Secret-Key Agreement with Public Discussion over Multi-Antenna Transmitters with Amplitude Constraints
Type
Conference PaperKAUST Department
Communication Theory LabComputer, Electrical and Mathematical Science and Engineering (CEMSE) Division
Electrical and Computer Engineering Program
Date
2017Permanent link to this record
http://hdl.handle.net/10754/670695
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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 .Citation
Rezki, Z., & Alouini, M.-S. (2017). Secret-key agreement with public discussion over multi-antenna transmitters with amplitude constraints. 2017 IEEE International Symposium on Information Theory (ISIT). doi:10.1109/isit.2017.8006786Conference/Event name
2017 IEEE International Symposium on Information Theory (ISIT)Additional Links
https://ieeexplore.ieee.org/document/8006786ae974a485f413a2113503eed53cd6c53
10.1109/ISIT.2017.8006786