Adjusted robust Soliton distribution (ARSD) with reshaped ripple size for LT codes

In this work, we improve the performance of robust Soliton distribution (RSD) for LT codes by reshaping its expected ripple size. Our goal is to make the ripple size as close to a constant θk as possible during BP decoding process, where 0 <; θ ≤ 1 is called ripple size ratio (RSR) and k is the total number of input symbols. We only adjust the proportion of degree 1, degree 2 and the maximum existing degree in RSD to minimize the mean squared error between the expected ripple size and the constant θk. In addition, we develop upper and lower bounds of RSR as well as an indicator for choosing RSD. Simulation results show that by carefully choosing RSR, the adjusted RSD (ARSD) is able to outperform RSD in terms of successful decoding rate. Compared to RSD, ARSD also reduces the average overhead needed to decode all k input symbols.