Research On Encoding/Decoding Technolgy Of LDPC Codes And Design Of Simulation Platform

Low-Density Parity-Check (LDPC) Codes are a class of channel codes based on graphs and iterative decoding whose performance is very close to the Shannon limit with low complexity and have strong error strength. Because of their outstanding performance, good encoding algorithm which has almost linear time complexity, decoding algorithm which could be implemented in parallel architecture, and the wildly application future, they have become one of the hottest topics in coding field today. In this paper, the theory and design a of LDPC codes are studied, which involves block codes principles, code encoding, decoding, construction of sparse parity-check matrix, density evolution and modeling LDPC codes.This paper gives some researches on the LDPC systems analysis and study based on exsisting principles, and also establishes foundation for future research.First of all, based on linear block codes, this paper introduces the basic principles of LDPC. The definition of LDPC is introduced from two sides which are the check sparse and the bi-partite graph, also a lot of theorems and properties about linear block codes and LDPC codes are proofed and deduced. Some resprensations are given including the check sparse matrix, generation matrix, check matrix generating way in this paper, weight and minimum distance. Besides, it gives overview about LDPC codes' constructing ways involving Gallager constructions, Mackay constructions, Luby constructions and Davey constructions, and also analyzes the influence on the performance of codes brought form the exsistence of short cycle such as 4-cycle and put up with a simple algorithm for removing 4-cycle.Then, on the side of low-density parity-check codes'decoding algorithms, this paper deeply studies hard-decision decoding algorithms such as Gallager's Bit Flipping (BF) algorithm, Weighted BF algorithm and soft-decision decoding algorithms such as Belief Propagation (BP) algorithm based on the probability domain and the log likelihood ratio domain. It also pays attention to the modified BP decoding algorithm including the BP-Based, normalized BP-Based, Offset BP-Based algorithm. Density evolution theory of LDPC codes is studied which can optimize the normalized and offset factor in order to optimize the LDPC codes. At last, it gives simulating comparation results of different decoding algorithms. The simulation results indicate that the performances of modified decoding algorithms are very close to BP algorithm after utilizing the best factor.Finally, on the side of low-density parity-check codes simulation designing, BP and LLR BP decoding algorithms are carried out by using the interface between function code and Simulink offered by S-function. LDPC encoding algorithm is also realized by using the Embedded Matlab function of User Defined-function library. A platform of LDPC encoding/decoding simulation system over AWGN channel is proposed based on Matlab/Simulink7.0. The results indicate that the proposed method of establishing LDPC encoding/decoding system module can efficiently applied in other complicated communication systems.