Second-Order Intrinsic Randomness for Correlated Non-Mixed and Mixed Sources

Tomohiko UYEMATSU  Tetsunao MATSUTA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E100-A   No.12   pp.2615-2628
Publication Date: 2017/12/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E100.A.2615
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Shannon Theory
asymptotic normality,  correlated sources,  intrinsic randomness,  second-order achievability,  

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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 δ-achievable rate region where a rate pair of two mappings must satisfy in order to obtain the approximation error within δ ∈ [0,1), and the second-order achievable rate region for correlated general sources. Then, we apply our results to non-mixed and mixed independently and identically distributed (i.i.d.) correlated sources, and reveal that the second-order achievable rate region for these sources can be represented in terms of the sum of normal distributions.