Reliable communication in networks with Byzantine link failures

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Abstract
We consider the problem of communication between nodes of a network whose links are subject to arbitrary failures: A failed link may not only stop transmitting messages but may corrupt them in any possible way. We characterize networks allowing communication in spite of at most t failures. Also, for every fixed link failure probability p ≤ .29, we construct a class of networks for which the probability of successful communication converges to 1 as the number of nodes grows. It is shown that the number of links in these networks is asymptotically smallest possible to assure reliable communication. Moreover, in these networks, communication can be completed in just two information exchange rounds. Finally, we give a protocol assuring reliable communication in the hypercube if link failure probability is p ≤ .02 and show that no such protocol exists if p ≥ .15.

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