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

UR - http://www.scopus.com/inward/citedby.url?scp=79952377927&partnerID=8YFLogxK

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 -