Network Coding with Myopic Adversaries

Sijie Li, Rawad Bitar, Sidharth Jaggi, Yihan Zhang

Abstract: We consider the problem of reliable communication over a network containing a hidden myopic adversary who can eavesdrop on some Z <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ro</inf> links, jam some Z <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">wo</inf> links, and do both on some Z <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rw</inf> links. We provide the first information-theoretically tight characterization of the optimal rate of reliable communication possible under all possible settings of the tuple (Z <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ro</inf> , Z <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">wo</inf> , Z <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rw</inf> ) 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.