Abstract
This paper gives improved Rényi entropy power inequalities (R-EPIs). Consider a sum S n = sum k=1 n X k of n independent continuous random vectors taking values on mathbb R d , and let α in [1, infty ]. An R-EPI provides a lower bound on the order-α Rényi entropy power of S n that, up to a multiplicative constant (which may depend in general on n, alpha , d ), is equal to the sum of the order- α Rényi entropy powers of the n random vectors X k k=1 n. For alpha =1 , the R-EPI coincides with the well-known entropy power inequality by Shannon. The first improved R-EPI is obtained by tightening the recent R-EPI by Bobkov and Chistyakov, which relies on the sharpened Young's inequality. A further improvement of the R-EPI also relies on convex optimization and results on rank-one modification of a real-valued diagonal matrix.
Original language | English |
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Article number | 7587398 |
Pages (from-to) | 6800-6815 |
Number of pages | 16 |
Journal | IEEE Transactions on Information Theory |
Volume | 62 |
Issue number | 12 |
DOIs | |
State | Published - Dec 2016 |
Keywords
- Renyi entropy
- Renyi entropy power
- entropy power inequality
All Science Journal Classification (ASJC) codes
- Information Systems
- Computer Science Applications
- Library and Information Sciences