Arbitrarily Varying Networks: Capacity-achieving Computationally Efficient Codes

TL;DR

This paper introduces a computationally efficient coding scheme for networks with malicious adversaries, achieving optimal communication rates without prior network knowledge, by leveraging shared randomness and linear network coding.

Contribution

It characterizes the optimal randomized capacity for networks with omniscient adversaries and proposes a distributed coding scheme that attains this capacity.

Findings

Achieves capacity matching the erasure outer bound.

Requires no prior knowledge of network topology.

Can be implemented in a distributed manner.

Abstract

We consider the problem of communication over a network containing a hidden and malicious adversary that can control a subset of network resources, and aims to disrupt communications. We focus on omniscient node-based adversaries, i.e., the adversaries can control a subset of nodes, and know the message, network code and packets on all links. Characterizing information-theoretically optimal communication rates as a function of network parameters and bounds on the adversarially controlled network is in general open, even for unicast (single source, single destination) problems. In this work we characterize the information-theoretically optimal randomized capacity of such problems, i.e., under the assumption that the source node shares (an asymptotically negligible amount of) independent common randomness with each network node a priori (for instance, as part of network design). We propose a novel computationally-efficient communication scheme whose rate matches a natural information-theoretically "erasure outer bound" on the optimal rate. Our schemes require no prior knowledge of network topology, and can be implemented in a distributed manner as an overlay on top of classical distributed linear network coding.