and a three-user MAC with common information at the cognitive receiver. Further, we compare these two sets of conditions and show that *Set1* is weaker than *Set2*. Moreover, we consider the Gaussian three-user C-IFC and find capacity results for the Gaussian case based on *Set2*. We also provide some numerical examples.

The rest of the paper is organized as follows. Section \[sec:definition\] introduces the three-user C-IFC model and the notations. In Section \[sec:Ach\], we obtain the achievable rate regions; while in Section \[sec:Cap\], we state the capacity results for the discrete memoryless three-user C-IFC. In Section \[sec:Gaussian\], Gaussian three-user C-IFC is investigated. Finally, Section \[sec:conclusion\] concludes the paper.

Channel Models and Preliminaries {#sec:definition}
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Throughout the paper, upper case letters (e.g. $X$) are used to denote RVs and lower case letters (e.g. $x$) show their realizations. The probability mass function (p.m.f) of a RV $X$ with alphabet set ${\mathcal{X}}$, is denoted by $p_X(x)$, where subscript $X$ is occasionally omitted. $A_\epsilon^n(X,Y)$ specifies the set of $\epsilon$-strongly, jointly typical sequences of length $n$. The notation $X^j_i$ indicates a sequence of RVs $(X_i,X_{i+1},...,X_j)$, where $X^j$ is used instead of $X^j_1$, for brevity. ${\mathcal{N}}(0,\sigma^2)$ denotes a zero mean normal distribution with variance $\sigma^2$.

![Three-user 