English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Shannon's Entropy Power Inequality can be viewed as characterizing theminimum differential entropy achievable by the sum of two independent randomvariables with fixed differential entropies. The entropy power inequality hasplayed a key role in resolving a number of problems in information theory. Itis therefore interesting to examine the existence of a similar inequality fordiscrete random variables. In this paper we obtain an entropy power inequalityfor random variables taking values in an abelian group of order 2^n, i.e. forsuch a group G we explicitly characterize the function f_G(x,y) giving theminimum entropy of the sum of two independent G-valued random variables withrespective entropies x and y. Random variables achieving the extremum in thisinequality are thus the analogs of Gaussians in this case, and these are alsodetermined. It turns out that f_G(x,y) is convex in x for fixed y and, bysymmetry, convex in y for fixed x. This is a generalization to abelian groupsof order 2^n of the result known as Mrs. Gerber's Lemma.

The Entropy Power Inequality and Mrs. Gerber's Lemma for Abelian Groups of Order 2^n