Network Coding with Myopic Adversaries

We consider the problem of reliable communication over a network containing a hidden myopic adversary who can eavesdrop on some Zrolinks, jam some Zwo links, and do both on some Zrw links. We provide the first information-theoretically tight characterization of the optimal rate of reliable communication possible under all possible settings of the tuple (Zro, Zwo, Zrw) by providing a novel coding scheme/analysis for a subset of parameter regimes. In particular, by leveraging the adversary's uncertainty on unobserved links our vanishing-error schemes bypass the Network Singleton Bound (which requires a zero-error recovery criteria) in a certain parameter regime where the capacity had been heretofore open. As a direct corollary we also obtain the capacity of the corresponding problem where information-theoretic secrecy against eavesdropping is required in addition to reliable communication.