Reliable Broadcast in Wireless Networks with Probabilistic Failures

We consider the problem of reliable broadcast in a wireless network in which nodes are prone to failure. Each node can fail independently with probability p. Failures are permanent. The primary focus is on Byzantine failures, but we also handle crash-stop failures. We consider two network models: a regular grid, and a random network. Our necessary and sufficient conditions for the Byzantine failure model indicate that p should be less than frac12, and the critical node degree is Theta(d_min+(lnn/ln(1/2p))+ln(1/2(1-p))) (where d_min is the minimum node degree associated with a non-empty neighborhood, and is a small constant). For a random network we prove that, for failure probability less than frac12, the critical average degree for reliable broadcast is O(lnn/frac12-p+frac12ln(1/2(1-p))). We briefly discuss the issue of crash-stop failures for which we have results that improve upon previously existing results for this model, when p approaches 0. We also identify an interesting similarity in the structure of various known results in the literature pertaining to a set of related problems in the realm of connectivity and reliable broadcast.