A Vector Generalization of Costa's Entropy-Power Inequality with Applications Academic Article uri icon


  • 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. 2006 IEEE.

published proceedings

  • IEEE Transactions on Information Theory

author list (cited authors)

  • Liu, R., Liu, T., Poor, H. V., & Shamai, S. S.

citation count

  • 54

complete list of authors

  • Liu, Ruoheng||Liu, Tie||Poor, H Vincent||Shamai, Shlomo Shitz

publication date

  • January 2010