Research On Encoding Theory And Key Techniques Of Structure Low-Density Parity-Check Codes

Designing codes with the ability to approach Shannon limit and low coding complexity is a challenging and meaningful issue in channel coding field. Low-density parity-check codes (LDPC) are a class of capacity approaching channel codes based on graphs with low-complexity iterative decoding algorithm and near Shannon limit performance, whose performance is better than Turbo codes with long code length. Due to their advantages LDPC codes, their applications in reliable communications have received great interests and have become one of most attractive field in channel coding community.LDPC codes are prolonged in the conflict between high complexity and good performance, which becomes the bottleneck in applications of LDPC codes. That the encoding complexity of random codes is O(n~2) makes random constuctions impossible to applications. Algebraic constuctions of LDPC codes can reduce the encoding complexity and suit for hardware. Whereas algebraic constuctions may cause performance degradation. It is always the main topics on LDPC codes research that how to design high-performance and low-complexity codes. Imbursed by the great item "Research of Future Communication System Fundamental Theory and Technology (No.60496315)" and the basic item "Research of the algebra structure algorithm of the high performance and low complexity LDPC code" of National Natural Science Fund, this dissertation takes the encoding of LDPC codes as the primary research object from engineering angle, and make researchs by focusing on the girth of parity-check matrix to optimize the code structure. We improve the code performance by alleviating the harmful effect of short cycles on LDPC encoding and decoding and propose an encoding scheme with linear complexity, which applies to practical communication systems. The corresponding academic analysis and experimental simulations are followed by the methods in this paper.The research work in this paper begins with the analysis on effect factors of code performance, especially girth and average girth. Then an introduction of quasi-cyclic codes follows. We discuss the sufficiency-requirement factor between cycles and cyclic shift indexes and give an expression to count the length of the larged cycle. On these theoretical bases, the Column-Difference Matrix and Column-Difference Search Algorithm are proposed described to construct LDPC codes rapidly with large girth. A new class of QC-LDPC codes—CDS-LDPC codes based on all-1 matrixes are is presented which have arbitrary code length, code rate and girth up to 12.Designing masking matrixes and choosing cyclic shift indexes are two sticking points in constucting large girth structure LDPC codes. All-1 matrixes are the simplest masking metrixes. But there exists a upper bound on girth 12. Iterative-filling principle is put forward, which can overstep the 12-girth limit. Then the girth bound of Iterative-filling matrixes is studied.A new class of LDPC codes--CI-LDPC codes based on Column-Difference Search Algorithm and Iterative-filling principle is proposed. The corresponding academic analysis and design method of this code appears in the paper, too. In the following research,this paper summarizes and introduces the linear encoding structures. The linear encoder of CI-LDPC codes based on Quasi-Triangular matrix are designed and correlative academic analysis work is carried out.In the last part, by improving the PEG algorithm, the naissance of PEGQT algorithm is brought about. The new Algorithm can give better masking matrixes. Based on PEGQT Algorithm and Column-Difference Search Algorithm, another new class of LDPC codes—CP-LDPC codes are designed in this thesis. The most prominent characteristic is that the structure of this code is optimized in two ways: girth and girth distribution. It makes easy to find good codes.