The Curious Case of the Diamond Network

Abstract: This work considers the one-shot capacity of communication networks subject to adversarial noise affecting a subset of network edges. In particular, we examine previously-established upper bounds on one-shot capacity. We introduce the Diamond Network as a minimal example to show that known cut-set bounds are not sharp in general. We then give a capacity-achieving scheme for the Diamond Network that implements an adversary detection strategy. Finally, we give a sufficient condition for tightness of the Singleton Cut-Set Bound in a family of two-level networks.