strategy is useful for the channels where the other primary user’s signal (as seen by each primary user) is strong enough and it is possible to decode this primary interference first. Then, the primary receiver decodes the message of the cognitive user and its own message by a joint typicality decoding. The receiver of the cognitive user pair uses joint typicality decoding. Next, deriving two sets of strong interference conditions, we show that the obtained inner bounds achieve capacity under these conditions by proving converse proofs. In these cases, decoding the unintended messages causes no additional constraint on the rate region. Therefore, the channel model is equal to the one in which all three messages are required at all receivers and the capacity region coincides with the capacity region of a three-user C-IFC in which each receiver should decode all three messages. In fact, we determine the conditions, referred to as *Set1*, under which the three-user C-IFC can be seen as a compound three-user MAC with common information. Under the second set of conditions, referred to as *Set2*, the considered channel can be seen as a compound of three channels: two *two-user MAC*s with common information at the primary receivers 