On the duality of Gaussian multiple-access and broadcast channels

Nihar Jindal, Sriram Vishwanath, Andrea Goldsmith

Research output: Contribution to journalArticlepeer-review

323 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)768-783
Number of pages16
JournalIEEE Transactions on Information Theory
Issue number5
StatePublished - May 2004
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


  • Broadcast channel (BC)
  • Channel capacity
  • Duality
  • Fading channels
  • Multiple-access channel (MAC)
  • Multiple-input multiple-output (MIMO) systems


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