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SecondOrder Intrinsic Randomness for Correlated NonMixed and Mixed Sources
Tomohiko UYEMATSU Tetsunao MATSUTA
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E100A
No.12
pp.26152628 Publication Date: 2017/12/01
Online ISSN: 17451337 Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications) Category: Shannon Theory Keyword: asymptotic normality, correlated sources, intrinsic randomness, secondorder achievability,
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Summary:
We consider the intrinsic randomness problem for correlated sources. Specifically, there are three correlated sources, and we want to extract two mutually independent random numbers by using two separate mappings, where each mapping converts one of the output sequences from two correlated sources into a random number. In addition, we assume that the obtained pair of random numbers is also independent of the output sequence from the third source. We first show the δachievable rate region where a rate pair of two mappings must satisfy in order to obtain the approximation error within δ ∈ [0,1), and the secondorder achievable rate region for correlated general sources. Then, we apply our results to nonmixed and mixed independently and identically distributed (i.i.d.) correlated sources, and reveal that the secondorder achievable rate region for these sources can be represented in terms of the sum of normal distributions.

