Zero Error Coordination

TL;DR

This paper studies zero error coordination in networks, introducing set coordination and exploring its connections to classical problems like Hide and Seek, with new results for two-node networks.

Contribution

It defines set coordination, links it to existing problems, and provides initial results for two-node network scenarios.

Findings

Set coordination generalizes empirical coordination.

Equivalence of two-node set coordination with Hide and Seek problem.

New results for two-node zero error coordination.

Abstract

In this paper, we consider a zero error coordination problem wherein the nodes of a network exchange messages to be able to perfectly coordinate their actions with the individual observations of each other. While previous works on coordination commonly assume an asymptotically vanishing error, we assume exact, zero error coordination. Furthermore, unlike previous works that employ the empirical or strong notions of coordination, we define and use a notion of set coordination. This notion of coordination bears similarities with the empirical notion of coordination. We observe that set coordination, in its special case of two nodes with a one-way communication link is equivalent with the "Hide and Seek" source coding problem of McEliece and Posner. The Hide and Seek problem has known intimate connections with graph entropy, rate distortion theory, Renyi mutual information and even error exponents. Other special cases of the set coordination problem relate to Witsenhausen's zero error rate and the distributed computation problem. These connections motivate a better understanding of set coordination, its connections with empirical coordination, and its study in more general setups. This paper takes a first step in this direction by proving new results for two node networks.