On Renyi Entropy Power Inequalities
On Renyi Entropy Power Inequalities
复制标题
DOI：
10.1109/tit.2016.2616135
复制
发表时间：
2016-12-01
影响因子：
2.5
通讯作者：
Sason, Igal
中科院分区：
文献类型：
--
作者：
Ram, Eshed;Sason, Igal
给出了改进的Renyi熵幂不等式（R-EPIs）.考虑取R-d上值的n个独立连续随机向量的和S-n = Sigma（n）（k=1）x（k），并令alpha ≠ [1，无穷大]。R-EPI提供了S-n的a阶Renyi熵功率的下界，该下界直到乘法常数（其通常可以取决于n，alpha，d）等于n个随机向量{X-k}（k=1）（n）的a阶Renyi熵功率之和。当α = 1时，R-EPI与著名的香农熵幂不等式一致。第一个改进的R-EPI是通过收紧Bobkov和Chistyakov最近的R-EPI得到的，它依赖于锐化的Young不等式。R-EPI的进一步改进还依赖于凸优化和真实的值对角矩阵的秩一修改的结果。
This paper gives improved Renyi entropy power inequalities (R-EPIs). Consider a sum S-n = Sigma(n)(k=1) x(k)of n independent continuous random vectors taking values on R-d, and let alpha epsilon [1, infinity]. An R-EPI provides a lower bound on the order-a Renyi 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-alpha Renyi entropy powers of the n random vectors {X-k}(k=1)(n). For alpha = 1, the R-EPI coincides with the wellknown 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.