When the behaviour of some parts of a network is 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 a conditional empirical distribution can be posed as an information theoretic problem. In standard empirical coordination 1 , a mathematical criterion should be satisfied with perfect precision.

We propose an extension of the framework by introducing a fidelity parameter in the coordination requirement. Within the new framework, some new problems are stated and solved which can be useful in real applications. For example, we can handle 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).

One basic conclusion of the thesis is that when we design coding schemes that achieve empirical coordination according to a conditional empirical distribution and subject to the fidelity criteria, we do not lose in optimality if we restrict our search in all coding schemes that achieve standard empirical coordination according to some conditional empirical distribution, from a class of conditional empirical distributions which is close enough to the desired conditional empirical distribution.

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