Correction of adversarial errors in networks

We design codes to transmit information over a network, some subset of which is controlled by a malicious adversary. The computationally unbounded, hidden adversary knows the message to be transmitted, and can observe and change information over the part of the network he controls. The network nodes do not share resources such as shared randomness or a private key. We first consider a unicast problem in a network with |ε| parallel, unit-capacity, directed edges. The rate-region has two parts. If the adversary controls a fraction p < 0.5 of the |ε| edges, the maximal throughput equals (1 -p)|ε|. We describe low-complexity codes that achieve this rate-region. We then extend these results to investigate more general multicast problems in directed, acyclic networks.