Bounds on the communication rate needed to achieve SK capacity in the hypergraphical source model

Manuj Mukherjee; Chung Chan; Navin Kashyap; Qiaoqiao Zhou

doi:10.1109/ISIT.2016.7541750

Bounds on the communication rate needed to achieve SK capacity in the hypergraphical source model

Manuj Mukherjee, Chung Chan, Navin Kashyap, Qiaoqiao Zhou

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

9 Scopus citations

Abstract

In the multiterminal source model of Csiszár and Narayan, the communication complexity, R_SK, for secret key (SK) generation is the minimum rate of communication required to achieve SK capacity. An obvious upper bound to R_SK is given by R_CO, which is the minimum rate of communication required for omniscience. In this paper we derive a better upper bound to R_SK for the hypergraphical source model, which is a special instance of the multiterminal source model. The upper bound is based on the idea of fractional removal of hyperedges. It is further shown that this upper bound can be computed in polynomial time. We conjecture that our upper bound is tight. For the special case of a graphical source model, we also give an explicit lower bound on R_SK. This bound, however, is not tight, as demonstrated by a counterexample.

Original language	English
Title of host publication	Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2504-2508
Number of pages	5
ISBN (Electronic)	9781509018062
DOIs	https://doi.org/10.1109/ISIT.2016.7541750
State	Published - 10 Aug 2016
Externally published	Yes
Event	2016 IEEE International Symposium on Information Theory, ISIT 2016 - Barcelona, Spain Duration: 10 Jul 2016 → 15 Jul 2016

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2016-August
ISSN (Print)	2157-8095

Conference

Conference	2016 IEEE International Symposium on Information Theory, ISIT 2016
Country/Territory	Spain
City	Barcelona
Period	10/07/16 → 15/07/16

Bibliographical note

Publisher Copyright:
© 2016 IEEE.

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10.1109/ISIT.2016.7541750

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Mukherjee, M., Chan, C., Kashyap, N., & Zhou, Q. (2016). Bounds on the communication rate needed to achieve SK capacity in the hypergraphical source model. In Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory (pp. 2504-2508). Article 7541750 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2016-August). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2016.7541750

Mukherjee, Manuj ; Chan, Chung ; Kashyap, Navin et al. / Bounds on the communication rate needed to achieve SK capacity in the hypergraphical source model. Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory. Institute of Electrical and Electronics Engineers Inc., 2016. pp. 2504-2508 (IEEE International Symposium on Information Theory - Proceedings).

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abstract = "In the multiterminal source model of Csisz{\'a}r and Narayan, the communication complexity, RSK, for secret key (SK) generation is the minimum rate of communication required to achieve SK capacity. An obvious upper bound to RSK is given by RCO, which is the minimum rate of communication required for omniscience. In this paper we derive a better upper bound to RSK for the hypergraphical source model, which is a special instance of the multiterminal source model. The upper bound is based on the idea of fractional removal of hyperedges. It is further shown that this upper bound can be computed in polynomial time. We conjecture that our upper bound is tight. For the special case of a graphical source model, we also give an explicit lower bound on RSK. This bound, however, is not tight, as demonstrated by a counterexample.",

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Mukherjee, M, Chan, C, Kashyap, N & Zhou, Q 2016, Bounds on the communication rate needed to achieve SK capacity in the hypergraphical source model. in Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory., 7541750, IEEE International Symposium on Information Theory - Proceedings, vol. 2016-August, Institute of Electrical and Electronics Engineers Inc., pp. 2504-2508, 2016 IEEE International Symposium on Information Theory, ISIT 2016, Barcelona, Spain, 10/07/16. https://doi.org/10.1109/ISIT.2016.7541750

Bounds on the communication rate needed to achieve SK capacity in the hypergraphical source model. / Mukherjee, Manuj; Chan, Chung; Kashyap, Navin et al.
Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory. Institute of Electrical and Electronics Engineers Inc., 2016. p. 2504-2508 7541750 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2016-August).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Mukherjee M, Chan C, Kashyap N, Zhou Q. Bounds on the communication rate needed to achieve SK capacity in the hypergraphical source model. In Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory. Institute of Electrical and Electronics Engineers Inc. 2016. p. 2504-2508. 7541750. (IEEE International Symposium on Information Theory - Proceedings). doi: 10.1109/ISIT.2016.7541750

Bounds on the communication rate needed to achieve SK capacity in the hypergraphical source model

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