Empirical Coordination over Networks Subject to Fidelity Criteria

QC 20230303

Abstract

Communication is one of the most important and expensive resources in a network with different parts who desire to establish coordinated behavior. When the actions of some parts are distributed according to a probability distribution which is given by the nature of the problem, finding the minimum communication requirements to coordinate the actions of some other parts according to an empirical distribution can be posed as a network information theory problem. Two different notions of information theoretic coordination are studied in the literature: empirical and strong.

This thesis deals with empirical coordination. In the standard empirical coordination framework, a mathematical criterion should be satisfied with perfect precision. This requirement can be restrictive in practice. A possible extension of the framework of empirical coordination is proposed in this thesis by introducing in the coordination requirement a fidelity parameter. Within the new framework, some new problems are stated and solved which can be useful in real applications. For example, they can be handled situations where the capacity of the network is not enough for the establishment of standard empirical coordination but is enough for the establishment of a weaker type of coordination; or situations where the quality of the coordination can vary according to the good or bad condition of the network (which is not known at the encoder).

Two different classes of problems of empirical coordination subject to fidelity criteria are studied: empirical coordination of multi-agent systems, and interference coordination over noisy channels.  In the first class, the nodes of a multi-agent system establish coordinated behavior by using the rate-limited communication links that are available between them. In the second class, two nodes control the interference created to an external observer while communicating over a noisy channel. For both classes of problems, the capacity region of two different setups is derived (fully or partially). Furthermore, the mathematical properties that the chosen fidelity metric should satisfy are discussed.

One of the main conclusions of the thesis is that there is a connection between the proposed framework and the framework of empirical coordination. Specifically, it turns out that when we design optimal coding schemes that achieve empirical coordination according to an empirical distribution and subject to the fidelity criteria, it is necessary and sufficient (at least in some simple setups) to consider all coding schemes that achieve standard empirical coordination according to some empirical distribution, from a class of empirical distributions which is close enough to the desired empirical distribution. This observation allows us to separate the proofs of the proposed framework into two discrete steps: first, we derive the capacity region for the standard framework and, then, we apply an appropriate transformation to this capacity region to get the rate-distortion region for the framework of empirical coordination subject to fidelity criteria.

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