TY - GEN
T1 - Dispersion Bound for the Wyner-Ahlswede-Körner Network via Reverse Hypercontractivity on Types
AU - Liu, Jingbo
N1 - 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 Verd\u00FA 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.
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.
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.
UR - https://www.scopus.com/pages/publications/85052487162
UR - https://www.scopus.com/pages/publications/85052487162#tab=citedBy
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 -