Improved Optimization Design of Degree Distributions in Fountain Codes

Digital fountain codes are designed to realize a reliable transmission of large-scale data and Luby Transform (LT) codes are the first practical digital fountain codes to be realized. Luby discovered that the performance and decoding efficiency are mainly determined by the degree distribution used in LT codes. So this paper focuses on designing good degree distributions for LT codes over the binary erasure channel (BEC). An improved approach to optimize the degree distribution is proposed based on the asymptotic analysis of LT codes. More importantly, the overhead and the desired erasure ratio pair set for the proposed optimization model can be realized in the asymptotic analysis of the optimal degree distribution. Simulation results show that the optimal degree distribution can provide better bit erasure ratio performance especially at low overheads.