Strong Coordination over Multi-hop Line Networks

TL;DR

This paper investigates the trade-offs between communication, local randomness, and common randomness needed for strong coordination in multi-hop line networks, proposing an optimal coding scheme based on channel resolvability codes.

Contribution

It introduces a new achievable coding scheme for strong coordination in multi-hop line networks and characterizes the optimal trade-offs among key resources.

Findings

Derived the rate trade-offs for strong coordination in multi-hop line networks.

Proposed a layered channel resolvability coding scheme.

Identified settings where the scheme achieves optimal trade-offs.

Abstract

We analyze the problem of strong coordination over a multi-hop line network in which the node initiating the coordination is a terminal network node. We assume that each node has access to a certain amount of randomness that is local to the node, and that the nodes share some common randomness, which are used together with explicit hop-by-hop communication to achieve strong coordination. We derive the trade-offs among the required rates of communication on the network links, the rates of local randomness available to network nodes, and the rate of common randomness to realize strong coordination. We present an achievable coding scheme built using multiple layers of channel resolvability codes, and establish several settings in which this scheme is proven to offer the best possible trade-offs.