Secret-key agreement with public discussion over multi-antenna transmitters with amplitude constraints

Zouheir Rezki; Mohamed Slim Alouini

doi:10.1109/ISIT.2017.8006786

Secret-key agreement with public discussion over multi-antenna transmitters with amplitude constraints

Zouheir Rezki, Mohamed Slim Alouini

Electrical and Computer Engineering

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

8 Scopus citations

Abstract

We consider secret-key agreement with public discussion over a multiple-input single output (MISO) Gaussian channel with an amplitude constraint. We prove that the capacity is achieved by a discrete input, i.e., an input whose support is sparse. The proof follows from the concavity of the conditional mutual information in terms of the input distribution and hence the Karush-Kuhn-Tucker (KKT) condition provides a necessary and sufficient condition for optimality. Then, a contradiction argument that rules out the non-sparsity of any optimal input's support is utilized. The latter approach is essential to apply the identity theorem in a multidimensional setting as Rⁿ is not an open subset of Cⁿ.

Original language	English (US)
Title of host publication	2017 IEEE International Symposium on Information Theory, ISIT 2017
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1534-1538
Number of pages	5
ISBN (Electronic)	9781509040964
DOIs	https://doi.org/10.1109/ISIT.2017.8006786
State	Published - Aug 9 2017
Event	2017 IEEE International Symposium on Information Theory, ISIT 2017 - Aachen, Germany Duration: Jun 25 2017 → Jun 30 2017

Publication series

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

Conference

Conference	2017 IEEE International Symposium on Information Theory, ISIT 2017
Country/Territory	Germany
City	Aachen
Period	06/25/17 → 06/30/17

Bibliographical note

Publisher Copyright:
© 2017 IEEE.

Keywords

Discrete input
Information-theoretic security
Karush-Kuhn-Tucker (KKT) conditions
Secret-key agreement

ASJC Scopus subject areas

Theoretical Computer Science
Information Systems
Applied Mathematics
Modeling and Simulation

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10.1109/ISIT.2017.8006786

Cite this

Rezki, Z., & Alouini, M. S. (2017). Secret-key agreement with public discussion over multi-antenna transmitters with amplitude constraints. In 2017 IEEE International Symposium on Information Theory, ISIT 2017 (pp. 1534-1538). Article 8006786 (IEEE International Symposium on Information Theory - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2017.8006786

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abstract = "We consider secret-key agreement with public discussion over a multiple-input single output (MISO) Gaussian channel with an amplitude constraint. We prove that the capacity is achieved by a discrete input, i.e., an input whose support is sparse. The proof follows from the concavity of the conditional mutual information in terms of the input distribution and hence the Karush-Kuhn-Tucker (KKT) condition provides a necessary and sufficient condition for optimality. Then, a contradiction argument that rules out the non-sparsity of any optimal input's support is utilized. The latter approach is essential to apply the identity theorem in a multidimensional setting as Rn is not an open subset of Cn.",

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Rezki, Z & Alouini, MS 2017, Secret-key agreement with public discussion over multi-antenna transmitters with amplitude constraints. in 2017 IEEE International Symposium on Information Theory, ISIT 2017., 8006786, IEEE International Symposium on Information Theory - Proceedings, Institute of Electrical and Electronics Engineers Inc., pp. 1534-1538, 2017 IEEE International Symposium on Information Theory, ISIT 2017, Aachen, Germany, 06/25/17. https://doi.org/10.1109/ISIT.2017.8006786

Secret-key agreement with public discussion over multi-antenna transmitters with amplitude constraints. / Rezki, Zouheir; Alouini, Mohamed Slim.
2017 IEEE International Symposium on Information Theory, ISIT 2017. Institute of Electrical and Electronics Engineers Inc., 2017. p. 1534-1538 8006786 (IEEE International Symposium on Information Theory - Proceedings).

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

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N2 - We consider secret-key agreement with public discussion over a multiple-input single output (MISO) Gaussian channel with an amplitude constraint. We prove that the capacity is achieved by a discrete input, i.e., an input whose support is sparse. The proof follows from the concavity of the conditional mutual information in terms of the input distribution and hence the Karush-Kuhn-Tucker (KKT) condition provides a necessary and sufficient condition for optimality. Then, a contradiction argument that rules out the non-sparsity of any optimal input's support is utilized. The latter approach is essential to apply the identity theorem in a multidimensional setting as Rn is not an open subset of Cn.

AB - We consider secret-key agreement with public discussion over a multiple-input single output (MISO) Gaussian channel with an amplitude constraint. We prove that the capacity is achieved by a discrete input, i.e., an input whose support is sparse. The proof follows from the concavity of the conditional mutual information in terms of the input distribution and hence the Karush-Kuhn-Tucker (KKT) condition provides a necessary and sufficient condition for optimality. Then, a contradiction argument that rules out the non-sparsity of any optimal input's support is utilized. The latter approach is essential to apply the identity theorem in a multidimensional setting as Rn is not an open subset of Cn.

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Rezki Z, Alouini MS. Secret-key agreement with public discussion over multi-antenna transmitters with amplitude constraints. In 2017 IEEE International Symposium on Information Theory, ISIT 2017. Institute of Electrical and Electronics Engineers Inc. 2017. p. 1534-1538. 8006786. (IEEE International Symposium on Information Theory - Proceedings). doi: 10.1109/ISIT.2017.8006786

Secret-key agreement with public discussion over multi-antenna transmitters with amplitude constraints

Abstract

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Bibliographical note

Keywords

ASJC Scopus subject areas

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