Gaussian broadcast channel

Two users case

Scalar Gaussian broadcast channel belongs to the class of degraded broadcast channel.  (The users can be absolutely ranked by their channel strength)  

When the transmitter has more than one antenna, the Gaussian broadcast channel is non-degraded.

Sender of power $P$ transmit to two receivers, one with Gaussian noise power $N_1$ and the other with $N_2$.  assume $N_1 < N_2$.   The capacity region is
$$\begin{align*} R_1 &< C \left(\frac{\alpha P}{N_1}\right) \\ R_2 &< C \left(\frac{(1-\alpha) P}{\alpha P + N_2}\right) \\ \end{align*}$$ where $0 \leq \alpha \leq 1$

The weaker receiver $Y_2$ decodes its own message treating the other user's message as interference.  The stronger receiver $Y_1$ decodes $Y_2$'s message and cancels it before decoding his own.

Note:  The role of transmitter side information reduces with the growth in the number of TX antennas.  With either CSIT or CDIT and under the ZMSW model the asymptotic growth is linear as $\mathcal{C} \min(M,K)$.