Abstract—The advent of practical rateless codes enables implementation of highly efficient packet-level forward error correction (FEC) strategies for reliable data broadcasting in loss-prone wireless networks. Yet, the critical question of accurately quantifying the proper amount of redundancy has remained largely unsolved. In this paper, we exploit advances in extreme value theory to rigorously address this problem. Under the asymptotic regime of a large number of receivers, we derive a closed-form expression for the cumulative distribution function (CDF) of the completion time of file distribution. We show the existence of a phase transition associated with this CDF and accurately locate the transition point. We derive tight convergence bounds demonstrating the accuracy of the asymptotic estimate for the practical case of a finite number of receivers. We also provide an asymptotic closed-form expression on the expected completion time under heterogeneous packet loss. We demonstrate the benefits of our approach through simulation and through real experiments on a testbed of 20 Tmote Sky sensors. Specifically, we augment the existing Rateless Deluge software dissemination protocol with an extreme value FEC strategy. The experimental results reveal reduction by a factor of five in retransmission request messages and by a factor of two in total dissemination time, at the cost of a marginally higher number of data packet transmissions in the order of 5%. I
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