Abstract
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 language | English (US) |
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Article number | 5437423 |
Pages (from-to) | 1865-1879 |
Number of pages | 15 |
Journal | IEEE Transactions on Information Theory |
Volume | 56 |
Issue number | 4 |
DOIs | |
State | Published - Apr 2010 |
All Science Journal Classification (ASJC) codes
- Information Systems
- Computer Science Applications
- Library and Information Sciences
Keywords
- Entropy-power inequality (EPI)
- Extremal entropy inequality
- Information-theoretic security
- Mutual information and minimum mean-square error (MMSE) estimate
- Vector Gaussian broadcast channel