TY - GEN
T1 - The common information of N dependent random variables
AU - Wei, Liu
AU - Ge, Xu
AU - Biao, Chen
PY - 2010
Y1 - 2010
N2 - This paper generalizes Wyner's definition of common information of a pair of random variables to that of N random variables. We prove coding theorems that show the same operational meanings for the common information of two random variables generalize to that of N random variables. As a byproduct of our proof, we show that the Gray-Wyner source coding network can be generalized to N source squences with N decoders. We also establish a monotone property of Wyner's common information which is in contrast to other notions of the common information, specifically Shannon's mutual information and Gács and Körner's common randomness. Examples about the computation of Wyner's common information of N random variables are also given.
AB - This paper generalizes Wyner's definition of common information of a pair of random variables to that of N random variables. We prove coding theorems that show the same operational meanings for the common information of two random variables generalize to that of N random variables. As a byproduct of our proof, we show that the Gray-Wyner source coding network can be generalized to N source squences with N decoders. We also establish a monotone property of Wyner's common information which is in contrast to other notions of the common information, specifically Shannon's mutual information and Gács and Körner's common randomness. Examples about the computation of Wyner's common information of N random variables are also given.
UR - http://www.scopus.com/inward/record.url?scp=79952377927&partnerID=8YFLogxK
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U2 - 10.1109/ALLERTON.2010.5706995
DO - 10.1109/ALLERTON.2010.5706995
M3 - Conference contribution
AN - SCOPUS:79952377927
SN - 9781424482146
T3 - 2010 48th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2010
SP - 836
EP - 843
BT - 2010 48th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2010
T2 - 48th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2010
Y2 - 29 September 2010 through 1 October 2010
ER -