# Adversarial Network Coding

## TL;DR

This paper introduces a combinatorial framework for adversarial network coding, providing bounds on various capacities for point-to-point and multi-source networks, along with capacity-achieving schemes for certain adversarial models.

## Contribution

It presents a novel method to extend capacity bounds from point-to-point channels to complex networks with adversaries, and describes coding schemes for specific adversarial scenarios.

## Key findings

- Upper bounds on one-shot, zero-error, and compound zero-error capacities for channels.
- General technique to transfer capacity bounds from point-to-point to networks.
- Capacity-achieving codes for certain adversarial models.

## Abstract

A combinatorial framework for adversarial network coding is presented. Channels are described by specifying the possible actions that one or more (possibly coordinated) adversaries may take. Upper bounds on three notions of capacity (the one-shot capacity, the zero-error capacity, and the compound zero-error capacity) are obtained for point-to-point channels, and generalized to corresponding capacity regions appropriate for multi-source networks. A key result of this paper is a general method by which bounds on these capacities in point-to-point channels may be ported to networks. This technique is illustrated in detail for Hamming-type channels with multiple adversaries operating on specific coordinates, which correspond, in the context of networks, to multiple adversaries acting on specific network edges. Capacity-achieving coding schemes are described for some of the considered adversarial models.