The Research On The Low-density Parity-check Codes And Their Application

Since Shannon proposed and proved famous coding theorem in 1948, people have been making great efforts to look for a kind of good code, whose performance could approach to the Shannon's theoretical limit. From early block codes, algebra codes, RS codes and convolutional codes to Turbo codes and low density parity check codes (LDPC codes);the coded system performance is closing to the theoretical limit. The appearance of the two codes is a great breakthough on channel coding theorem in the field of communication. But because the performance of LDPC codes is superior to that of Turbo codes, people's attention is more mainly focused on LDPC code rather than Turbo codes at the moment.As a new coding technology, LDPC codes arouse many scholars' concern not in the hand of coding and decoding, but in the hand of application. This paper gives a systematic investigation of LDPC codes. First, the definitions of LDPC codes are introduced from the aspect of parity matrix and bipartite graph. Then the structures of LDPC codes and the thought of their encoding and decoding are discussed. Some original methods of constructing LDPC codes are presented. On the base of the characteristic of LDPC code and the disadvantage of coding, a kind of LDPC codes based on identity matrix is designed, which can make use of block interleavers to reduce the cycles. It shows by the MATLAB simulation that the error performance is improved with the new kind of LDPC codes. Finally, the applications of LDPC codes to IEEE802.16a and picture transmit are discussed.LDPC codes have raised a large interest in the coding community with its excellent performance and relative simple analysis in mathematics. The study on LDPC codes gives new blood to other coding schemes, bring new recognize to other codes such as Turbo codes. Such codes with excellent performance must be developed further in theory and be widely used in practice.