On a class of optimal rateless codes

In this paper we analyze a class of systematic fountain/rateless codes constructed using Bernoulli(1/2) random variables. Using simple bounds we then show that this class of codes stochastically minimizes the number of coded packets receptions needed to successfully decode all the information packets. This optimality holds over a large class of random codes that includes Bernoulli(q) random codes with q les 1/2 and LT codes. We then conclude by demonstrating asymptotic optimality for intermediate decoding of the same codes.