Allocation of Network Error Correction Flow to Combat Byzantine Attacks

This paper studies the allocation of information flows in noiseless, memoryless communication networks in the presence of omniscient Byzantine adversary. In such networks, adversary may maliciously modify some edge-flows, and legitimate users should resort to network error correction strategies to transmit data reliably. Unlike prior papers, which focused on the capacities of the networks, we consider the expense of resources used by the flow. Hereby, this paper uses an optimization problem to define the concept of minimum cost network error correction flows. We provide a necessary and sufficient condition of feasibility of the allocation problem, and derive a cut-set outer bound on the feasible region. Using this cut-set bound, we can find the minimum cost network error correction flow in some instances. Moreover, we also consider the relationship between incoming edge-flows and outgoing edge-flows of a vertex. As for the directed acyclic graphs, we propose an algorithm to allocate the network error correction flow. This algorithm is with polynomial time complexity, and proves to be optimal when recoding at intermediate nodes is forbidden. Additionally, in order to justify the necessity of recoding at intermediate nodes, we analyze the benefit of intermediate recoding. On the one hand, we construct a series of instances to prove that intermediate recoding can bring enormous benefits in some networks. On the other hand, numerical analysis shows that the benefit is modest in small random graphs.