which is still very useful in practical applications if one considers a phase for obtaining this side information. From an information theoretic point of view, Cognitive Interference Channel (C-IFC) was first introduced in [@DevrMitTar06] to model an overlay cognitive radio and refers to a two-user Interference Channel (IFC) in which the cognitive user (secondary user) has the ability to obtain the message being transmitted by the other user (primary user), either in a non-causal or causal manner. For the non-causal C-IFC, where the cognitive user has non-causal full or partial knowledge of the primary user’s transmitted message, an achievable rate region was first derived in [@DevrMitTar06], by combining the Gel’fand-Pinsker (GP) binning [@GelfPin80] with a well known simultaneous superposition coding scheme (rate splitting) applied to IFC [@HanKob81]. Subsequently, several achievable rate regions and capacity results in some special cases for the C-IFC have been established [@JoviVis09]-[@JiangXin08]. Yet, capacity results have been known only in special cases. C-IFC with strong interference conditions is one of these cases, where interference is such that both messages can be decoded at both receivers with no rate penalty. Strong interference conditions for C-IFC and the capacity regions under these conditions have been derived in [@MariYatKra07; 