Secret-Key Agreement with Public Discussion over Multi-Antenna Transmitters with Amplitude Constraints

Zouheir Rezki, Mohamed-Slim Alouini

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 R n is not an open subset of C n .
Original languageEnglish (US)
Title of host publication2017 IEEE International Symposium on Information Theory (ISIT)
PublisherIEEE
Pages1534-1538
Number of pages5
ISBN (Print)9781509040964
DOIs
StatePublished - 2017

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