The i-shot capacities of the Diamond, Butterfly, and E_t networks under a fixed-edge adversary are log_{|A|}(|A|^i - b)/i, while a switching adversary yields no gain over one-shot capacity.
The Curious Case of the Diamond Network
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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.
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Multishot Capacity of Networks with Restricted Adversaries
The i-shot capacities of the Diamond, Butterfly, and E_t networks under a fixed-edge adversary are log_{|A|}(|A|^i - b)/i, while a switching adversary yields no gain over one-shot capacity.