Zero Error Coordination
Mahed Abroshan, Amin Gohari, Sidharth Jaggi

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…
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