Robust LT designs in binary erasures

Fountain codes are used in many applications where the channels are time varying and it is difficult at the transmitter to predict the appropriate code rate. In this situation, fixedrate codes are not suitable. Despite the good performance of fountain codes, universally optimal codes do not exist in the finite-length regime. In this paper, we design new fountain codes that are robust to the communication system's parameters such as erasure probability as well as the source length. We employ density evolution together with linear programming to design robust fountain codes offering some of the attractive properties of universally optimal codes. Different objectives are used in the analysis such as minimizing the erasure probability and maximizing the code rate. Analytically, results indicate that fountain codes can decrease the failure probability to the level of 10-12 using the optimized parameters at source length k = 128, code rate R = 1/2 and erasure probability ϵ = 0. Further, simulation results show that the code rate can be improved significantly. For example, at a source length k = 512, Shokrollahi distribution [1] achieves code rate R = 0.7268 while our novel design provides a code rate R = 0.76331, that is, an improvement of 5%.