Network Coding with Myopic Adversaries

TL;DR

This paper characterizes the maximum reliable communication rate over networks with a myopic adversary, introducing new coding schemes that surpass previous bounds and also achieve secrecy in certain regimes.

Contribution

It provides the first tight information-theoretic capacity characterization for networks with myopic adversaries, including novel coding schemes that outperform existing bounds.

Findings

Derived capacity bounds for all adversary parameter regimes

Developed coding schemes that bypass the Network Singleton Bound

Achieved secrecy capacity alongside reliable communication

Abstract

We consider the problem of reliable communication over a network containing a hidden {\it 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.