Research On Improved Decoding Algorithm Of LDPC Codes For Low Complexity

With the development of society, people’s daily life become increasingly dependent on reliable transmission of information. Now channel coding techniques are adopted by digital communication system. Because of its good performance close to the Shannon limit and high coding gain, LDPC codes have become the standard of DVB-S2, WLAN, WIMAX communications, which are not only one of the hottest research topics in the field of communication currently, but also the fourth generation mobile communication system’s strong contender.The decoding algorithm of the LDPC codes can be divided into two categories: hard-decision decoding algorithm and soft-decision decoding algorithm. Both of them are based on iterative algorithm, which can be successfully decoded after several iterations. The BF algorithm and WBF algorithm are Commonly used hard-decision decoding algorithm. Although this kind of algorithm need small operation and have low complexity, but their error correction capability are also limited and performance are relatively poor. The soft-decision algorithm include BP decoding algorithm, the log-likelihood ratio domain BP decoding algorithm(Log-BP), the Min-Sum decoding algorithm and its improved algorithm, whose performance are very close to the Shannon limit, but the decoding algorithm contains hyperbolic tangent function and inverse hyperbolic function, namely high complexity, making the hardware implementation is very difficult.This paper firstly introduces the basic principles of the Log- BP decoding algorithm and the WBF algorithm, and simulates their performance in detail. By analyzing their performance under different parameters and comparing advantages and disadvantages of these two algorithms, we propose a new WFBP(weighted Bit Flipping-Belief Propagation Algorithm) algorithm. The WFBP algorithm combines the Log-BP decoding algorithm with the WBF algorithm. At initial decoding stage, we use the Log-BP decoding algorithm, while in the latter part we use the WBF algorithm when the decoding error rate is not very large. If we set Suitable number of iterations of these two algorithm, it not only can reduce the computational difficulty of the soft-decision decoding algorithm, but also can enhance the limited error correction capability of the hard-decision decoding algorithm. We have simulated the performance of the WFBP algorithm, it is observed that the WFBP algorithm performance is close to the original Log- BP decoding algorithm, but its complexity is greatly reduced. Compared with the Log- BP decoding algorithm, it reduces the amount of exponential and logarithmic computation, which has become a simplified and practical algorithm.On this basis, the paper also presents a new RFBP(Reliability Bit Flipping-Belief Propagation Algorithm) algorithm, which can keep an unchanged basic Log-BP iterative structure, when the variable node can be decoded at a high accuracy, we use an improved bit-flipping algorithm to enhance the error correction capability. The RFBP algorithm uses parity reliability as bit-flipping criteria and determines the changed bit in accordance with the minimum calculation. Besides we can reference the specific circumstances of the channel and consider whether to flip multiple bits or not. In order to verify its performance, we use codes of different length to simulate. By comparing the performance of these three algorithms, it can be seen that the RFBP algorithm has a small performance loss of 0.1d B ~ 0.2d B, but it greatly accelerates the convergence speed of the iteration and reduces the decoding complexity. Compared with Log- BP decoding algorithm, although a performance loss of 0.1d B ~ 0.2d B, it avoids a large number of hyperbolic tangent function and inverse hyperbolic function operations, the complexity is greatly reduced. Compared with another proposed WFBP algorithm, the number of multiplications and additions of RFBP algorithm have significantly reduced and the number of iterations have also been reduced, and the performance has improved markedly.Based on the above discussion, compared with the Log-BP algorithm, these two proposed algorithm have been simpler, and the complexity is greatly reduced at the cost of a small performance loss, which have become two methods having important researching value. In these two algorithms, the RFBP algorithm has superior performance and lower complexity, which can be more practical in communication system.