Entropies of Weighted Sums in Cyclic Groups and an Application to Polar Codes

In this note, the following basic question is explored: in a cyclic group, how are the Shannon entropies of the sum and difference of i.i.d. random variables related to each other? For the integer group, we show that they can differ by any real number additively, but not too much multiplicatively; o...

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Bibliographic Details
Main Authors: Emmanuel Abbe, Jiange Li, Mokshay Madiman
Format: Article
Language:English
Published: MDPI AG 2017-09-01
Series:Entropy
Subjects:
Online Access:https://www.mdpi.com/1099-4300/19/9/235

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