Construction And Decoder Design Of LDPC Code Based On Replacement

Many communication scholars began to study LDPC(low density parity check codes,LDPC)since the twentieth Century.There are many reasons for this code to cause widespread concern.On the one hand,the LDPC code is essentially equivalent to the matrix of mathematics,so it can be flexibly constructed.On the other hand,we can use a variety of means to making fast and easy decoding,such as CPU,GPU,FPGA,etc.The most important part is that it's high capacity and close to the Shannon limit.At the present stage,LDPC as forward error correction technology has been widely used in high speed data transmission and deep space communication.Compared to other construction methods of LDPC,the LDPC construction method based on graph theory has the following advantages: Firstly,graph theory as a branch of mathematics,has a profound theoretical background of mathematics,which made the necessary preparations about theoretical analysis for the construction of LDPC.Secondly,graph theory has the characteristics of simple model and strong generalization ability,which makes many difficulties can be described and solved by graph theory.Thirdly,the graph theory model can be described by use the matrix and be analyzed and solved by the linear algebra and matrix theory,so the expression is simple but rich generalization,and easy to conduct in-depth theoretical analysis.Finally,LDPC codes constructed based on graph theory can keep initial girth,row weight and column weight unchanged,so that it can inherit the advantages of the original graphs and get good LDPC codeseasily.In this paper,the LDPC codes are constructed by using the replacement method and the simulation of the LDPC code is carried out.The main contents are as follows:The first chapter introduces the error-correcting code,which introduces the composition of the digital communication system and channel model,error control system and classification about error-correcting code,then finally leads to the concepts of maximum likelihood code and error correction code.Chapter 2 introduces linear block codes.In the process of introducing block codes,it is stated that generate and check matrices respectively,finally the information to be transmitted is generated by the processing of check matrix,finally,it become the encoded information.The chapter 3 describes the LDPC code and the current application.In this section,we first explain how the LDPC codes are defined,and then describe how the LDPC is described by using the Tanner graph.Then,the concept of degrees in LDPC is explained.Since the decoding performance is made as good as possible,so it is necessary to avoid the presence of a ring of length 4 when constructing a LDPC.A test of a ring of length 4 is given.Finally,according to the latest development trend of LDPC code,we introduced recent utilization of LDPC.Then,a construction method of LDPC codes based on graph theory is proposed.Firstly,the essential knowledge of graph theory and its replacement construction method are introduced.Secondly,the concept of rotation graph is introduced.An example of two graph substitutions is given.Then the design steps of QC cyclic LDPC codes are introduced.Then we introduce the steps of construct graph of LDPC.In order to further illustrate the LDPC's replacement construction method,another example of an iterative construction method is given.In this paper,two codes are designed and simulated by using Min-Sum decoding algorithm.Firstly,the commonly decoding algorithms of LDPC are introduced,and the advantages and disadvantages of different decoding algorithms are given.LDPC decoder is designed by using topdown design method,and the realization of decoding module is given in detail.Finally,we use the minimum sum algorithm and introduce the quantization concept in the minimum sum algorithm.The quantization and decoding of LDPC codes are carried out for different iterations and quantization bits,and the results of quantization and decoding are given.Finally,we selecting theappropriate quantization bit number and the number of iterations which make the decoding performance better.Finally,in this paper,the main contents of LDPC construction and decoding and the author's work are summarized,the future work about LDPC encoding and decoding were introduced.