Performance Analysis And Constructions Of BC-LDPC Codes

LDPC (Low density parity check) codes is a kind of linear block codes which are defined by the parity-check matrices (PCM). It is proposed by Gallager in the early 1860, with near Shannon limit performance. However, the random generated sparse PCM of LDPC codes obviously increase the encoding complexity. As a result, the block circulant LDPC(BC-LDPC) codes with specific structure have been widely used. Unlike random constructed LDPC codes, the PCM of BC-LDPC codes are composed of sub-block matrix. Each sub-block matrix can be indicated by an integer, so the PCM of a BC-LDPC code can be represented by a small dimensional matrix, which greatly reduces the complexity of encoding and decoding. This thesis focuses on the performance analysis and optimized construction method of BC-LDPC codes.Firstly, this thesis studies the encoding/decoding algorithms of BC-LDPC codes and their implemen-tation complexity. Based on the commonly used "α-0-α" and dual diagonal structure, the encoding of BC-LDPC codes can be implemented with linear complexity. The important iterative decoding algorithms, such as belief propagation (BP) algorithm and min-sum (MS) algorithm, also are introduced and simulated according to some BC-LDPC codes.Secondly, the thesis studies the discretized density evolution (DE) algorithm and Gaussian approximation DE algorithm, which can be used to analyze the BP/MS decoding thresholds of BC-LDPC codes. Moreover, the degree distributions of BC-LDPC codes can be further optimized according to the threshold analysis. We give an example of the threshold analysis and optimization process for the BC-LDPC codes with finite dimension. The simulation results show that the optimized BC-LDPC codes with finite number of row/column can achieve noticeable performance gain by using DE analysis. The correction factor in normalized MS algorithms also can be optimized by the threshold analysis and the simulation results in this thesis verify the reliability and validity of the factor optimization.Then, the thesis studies the construction method of BC-LDPC ccodes, where the masking method based on finite geometric and joint ACE-Cycle optimization method are introduced. After analyzing these meth-ods, we construct the BC-LDPC codes and give the decoding simulation results. Meanwhile, we propose an improved construction method by embedding multiple cyclic shift matrices in one sub-block matrix. The simulation results of the improved constructed BC-LDPC codes based on the structures of the high rate BC-LDPC codes in IEEE 802.11n show that a gain of about 0.11dB can be achieved at BER@-5, when the maximum column weight is 12 instead of 4.Finally, the thesis studies the construction and optimization problems of low rate BC-LDPC codes with Raptor-like structure. By analyzing the decoding thresholds of low-rate BC-LDPC codes, we also describe the optimization schemes using EXIT analysis. PEXIT algorithm to optimize the decoding threshold of OC-LDPC codes with Raptor-like structure which is proposed by CRC company and give the specific process of optimization and analysis of the threshold. Low rate BC-LDPC codes with Raptor-like structure are con-structed according to the results of threshold optimization. Compared with BC-LDPC codes proposed by QUALCOMM and CRC, the optimized low-rate BC-LDPC codes obtain significant performance gain.