Correlated sources with actions

In this paper, we consider the problem of distributed compression of correlated sources with action-dependent joint distribution. This setup is an extension of the Slepian Wolf model, but where actions taken by the encoder or the decoder and affect the generation of one of the sources. In both cases, we characterize the set of achievable rates completely, and show how the actions in the system affect the rate region in a nontrivial manner. We further study a network coding problem in a general network setup with two sources and one destination, where actions are taken at the encoder. In this case, we derive generalized cut-set bounds, and characterize the set of achievable rates using single letter expressions.