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

Tomohiko UYEMATSU; Tetsunao MATSUTA

doi:10.1587/transfun.E100.A.2615

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

Tomohiko UYEMATSU, Tetsunao MATSUTA

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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.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E100-A No.12 pp.2615-2628

Publication Date: 2017/12/01

Publicized

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

Authors

Tomohiko UYEMATSU
Tokyo Institute of Technology
Tetsunao MATSUTA
Tokyo Institute of Technology

Keyword

asymptotic normality, correlated sources, intrinsic randomness, second-order achievability

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Tomohiko UYEMATSU, Tetsunao MATSUTA, "Second-Order Intrinsic Randomness for Correlated Non-Mixed and Mixed Sources" in IEICE TRANSACTIONS on Fundamentals, vol. E100-A, no. 12, pp. 2615-2628, December 2017, doi: 10.1587/transfun.E100.A.2615.
Abstract: 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.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E100.A.2615/_p

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@ARTICLE{e100-a_12_2615,
author={Tomohiko UYEMATSU, Tetsunao MATSUTA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Second-Order Intrinsic Randomness for Correlated Non-Mixed and Mixed Sources},
year={2017},
volume={E100-A},
number={12},
pages={2615-2628},
abstract={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.},
keywords={},
doi={10.1587/transfun.E100.A.2615},
ISSN={1745-1337},
month={December},}

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TY - JOUR
TI - Second-Order Intrinsic Randomness for Correlated Non-Mixed and Mixed Sources
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2615
EP - 2628
AU - Tomohiko UYEMATSU
AU - Tetsunao MATSUTA
PY - 2017
DO - 10.1587/transfun.E100.A.2615
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E100-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2017
AB - 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.
ER -