consider the discrete memoryless three-user C-IFC and present two achievable rate regions for this setup. The coding schemes contain superposition coding in the encoding part. In the decoding part, all messages are common to all receivers, i.e., all three receivers decode $m_1$, $m_2$ and $m_3$. In the scheme of the first achievable rate region, the simultaneous joint decoding is utilized at all receivers. However, in the second scheme, Rx1 first decodes the other primary user’s message $m_2$, while treating the remaining signals as noise, i.e., the signals of $m_1$ and $m_3$ plus additive noise. This strategy is useful for the channels where the signal of $m_2$ at Rx1 is strong enough and it is possible to decode this primary interference first. Then, Rx1 decodes the message of the cognitive user $m_3$ and its own message $m_1$ by a joint typicality decoding. Rx2 proceeds similarly, while, Rx3 uses joint typicality decoding. Detailed proofs are provided in Appendix \[app:ach\_proof\].

Let ${\mathcal{P}}$ denotes the set of all joint p.m.fs $p(.)$, that factor as

[c]{} p(x\_1,x\_2,x\_3)=p(x\_1)p(x\_2)p(x\_3|x\_1,x\_2).\[eqn:pmf\_ach\]

\[thm:ach1\] The union of rate regions given by

[rcl]{} R\_[3]{}&& I(X\_3;Y\_3|X\_1,X\_2) \[eqn:ach1\_I\]\
R\_[1]{}+R\_[3]{}&& {I(X\_1,X\_3;Y\_1|X\_2),I(X\_1,X\_3;Y\_3|X\_2)} \[eqn:ach1\_II\]\
R\_[2]{}+R\_[3]{}&& {I(X\_2,X\_3;Y\_2|X\_1),I(X\_2,X\_3;Y\_3|X\_1)} \[eqn:ach1\_III\]\
R\_[1]{}+R\_[2]{}+R\_[3]{}&&{I(X\_1,X\_2,X\_3;Y\_1),I(X\_1,X\_2,X\_3;Y\_2),I(X\_1,X\_2,X\_3;Y\_3)} \[eqn:ach1\_IV\]

is achievable for the three-user C-IFC (denoted as 