• DocumentCode
    1758711
  • Title

    Beyond the Entropy Power Inequality, via Rearrangements

  • Author

    Liyao Wang ; Madiman, Mokshay

  • Author_Institution
    Dept. of Phys., Yale Univ., New Haven, CT, USA
  • Volume
    60
  • Issue
    9
  • fYear
    2014
  • fDate
    Sept. 2014
  • Firstpage
    5116
  • Lastpage
    5137
  • Abstract
    A lower bound on the Rényi differential entropy of a sum of independent random vectors is demonstrated in terms of rearrangements. For the special case of Boltzmann-Shannon entropy, this lower bound is better than that given by the entropy power inequality. Several applications are discussed, including a new proof of the classical entropy power inequality and an entropy inequality involving symmetrization of Lévy processes.
  • Keywords
    entropy; stochastic processes; vectors; Boltzmann-Shannon entropy; Lévy process symmetrization; Rényi differential entropy; entropy power inequality; rearrangements; sum-of-independent random vectors; Convergence; Convolution; Electronic mail; Entropy; Probability density function; Random variables; Vectors; Entropy power inequality; R??nyi entropy; majorization; spherically symmetric rearrangement;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/TIT.2014.2338852
  • Filename
    6855366
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1758711