Ldpc Codes

This paper mainly discusses the theory of low-density parity-check codes. The subject of low-density parity-check codes is an important branch of information theory, which can approach Shannon capacity limit with very low decoding complexity .It has very splendid foreground both theoretically and practically. This paper introduces basic theory of LDPC codes systemically, which include the design of encoder and decoder, the performance of sum-product algorithm and the convergence of decoding algorithm. Furthermore, this paper specifies optimal structures of LDPC codes and average iterative times of regular LDPC codes' decoder. We have achieved several results important to the theory and application of LDPC code, which are outlined as follows:1. The low-density parity-check code is a special family of linear block codes, so this paper firstly presents the basic theory of linear block codes, and detailed discusses the method of encoding and decoding. Especially we deeply investigate the MAP algorithm and trellis diagram of linear block codes, and these important theories are the bases of LDPC codes.2. We investigate the basic theory of LDPC codes, including encoding algorithm and decoding algorithm, and introduce the orientation of research and foundation of application holistically. Firstly, this paper specifies the main method of encoding, the basic structure of LDPC codes-random structure and deterministic structure. And then this paper places emphasis on the main decoding algorithm of LDPC codes, and presents some important measurements of sum-product algoritm, and update messages based on them are also specified successively. After lots of experiments, we compare the performance between regular and irregular LDPC codes by the chart of bit error rate.3. The qualitative analysis of LDPC codes' sum-product algorithm is an important standard to study LDPC codes. This paper summarizes some basic methods of qualitative analysis, such as the density evolution theory, Gaussian approximation and extrinsic information transfer chart, and some important characteristics of these methods are also specified. Moreover, we ameliorate the analysis method of LDPC codes' threshold, by combining the method of Gaussian approximation and EXIT. And using EXIT, we get the optimal structure of LDPC codes and estimate average iterative times of sum-product algorithm. These results can directly use as a reference of the design of LDPC codes' encoder and decoder.4.The low density parity check code is a type code which can achieve Shannon capacity, but some encoding methods existed are confronted with deadly problems ,such as the delay of encoding are very long ,the storage space need very huge, and the complexity of encoding is out of optimism and so on. For these problems, we present a special LDPC codes-multiple-serialconcatenate low-density parity-check codes. With the structure of Turbo codes, the subcode basing on LDPC codes and sum-product algorithm, this code shows very excellent performance on AWGN channel. After plenty of simulations, this code is superior to other kind of LDPC codes in complexity of encoding. Especially, with high coding rate, multiple-serial concatenate low-density parity-check codes have better performance than regular codes.