| As a new kind of channel coding technologies, fountain codes have attracted extensive attention of researchers because of its advantages such as flexible rate-control, low complexity of coding and transmission without feedback channel. In recent years, fountain codes have been applied into fields like reliable broadcast communications and multi-source download and they have showed good application prospect in many fields. Although fountain codes were put forward based on the erasure channel, many studies have shown that they also perform well over the noisy channel. This paper focuses on Raptor codes and studies their decoding algorithms over the AWGN channel. Our contributions are as follows:Firstly, this paper makes deeper and more comprehensive research on performance of the Min-Sum algorithm and its improved algorithms in decoding of Raptor codes. The BP algorithm is complicated although it shows good performance. The Min-Sum algorithm has much lower complexity compared to the BP algorithm. We simulate the performance of MinSum algorithm and its improved algorithm over the AWGN channel. We draw the conclusion from the results that when we use the Normalized Min-Sum algorithm for both the inner and outer codes of Raptor codes, the performance is close to that of the BP algorithm by using reasonable correction factors.Secondly, this paper proposes to apply layered decoding algorithm into Raptor codes innovatively. The advantage of layered decoding algorithm is that it can reduce the iteration times markedly, which helps the decoding converge much faster. To investigate the performance of layered belief propagation(LBP)algorithm on Raptor codes, this paper simulates the performance of LBP algorithm over AWGN channel. The simulation results show that LBP algorithm can converge much faster than BP algorithm without any loss of BER performance.Finally, we propose LNMS algorithm based on the Normalized Min-Sum algorithm. This algorithm combines the Normalized Min-Sum and layered decoding algorithm for the decoding of Raptor codes. This paper describes the procedure of the LNMS algorithm and simulates its performance. The simulation results show that the performance of LNMS algorithm can be close to BP algorithm and it converges faster than the Normalized Min-Sum algorithm. |
