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