Zero-error communication over networks

TL;DR

This paper explores zero-error communication over networks, introducing the concept of channel ambiguity to determine the possibility of simulating channels and establishing error-free communication between network nodes, even with some corrupted players.

Contribution

It introduces the ambiguity of a channel as a new measure to characterize channel simulation capabilities and extends this to networks with potentially corrupted players.

Findings

Channel ambiguity fully characterizes channel simulation possibilities.

Exact calculation of zero-error communication potential in networks.

Framework for analyzing error-free communication with corrupted nodes.

Abstract

Zero-Error communication investigates communication without any error. By defining channels without probabilities, results from Elias can be used to completely characterize which channel can simulate which other channels. We introduce the ambiguity of a channel, which completely characterizes the possibility in principle of a channel to simulate any other channel. In the second part we will look at networks of players connected by channels, while some players may be corrupted. We will show how the ambiguity of a virtual channel connecting two arbitrary players can be calculated. This means that we can exactly specify what kind of zero-error communication is possible between two players in any network of players connected by channels.