Network Decoding Against Restricted Adversaries

We initiate the study of the one-shot capacity of communication (coded) networks with an adversary having access only to a proper subset of the network edges. We introduce the Diamond Network as a minimal example to show that known cut-set bounds are not sharp in general, and that their non-sharpness comes precisely from restricting the action of the adversary to a region of the network. We give a capacity-achieving scheme for the Diamond Network that implements an adversary detection strategy. We also show that linear network coding does not suffice in general to achieve capacity, proving a strong separation result between the one-shot capacity and its linear version. We then give a sufficient condition for tightness of the Singleton Cut-Set Bound in a family of two-level networks. Finally, we discuss how the presence of nodes that do not allow local encoding and decoding does or does not affect the one-shot capacity.