TY - GEN

T1 - Dispersion Bound for the Wyner-Ahlswede-Körner Network via Reverse Hypercontractivity on Types

AU - Liu, Jingbo

N1 - Funding Information:
The author thanks Prof. Ramon van Handel for his generous scholarship and many inspiring discussions, including supplying reference [11] and the composition argument in (39), and Professor Sergio Verdu for his unceasing support and guidance on research along this line. This work is supported by NSF grants CCF-1350595, CCF-1016625, CCF-0939370, and DMS-1148711, by ARO Grants W911NF-15-1-0479 and W911NF-14-1-0094, and AFOSR FA9550-15-1-0180, and by the Center for Science of Information.
Funding Information:
VI. ACKNOWLEDGEMENT The author thanks Prof. Ramon van Handel for his generous scholarship and many inspiring discussions, including supplying reference [11] and the composition argument in (39), and Professor Sergio Verdú for his unceasing support and guidance on research along this line. This work is supported by NSF grants CCF-1350595, CCF-1016625, CCF-0939370, and DMS-1148711, by ARO Grants W911NF-15-1-0479 and W911NF-14-1-0094, and AFOSR FA9550-15-1-0180, and by the Center for Science of Information.

PY - 2018/8/15

Y1 - 2018/8/15

N2 - Using the functional-entropic duality and the reverse hypercontractivity of the transposition semigroup, we lower bound the error probability for each joint type in the Wyner-Ahlswede-Korner problem. Then by averaging the error probability over types, we lower bound the c-dispersion (which characterizes the second-order behavior of the weighted sum of the rates of the two compressors when a nonvanishing error probability is small) as the variance of the gradient of inf- P- Uvert X cH(Yvert U)+ I(U;X) with respect to Q- XY, the per-letter side information and source distribution. On the other hand, using the method of types we derive a new upper bound on the c-dispersion, which improves the existing upper bounds but has a gap to the aforementioned lower bound.

AB - Using the functional-entropic duality and the reverse hypercontractivity of the transposition semigroup, we lower bound the error probability for each joint type in the Wyner-Ahlswede-Korner problem. Then by averaging the error probability over types, we lower bound the c-dispersion (which characterizes the second-order behavior of the weighted sum of the rates of the two compressors when a nonvanishing error probability is small) as the variance of the gradient of inf- P- Uvert X cH(Yvert U)+ I(U;X) with respect to Q- XY, the per-letter side information and source distribution. On the other hand, using the method of types we derive a new upper bound on the c-dispersion, which improves the existing upper bounds but has a gap to the aforementioned lower bound.

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U2 - 10.1109/ISIT.2018.8437705

DO - 10.1109/ISIT.2018.8437705

M3 - Conference contribution

AN - SCOPUS:85052487162

SN - 9781538647806

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 1854

EP - 1858

BT - 2018 IEEE International Symposium on Information Theory, ISIT 2018

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2018 IEEE International Symposium on Information Theory, ISIT 2018

Y2 - 17 June 2018 through 22 June 2018

ER -