On The Duality of Multiple-Access and Broadcast Channels

We show that the Gaussian multiple-access channel and the Gaussian broadcast channel are fundamentally related and are essentially duals of each other. The dual channels we consider have the same channel gains and the same noise power at all receivers. We show that the capacity region of a broadcast channel (both constant and fading) can be written in terms of the capacity region of the dual multiple-access channel, and vice versa. We can use this result to find the capacity region of the MAC if the capacity region of only the broadcast channel is known, and vice versa. For fading channels we show duality under ergodic capacity, but duality also holds for different notions of Shannon capacity for fading channels such as outage capacity and minimum rate capacity. Using duality, many results known for only one of the two channels are now known for the dual channel as well.