Gaussian interference channel

The sum capacity is known for two special cases:

Strong interference: Capacity is achieved by decoding and canceling the interference before decoding the desired signal.  The condition is defined as $I_2 \ge S_1$ and $I_1 \ge S_2$
$$\begin{align*} R_1 & \leq C(S_1), \\ R_2 & \leq C(S_2), \\ R_1 + R_2 & \leq \min \lbrace C(S_1+I_1), C(S_2+I_2)  \rbrace \end{align*}$$

Weak interference:  Capacity is achieved by treating interference as Gaussian noise

$$C_{sum} = C \left( \frac{S_1}{1+I_1} \right) + C \left( \frac{S_2}{1+I_2} \right)$$