Improved Fountain Codes For Bi-Awgn Channels

While gaining increasing popularity, fountain codes, including Luby transform (LT) codes and Raptor codes, are known to perform poorly over noisy channels. In this paper, we present a method which gives new output degree distributions that can significantly improve the decoding performance of these codes in binary input-additive white Gaussian noise (BI-AWGN) channels. We start from an observation that the variable nodes (VNs) in the decoding graph of LT codes can be grouped into different categories based on the timing when they receive their initial non-zero log-likelihood (LLR) values. In general, the earlier the VNs are updated with non-zero LLRs, the lower the decoding error rate is. By utilizing the " And-Or tree" technique, we then theoretically derive the exact fractions of VNs falling into different categories for any given output degree distribution. Furthermore, we formulate an optimization process so that new output degree distributions can be designed with more number of VNs being in lower categories. The simulation results demonstrate that the designed degree distribution significantly outperforms existing distributions across a wide range of signalto- noise ratio (SNR) and overhead values.