Broadcast Channels with Privacy Leakage Constraints

Ziv Goldfeld, Gerhard Kramer, Haim H. Permuter

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


The broadcast channel (BC) with one common and two private messages with leakage constraints is studied, where leakage rate refers to the normalized mutual information between a message and a channel symbol string. Each private message is destined for a different user and the leakage rate to the other receiver must satisfy a constraint. This model captures several scenarios concerning secrecy, i.e., when both, either or neither of the private messages are secret. Inner and outer bounds on the leakage-capacity region are derived when the eavesdropper knows the codebook. The inner bound relies on a Marton-like code construction and the likelihood encoder. A uniform approximation lemma is established that states that the marginal distribution induced by the encoder on each of the bins in the Marton codebook is approximately uniform. Without leakage constraints the inner bound recovers Marton's region and the outer bound reduces to the UVW-outer bound. The bounds match for semi-deterministic (SD) and physically degraded (PD) BCs, as well as for BCs with a degraded message set. The leakage-capacity regions of the SD-BC and the BC with a degraded message set recover past results for different secrecy scenarios. A Blackwell BC example illustrates the results and shows how its leakage-capacity region changes from the capacity region without secrecy to the secrecy-capacity regions for different secrecy scenarios.

Original languageEnglish
Article number7934050
Pages (from-to)5138-5161
Number of pages24
JournalIEEE Transactions on Information Theory
Issue number8
StatePublished - 1 Aug 2017


  • Broadcast channel
  • Marton's inner bound
  • Physical-layer security
  • Privacy leakage
  • Secrecy

ASJC Scopus subject areas

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


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