TY - JOUR
T1 - Chain independence and common information
AU - Makarychev, Konstantin
AU - Makarychev, Yury
N1 - Funding Information:
Manuscript received July 30, 2001; revised February 28, 2012; accepted March 13, 2012. Date of publication July 10, 2012; date of current version July 10, 2012. Y. Makarychev was supported in part by the National Science Foundation Career Award CCF-1150062. K. Makarychev is with Microsoft Research, Redmond, WA 98052 USA (e-mail: [email protected]). Y. Makarychev is with the Toyota Technological Institute at Chicago, Chicago, IL 60637 USA (e-mail: [email protected]). Communicated by İ. E. Telatar, Associate Editor for Shannon Theory, and I. Kontoyiannis, Associate Editor At Large. Digital Object Identifier 10.1109/TIT.2012.2196022
PY - 2012
Y1 - 2012
N2 - We present a new proof of a celebrated result of Gcs and Krner that the common information is far less than the mutual information. Consider two sequences α{1},....,α n and β{1},...., β n of random variables, where pairs (α{1},β{1}),\ ldots, (α{n},β{n}) are independent and identically distributed. Gcs and Krner proved that it is not possible to extract common information from these two sequences unless the joint distribution matrix of random variables (α{i},β{i}) is a block matrix.
AB - We present a new proof of a celebrated result of Gcs and Krner that the common information is far less than the mutual information. Consider two sequences α{1},....,α n and β{1},...., β n of random variables, where pairs (α{1},β{1}),\ ldots, (α{n},β{n}) are independent and identically distributed. Gcs and Krner proved that it is not possible to extract common information from these two sequences unless the joint distribution matrix of random variables (α{i},β{i}) is a block matrix.
KW - Chain independent random variables
KW - common information
KW - rate region
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U2 - 10.1109/TIT.2012.2196022
DO - 10.1109/TIT.2012.2196022
M3 - Article
AN - SCOPUS:84863946676
SN - 0018-9448
VL - 58
SP - 5279
EP - 5286
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 8
M1 - 6200860
ER -