TY - GEN
T1 - Sufficient conditions for the equality of exact and Wyner common information
AU - Vellambi, Badri N.
AU - Kliewer, Jorg
N1 - Publisher Copyright:
© 2016 IEEE.
PY - 2017/2/10
Y1 - 2017/2/10
N2 - The minimum common randomness required for the approximate and separate generation of a pair of correlated discrete memoryless sources is quantified by Wyner's notion of common information. Recently, Kumar, Li, and El Gamal introduced the notion of exact common information as the minimum common randomness required for the exact and separate generation of a pair of correlated discrete memoryless sources. This new notion of common information, which does not have a general single-letter characterization, was shown to match Wyner's notion for the symmetric binary erasure source. In this work, we present two conditions on the joint statistics of the pair of sources under either of which the exact and Wyner's notions of common information coincide. Though the conditions are implicit, we prove the equality of Wyner and exact common information for the generalized binary Z-source, generalized erasure source and the noisy typewriter source by establishing that these sources meet either of these conditions.
AB - The minimum common randomness required for the approximate and separate generation of a pair of correlated discrete memoryless sources is quantified by Wyner's notion of common information. Recently, Kumar, Li, and El Gamal introduced the notion of exact common information as the minimum common randomness required for the exact and separate generation of a pair of correlated discrete memoryless sources. This new notion of common information, which does not have a general single-letter characterization, was shown to match Wyner's notion for the symmetric binary erasure source. In this work, we present two conditions on the joint statistics of the pair of sources under either of which the exact and Wyner's notions of common information coincide. Though the conditions are implicit, we prove the equality of Wyner and exact common information for the generalized binary Z-source, generalized erasure source and the noisy typewriter source by establishing that these sources meet either of these conditions.
KW - Distributed source generation
KW - Wyner common information
KW - channel resolvability
KW - exact common information
KW - letter typicality
UR - http://www.scopus.com/inward/record.url?scp=85015248370&partnerID=8YFLogxK
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U2 - 10.1109/ALLERTON.2016.7852255
DO - 10.1109/ALLERTON.2016.7852255
M3 - Conference contribution
AN - SCOPUS:85015248370
T3 - 54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016
SP - 370
EP - 377
BT - 54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016
Y2 - 27 September 2016 through 30 September 2016
ER -