On the Duality of Gaussian Multiple-Access and Broadcast Channels

TLDR

The paper defines a duality between Gaussian multiple‑access and broadcast channels. The duality is established for channels that share identical gains and noise power at all receivers. The authors show that the capacity region of a Gaussian broadcast channel can be expressed via the capacity region of its dual multiple‑access channel (and vice versa), a relationship that holds for constant, fading, outage, and minimum‑rate capacities and allows known results for one channel to be transferred to the other.

Abstract

We define a duality between Gaussian multiple-access channels (MACs) and Gaussian broadcast channels (BCs). 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 the BC (both constant and fading) can be written in terms of the capacity region of the dual MAC, and vice versa. We can use this result to find the capacity region of the MAC if the capacity region of only the BC is known, and vice versa. For fading channels we show duality under ergodic capacity, but duality also holds for different capacity definitions for fading channels such as outage capacity and minimum-rate capacity. Using duality, many results known for only one of the two channels can be extended to the dual channel as well.