On Equivalence for Networks of Noisy Channels under Byzantine Attacks

Abstract

We consider the problem of finding network coding capacities of networks of independent point-to-point channels in the presence of a Byzantine adversary. We assume that the adversary knows all messages, and noise values and the code used to communicate across the network. The adversary controls an unknown subset of edges and can replace the channel output vectors from those edges. We show that finding the capacity for the above network is equivalent to finding the capacity of a network that is obtained by replacing each finite input alphabet point-to-point channel by a noiseless link of the noisy channel capacity. Our result shows the asymptotic optimality of separation between channel coding for each link followed by network coding for the resulting network under the corresponding model of adversarial attack.