of the best distribution, and have no Short loops, but also can be fast encoded (the encoding complexity is proportional to the unit cyclic Shift matrix's dimension of L, it has a lot of improvements compared to the method of Richardson's method, and has the same complexity with Seho-Myung's method.) Since it satisfies the best distribution and no Short loops, simulation results Show that the decoding performance has an improvement compared with Seho-Myung's method and has not degraded the error-rate performance compared to randomly constructed LDPC code.