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We generalize the problem of controlling the interference created to an external observer while communicating over a discrete memoryless channel (DMC) which was studied in \cite{serrano:2014}. In particular, we consider the scenario where the transmission is established over a compound DMC channel with unknown state at both the encoder and the decoder. Depending on the exact state of the channel, we ask for a different level of average precision on the establishment of the interference coordination with the external observer. For this set-up, we fully characterize the capacity region.

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