Research On Coding And Decoding Of LDPC Codes

Channel coding is an important component for digital communications systems and computer systems, and LDPC channel coding technology is one of the encoding results. Half of the binary bit-rate LDPC codes in AWGN channel performance only with a tap of 0.0045dB to the Shannon information theory limit. It is the latest error-correcting codes from the Shannon limit. Gallager proposed LDPC codes in 1962, after Mackay and others re-discovered it In 1996, with best performance, completely decoding algorithm in parallel scheme, decoding complexity of linear growth and easily realized for hardware design, LDPC codes has already been widely used in many practical systems, such as wireless communication system, deep-space communication system, and storage system.This thesis reviews the channel coding technology development at first, and introduces the basic concept of LDPC codes and principles. For the focus of research in several directions: Check matrix of structure, related to encoding and decoding ,simplified algorithm , analysis and estimated of the performance, author Put forward own innovative solutions. The focus of this paper is a new calibration matrix of the structure and the optimization algorithm.the construction of the Check matrix is a precondition for coding, a good program construction can greatly simplify the complexity. This thesis reviews main construction types of low-density parity matrix: randomized method, semi-random method and structured construction method, and compare their advantages and disadvantages,then propose a method of construction based on Continuously Variable Length, whose parity check matrix has large girth, and the block length and code rate can be increased. Furthermore, we make use of the compression for code rate to achieve a high code rate and change agilely.The decoding algorithm is the key to LDPC code and the complexity of decoding direct impact realization of the system. It has three kinds of decoding algorithms: hard-decision method, soft-decision methods and hybrid decoding, classical algorithm is BF and BP. To hard-decision methods, author optimizes the WVBF, mainly set the scientific and rational decision threshold and ensures the system performance at the same time greatly simplified the complexity of the decoding. By simulation it has best performance and significantly reduced the number of iterations required for decoding. We analyses decoding performance of LDPC codes with Density Evolution and Gaussian Approximation. It helps to optimize the degree distribution for low-density parity, accurately evaluate the performance matrix without simulations and determine the channel value limit.