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We study the problem of achieving average consensus between a group of agentsover a network with erasure links. In the context of consensus problems, theunreliability of communication links between nodes has been traditionallymodeled by allowing the underlying graph to vary with time. In other words,depending on the realization of the link erasures, the underlying graph at eachtime instant is assumed to be a subgraph of the original graph. Implicit inthis model is the assumption that the erasures are symmetric: if at time t thepacket from node i to node j is dropped, the same is true for the packettransmitted from node j to node i. However, in practical wireless communicationsystems this assumption is unreasonable and, due to the lack of symmetry,standard averaging protocols cannot guarantee that the network will reachconsensus to the true average. In this paper we explore the use of channelcoding to improve the performance of consensus algorithms. For symmetricerasures, we show that, for certain ranges of the system parameters, repetitioncodes can speed up the convergence rate. For asymmetric erasures we show thattree codes (which have recently been designed for erasure channels) can be usedto simulate the performance of the original "unerased" graph. Thus, unlikeconventional consensus methods, we can guarantee convergence to the average inthe asymmetric case. The price is a slowdown in the convergence rate, relativeto the unerased network, which is still often faster than the convergence rateof conventional consensus algorithms over noisy links.

Tree Codes Improve Convergence Rate of Consensus Over Erasure Channels