Rateless Codes with Optimum Intermediate Performance

In this paper, we design several degree distributions for rateless codes with optimum intermediate packet recovery rates. In rateless coding, the employed degree distribution significantly affects the packet recovery rate. Each degree distribution is designed based on the number of message packets, k, and desired coding overhead, ¿, which is the ratio of the number of received packets, n, to k, i.e., ¿ = n/k. Previously designed degree distributions are tuned for full recovery of the entire source packets for ¿´s slightly larger than 1, and as a consequence, they show very small packet recovery rates for ¿ < 1. Hence, finding degree distributions with maximal packet recovery rates in intermediate range, 0 < ¿ < 1, is of interest. We define packet recovery rates at three values of ¿ as our conflicting objective functions and employ NSGA-II multiobjective genetic algorithms optimization method to find several degree distributions with optimum packet recovery rates. We propose degree distributions for both cases of finite and infinite (asymptotic) k.