Researches On Simple-encoding LDPC Codes

The thesis focuses on the research of some simple-encoding LDPC (low-density parity-check) codes, including quasi-cyclic LDPC codes, concatenated zigzag codes, and concatenated single parity-check codes, which are simple to pratical implementation.In Chapter 1, background and significance of researching on simple-encoding LDPC codes are firstly introduced. Then the elementary knowledge of LDPC codes, including definition, construction, encoding, decoding and performance analysis, etc are introduced.In Chapter 2, two new technologies to construct quasi-cyclic or cyclic LDPC codes are proposed. The first is to search base incidence vectors of partially balanced incomplete block design at random, then the rest incidence vectors are abtained by cyclically shifting these base incidence vectors. It is more flexible to construct quasi-cyclic LDPC codes than traditional geometric or algebraic methods. Another is based on symmetric balanced incomplete block design. The characteristics of these codes include: both generator matrices and parity-check matrices are sparse and cyclic, which are simple to encode and decode; almost arbitrary rate codes can be easily constructed on-line, so they are rate-compatible codes. Finally, an efficient cycle-based method is proposed to compute the real minimum distances of quasi-cyclic LDPC codes.In Chapter 3, an application of linear interleavers in concatenated zigzag codes is investigated. A modified concept so called "summary distance" is employed to analyze and optimize the linear interleavers. Firstly, the relation between the minimum summary distance of even input weight and odd input weight is derived. It is proved that the minimum modified summary distance plus input weight is a tight lower bound of the minimum Hamming distance. Then, an efficient method to compute the girth among information sequences and the girth between information sequences and parity sequences is obtained. In the following, an efficient cycle-based method is proposed to compute the real minimum distances of quasi-cyclic LDPC codes. Finally, based on the results, several good concatenated zigzag codes with large minimum distances are given. Simulation results support the good performance of these concatenated zigzag codes.In Chapter 4, joint design of concatenated simple parity-check code and QAM (quadrature amplitude modulation) modulation is firstly studied. By analyzing the approximate union bound on concatenated simple parity-check code considered QAM modulation, it is found that enlarging the Euclidean distance between the parity bits and reducing the distance between the information bits can improve the BER (bit error ratio) performance of the coded modulation scheme. At last, the optimum power distribution between the parity bits and the information bits is obtained by computing the approximate union bound. And simulation results demonstrate the proposed scheme performs remarkably better than the traditional one. Secondly, a low-complexity soft-decision technique is proposed for popular Gray mapping modulation schemes, including M-PAM (M-ary pulse amplitude modulation), M-PSK (M-ary phase shift keying) and square M-QAM (M-ary quadrature amplitude modulation). Compared with the traditional method, the proposed technique can effectively reduce the computational complexity without any performance degradation.Chapter 5 concludes the thesis and indicates the future work.