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
$z_{ro}$
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.