The Research LDPC Codes Of Density Evlution Algorithm Under OFDM Channels

With the development of society, the requirement of the communication business is growing rapidly,which makes a higher demand for communication theory. We not only need to guarantee the high quality of digital communication transmission, but also are required to provide much greater transmission capacity.As the next generation wideband wireless access technology, orthogonal frequency division multiplexing (OFDM) technology included digital modulation, digital signal processing, and multi-carrier modulation technology, which makes this technology has the advantages on the utilization of spectrum, anti-jamming and multi-path fading. The application of this technology began in the 1960s, when just only applied to military field. In the 1970's, people used the discrete Fourier transform to implement carrier modulation in the practical technology of OFDM. With the high speed development of digital signal processing technology and integrated devices, OFDM system has been adopted in the DVB ADSL more and more widely. In the 90's, the research of OFDM technology into the wireless channel broadBand transmission. To reduce the bit error rate of OFDM systems, we would code for OFDM systems. Now there have RS code, convolution code etc are application, and the research of Turbo code applied to OFDM systems is more mature. The OFDM system which has been channel coding, the performance of the bit error rate have greatly improved.LDPC code is a good code which the most close to the Shannon limit by far, it is put forward by Gallager in 1963, In 1996 people found that the code has many advantages through Mackay research this code again, henceforth LDPC code have been concerned widespread. At present one of the hot issues of LDPC code is density evolution of research, because we can describe the performance of LDPC code of the error correction by threshold, the number of threshold is bigger, the more approximates to Shannon limit in certain code rate. So the paper aims to improve to density evolution method, optimized for LDPC code threshold, and make it close to shannon limit as possible. LDPC code and OFDM technology are two key technology of improve communication quality and transmission capacity in the future digital wireless communications, this paper on the basis of cognitive two technologies, which focusing on the theory of the LDPC code for the density evolution theory, the feasibility of the combined with two techniques and the method were discussed. The main contents are as follows:(1) Introduced the development of OFDM systems, basic theory and key technology in detail, which from help us to understand the technology substantially Research for OFDM channel estimation method deeply, puts forward the least-square estimation and minimum mean square error estimation two algorithms, this paper comparison algorithm of inferiority from error bit rate and mean square error two aspects.(2) Described the LDPC code in detail, we would understand the code of structure, classification, coding and decoding method through the introduction of LDPC code. Especially in decoding method, pays more attention to the research LLR BP algorithm and minimal sum decoding algorithm, comparing the different decoding complexity and bit error rate (ber), according to different structure of encoding, we used different decoding methods. This chapter will help us understand LDPC code better, at the same time lay the groundwork for the following research in the next research.(3) Calculating the thresholds by the density evolution algorithm, this chapter put forward two methods:continuous density evolution and gaussian approximation algorithm. For the regular and irregular LDPC code using two algorithms calculate the threshold separately. In the gaussian algorithm, not only for shaped like (j, j+n) regular code thresholds, but also the irregular code of the two nodes probability density were compared. In the improved algorithm, calculate the threshold of more quickly by improved Q function and analysis of fixed nodes.(4) After research the above problems, and puts forward to calculate the LDPC code threshold by the density evolution method under OFDM channel, and comparison with the condition of BCJR algorithm for whether the channel have spectrum zero. From the simulation can see, under the appropriate rates, two thresholds of channel were comparable. For higher rate, the thresholds of the DE algorithm was worse than BCJR algorithm. This shows as code rate are increased, inter-symbol are seriously, quality of channel and LDPC code performance will be worse, then for transmission system, its bit error rate of data transmission relative was increased. Though low code rate can guarantee a high thresholds, could not assurance information transmission speed. So we need compromise from the threshold and ISI two aspects, according to the actual situation of select appropriate code rate.(5) For the whole thesis is summarized, and puts forward the problems should be solved and the future research direction.This paper is mainly to studying the density evolution algorithm, specially for Gaussian approximation algorithm. We found that although in accuracy was declined, it would improve the speed of calculation, decrease the amount of computation by improved the Gaussian approximation, thus the costs are worth. With the OFDM systems in the combination, the calculating data also is more ideal.