degree of freedom perspective. In Section V, we describe an achievable region for the symmetric three user Gaussian IC. In Section VI, we generalize the results of Sections IV to a class of non-symmetric channels. We conclude in Section VII.

System Model
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We consider the three user Gaussian IC with three transmitter-receiver pairs and three independent messages, where message $m_k$ originates at transmitter $k$ and is intended for receiver $k$, for $k \in \{1,2,3\}$. The system model is shown in Figure $1$ and the channel equations are described by $$Y_j(i) = X_j(i) + \sum_{k=1, k \neq j}^3 h_{jk} X_k(i) + Z_j(i), \ \forall \ j \in \{1,2,3\},$$

![System Model for Three User Gaussian Interference Channel[]{data-label="fig : SystemModel"}](SystemModel){width="3"}

where $Y_j(i)$ is the received signal at the $j^{th}$ receiver at the $i^{th}$ channel use, $X_k(i)$ is the transmitted signal at the $k^{th}$ transmitter at the $i^{th}$ channel use, and $h_{jk}$ denotes the channel gain from the $k^{th}$ transmitter to the $j^{th}$ receiver. In the above equation, all the direct channel gains have been normalized to unity. $Z_j(i)$ is the zero mean, unit variance additive white Gaussian noise at receiver $j$ at time $i$. The Gaussian noise at each receiver is i.i.d. 