TY - GEN
T1 - Key generation with limited interaction
AU - Liu, Jingbo
AU - Cuff, Paul
AU - Verdu, Sergio
N1 - Publisher Copyright:
© 2016 IEEE.
PY - 2016/8/10
Y1 - 2016/8/10
N2 - The basic two-terminal key generation model is considered, where the communication between the terminals is limited. We introduce a preorder relation on the set of joint distributions called XY-absolute continuity, and we reduce the multi-letter characterization of the key-communication tradeoff to the evaluation of the XY-concave envelope of a functional. For small communication rates, the key bits per interaction bit is expressed with a 'symmetrical strong data processing constant'. Using hypercontractivity and Rényi divergence, we also prove a computationally friendly strong converse bound for the common randomness bits per interaction bit in terms of the supremum of the maximal correlation coefficient over a set of distributions, which is tight for binary symmetric sources. Regarding the other extreme case, a new characterization of the minimum interaction for achieving the maximum key rate (MIMK) is given, and is used to resolve a conjecture by Tyagi [1] about the MIMK for binary sources.
AB - The basic two-terminal key generation model is considered, where the communication between the terminals is limited. We introduce a preorder relation on the set of joint distributions called XY-absolute continuity, and we reduce the multi-letter characterization of the key-communication tradeoff to the evaluation of the XY-concave envelope of a functional. For small communication rates, the key bits per interaction bit is expressed with a 'symmetrical strong data processing constant'. Using hypercontractivity and Rényi divergence, we also prove a computationally friendly strong converse bound for the common randomness bits per interaction bit in terms of the supremum of the maximal correlation coefficient over a set of distributions, which is tight for binary symmetric sources. Regarding the other extreme case, a new characterization of the minimum interaction for achieving the maximum key rate (MIMK) is given, and is used to resolve a conjecture by Tyagi [1] about the MIMK for binary sources.
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U2 - 10.1109/ISIT.2016.7541833
DO - 10.1109/ISIT.2016.7541833
M3 - Conference contribution
AN - SCOPUS:84985905261
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 2918
EP - 2922
BT - Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2016 IEEE International Symposium on Information Theory, ISIT 2016
Y2 - 10 July 2016 through 15 July 2016
ER -