Network Coding with Myopic Adversaries

02/19/2021 ∙ by Sijie Li, et al. ∙ 0

We consider the problem of reliable communication over a network containing a hidden myopic adversary who can eavesdrop on some z_ro links, jam some z_wo links, and do both on some z_rw links. We provide the first information-theoretically tight characterization of the optimal rate of communication possible under all possible settings of the tuple (z_ro,z_wo,z_rw) by providing a novel coding scheme/analysis for a subset of parameter regimes. In particular, 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.

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