Strong Coordination with Side Information

We consider a strong coordination setup, where two nodes must produce a joint distribution on their actions that is close in total variation distance to independent and identical copies from a given joint probability distribution. The first node, which we call the encoder, observes an independent and identically distributed (i.i.d.) source. In order to coordinate the source with the reconstructed outputs of the second node (the decoder), they have access to a noiseless rate limited link and common randomness. The decoder also has additional side information. The reconstruction at the decoder is to be coordinated with the source process as well as the available side information. We allow the side information to be driven by another encoding process, which does not share common randomness with the two nodes. General inner and outer bounds on the rate-coordination region for this set up are derived, and our bounds match for an important special case. We also show an example with no encoding of the side information, where coordination of the source and reconstruction can be obtained as a union of three way coordination regions involving the side information as well.