LDPC Encoding And Decoding Algorithm And Application

Along with the continuous development of mobile communication system, the channel coding technology used by the system also changes frequently. It is a noticeable question that adopting which kind of channel coding scheme could satisfy the demand ofhigh performance system in the future. The research indicates that, the mobile communication system should adopt more advanced channel coding scheme in order to ensure enough performance with the extremely low signal-to-noise ratio (SNR).The low-density parity-check codes are one kind of sparse parity-check matrix based linear block error-correcting codes, which could highly approach the Shannon limit with iterative decoding. The recent research result tells us that, with the decoding algorithm of belief propagation (BP Algorithm), the optimized LDPC codes have performances surpassing Turbo codes, which could be within only 0.0045 dB of the Shannon limit. So far, LDPC codes are considered to be with the best performance, and now the research about LDPC is one of the most amazing highlights in the area of channel coding. And meanwhile, the application of LDPC codes has also been raised in practice and lists as essential technology of the fourth generation mobile communication system (4G).At present the research about LDPC codes is mainly divided into two aspects:one is doing theoretical research on the performance of LDPC codes, containingthe methods of constructing good and easy LDPC codes, research about fast and high efficiency decoding algorithms, analysis of weight distribution of LDPC codes, derivation of capacity of performance and code rate etc.; the other is paying attention to the practical application of LDPC codes, containing the application in the communication systems and magnetic recording systems, hardware realization etc.LDPC code belongs to the linear block code which is encoded by the information sequence multiplies generator matrix. Although the parity-check matrix of LDPC code is sparse, the generator matrix is not. The encoding complexity of it is linearly proportional to the square of code length. The code length is very large when it be used. Also, a significant amount of memory is needed to store their parity-check matrices. In this way, the encoding problem of LDPC codes may be an obstacle for their applications because they have high encoding complexity.With the profound understanding and grasping of the elementary theory of LDPC codes as basis, this thesis conducts thorough research on encoding algorithms of LDPC codes and proposes some improvements, then discusses in detail the performance of LDPC codes in BICM system. The main contents of this article are given as follows:1) The elementary theory and developing process of channel coding technology are introduced, and the appearance, present situation and developing prospect of LDPC codes are systematically summarized and discussed. This part is helpful to forming general cognition of LDPC codes and orients the main research direction and contents of this article.2) Concisely introduces and discusses the encoding-decoding principles of linear block codes and LDPC codes, and involves some important relative concepts such as the definition of LDPC codes, factor graph, the relation of normity and abnormity,GF(q) function, and direct encoding and so on. In the world scope recognizing the LDPC codes again started later and in our country the research on LDPC codes is comparatively more limited,so it requires urgently that researchers should profoundly understand and grasp the elementary theory of LDPC codes to prepare for the deep level research.3) Research and compare with two kinds of popular encoding algorithms (random construct algorithm and system construct algorithm),then give the performance of the above algorithms .Meanwhile,combining the merrit of two kinds of algorithms,we finally get a new and simple algorithm about normity LDPC codes,which use the speciality of optical orthogonal codes.It could control the least girth of Tanner graph,and also gain nearly cycling LDPC codes which can make linear encoding.This algorithm could drastically eliminate the girth which length is six.4) Introduce two kinds of popular decoding algorithms;In order to validate the capability of LDPC codes,which contain normity and abnormity, random construct and system construct algorithms,then give the performance of the above results. Meanwhile,emphasize to analyze the capability of SS-LDPC.From the results,we can learn that the capability of SS-LDPC is better than other nearly cycling LDPC codes,such as EG-LDPC,and is also better than random construct LDPC codes, such as Mackay-LDPC and PEG-LDPC.5) Simply introduce the system modle of BICM,then give the graph and algorithm flow of BICM; Emphasize to analyze the capability of SS-LDPC in BICM. From the results,we can learn that the capability of SS-LDPC in BICM is better than other normity LDPC codes, such as Mackay-LDPC and PEG-LDPC. Meanwhile in AWGN channel,we can validate that Gray mapping is best and 8PSK is the most adaptable to naity LDPC codes.6) The main work of this thesis is concluded and meanwhile the questions and research directions which should be concentrated on in the next steps are proposed.