MIMO Gaussian Broadcast Channels With Common, Private, and Confidential Messages

Ziv Goldfeld, Haim H. Permuter

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


The two-user multiple-input multiple-output Gaussian broadcast channel with common, private, and confidential messages is considered. The transmitter sends a common message to both users, a confidential message to the User 1 and a private (non-confidential) message to the User 2. The secrecy-capacity region is characterized by showing that certain inner and outer bounds coincide and that the boundary points are achieved by Gaussian inputs, which enables the development of a tight converse. The proof relies on the factorization of upper concave envelopes and a variant of dirty-paper coding (DPC). It is shown that the entire region is exhausted by using DPC to cancel out the signal of the non-confidential message at Receiver 1, thus making DPC against the signal of the confidential message unnecessary. A numerical example illustrates the secrecy-capacity results.

Original languageEnglish
Article number8610182
Pages (from-to)2525-2544
Number of pages20
JournalIEEE Transactions on Information Theory
Issue number4
StatePublished - 1 Apr 2019


  • Additive Gaussian channel
  • broadcast channel
  • dirty-paper coding multiple-input multiple-output (MIMO) communications
  • physical-layer security
  • upper concave envelopes

ASJC Scopus subject areas

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


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