A vector generalization of costa's entropy-power inequality with applications

Ruoheng Liu, Tie Liu, H. Vincent Poor, Shlomo Shamai

Research output: Contribution to journalArticlepeer-review

56 Scopus citations


This paper considers an entropy-power inequality (EPI) of Costa and presents a natural vector generalization with a real positive semidefinite matrix parameter. The new inequality is proved using a perturbation approach via a fundamental relationship between the derivative of mutual information and the minimum mean-square error (MMSE) estimate in linear vector Gaussian channels. As an application, a new extremal entropy inequality is derived from the generalized Costa EPI and then used to establish the secrecy capacity regions of the degraded vector Gaussian broadcast channel with layered confidential messages.

Original languageEnglish (US)
Article number5437423
Pages (from-to)1865-1879
Number of pages15
JournalIEEE Transactions on Information Theory
Issue number4
StatePublished - Apr 2010

All Science Journal Classification (ASJC) codes

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


  • Entropy-power inequality (EPI)
  • Extremal entropy inequality
  • Information-theoretic security
  • Mutual information and minimum mean-square error (MMSE) estimate
  • Vector Gaussian broadcast channel


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