On reliable broadcast in a radio network

We consider the problem of reliable broadcast in an infinite grid (or finite toroidal) radio network under Byzantine and crash-stop failures. We present bounds on the maximum number of failures that may occur in any given neighborhood without rendering reliable broadcast impossible. We improve on previously proved bounds for the number of tolerable Byzantine faults [6]. Our results indicate that it is possible to achieve reliable broadcast if slightly less than one fourth fraction of nodes in any neighborhood are faulty, and impossible otherwise. We also show that reliable broadcast is achievable with crash-stop failures if slightly less than half the nodes in any given neighborhood may be faulty. In particular, we establish exact thresholds under a specific distance metric.