Research On The Encoding/Decoding Algorithms Of LDPC Codes And Its Application For The Video Transmissions

In 1962 Gallager first proposed a new kind of block code, which was named as low-density parity-check (LDPC) code defined by a sparse parity-check matrix. Since the limited resource for the efficient computations at that time, people may incorrectly think that the concatenated codes were more efficient for the purpose of general error correction so that LDPC codes had been ignored for decades. However, after the advent of turbo codes and the extremely successful applications, LDPC codes were rediscovered by Mackay and Neal during the past decade by the aid of modern computer science and technologies and the rapid development of some related powerful theories, especially for the graph theories. It has been proved that the performance of LDPC codes is very close to the Shannon limits when combined with an iterative belief-propagation-based decoder.LDPC codes and turbo codes are similar in many aspects; both can extremely approach to the Shannon limits by their unique ways. The performance of turbo codes is better than any other codes at low SNR. While LDPC codes are relatively easy to be characterized, and can outperform turbo codes with sufficiently long block lengths. Its decoding complexity is also lower than turbo codes. In recent years, LDPC codes have attracted the worldwide attentions in the information theory and channel coding communities due to its impressive performance and great potentials in application.This thesis first introduces the fundamentals of digital communication and channel coding theory, and presents the state-of-the-art development of error-correcting code. In Chapter 2, we give a research on the basic principles and several encoding algorithms for LDPC codes.Chapter 3 maily focuses on BP algorithm and several other decoding algorithms, presenting the principles and reduced-complexity decoding approaches. In Chapter 4, simulation results of reduced-complexity decoding approaches are abtained over an AWGN channel, and the results are compared with the traditional BP algorithm results. Chapter 5 introduces the basic concepts of joint source and channel coding. In Chapter 6, we obtain simulations results of the applications of LDPC codes in the binary system and gray image transmission, and give the infection of code rate and iteration times to the image transmission performance. Chapter 7, for the image with abundant textures, author proposes a new joint source-channel coding scheme with combination of multi-layered image coding and unequal error protection (UEP) of LDPC codes, Experimental results show that the performance of UEP is much better than that of unequal error protection (EEP), and the reconstructed image remains to be the better texture features with a high compression ratio.