TY - GEN

T1 - Wyners common information for continuous random variables - A lossy source coding interpretation

AU - Xu, Ge

AU - Liu, Wei

AU - Chen, Biao

PY - 2011

Y1 - 2011

N2 - Wyners common information can be easily generalized for continuous random variables. We provide an operational meaning for such generalization using the Gray-Wyner network with lossy source coding. Specifically, a Gray-Wyner network consists of one encoder and two decoders. A sequence of independent copies of a pair of random variables (X, Y) ∼ p(x, y) is encoded into three messages, one of them is a common input to both decoders. The two decoders attempt to reconstruct the two sequences respectively subject to individual distortion constraints. We show that Wyners common information equals the smallest common message rate when the total rate is arbitrarily close to the rate-distortion function with joint decoding. A surprising observation is that such equality holds independent of the values of distortion constraints as long as the distortions are less than certain thresholds. An interpretation for such thresholds is given for the symmetric case.

AB - Wyners common information can be easily generalized for continuous random variables. We provide an operational meaning for such generalization using the Gray-Wyner network with lossy source coding. Specifically, a Gray-Wyner network consists of one encoder and two decoders. A sequence of independent copies of a pair of random variables (X, Y) ∼ p(x, y) is encoded into three messages, one of them is a common input to both decoders. The two decoders attempt to reconstruct the two sequences respectively subject to individual distortion constraints. We show that Wyners common information equals the smallest common message rate when the total rate is arbitrarily close to the rate-distortion function with joint decoding. A surprising observation is that such equality holds independent of the values of distortion constraints as long as the distortions are less than certain thresholds. An interpretation for such thresholds is given for the symmetric case.

UR - http://www.scopus.com/inward/record.url?scp=79957859070&partnerID=8YFLogxK

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U2 - 10.1109/CISS.2011.5766249

DO - 10.1109/CISS.2011.5766249

M3 - Conference contribution

AN - SCOPUS:79957859070

SN - 9781424498475

T3 - 2011 45th Annual Conference on Information Sciences and Systems, CISS 2011

BT - 2011 45th Annual Conference on Information Sciences and Systems, CISS 2011

T2 - 2011 45th Annual Conference on Information Sciences and Systems, CISS 2011

Y2 - 23 March 2011 through 25 March 2011

ER -