TY - GEN

T1 - Secret-Key Agreement with Public Discussion over Multi-Antenna Transmitters with Amplitude Constraints

AU - Rezki, Zouheir

AU - Alouini, Mohamed-Slim

N1 - KAUST Repository Item: Exported on 2021-08-21

PY - 2017

Y1 - 2017

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 R n is not an open subset of C n .

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 R n is not an open subset of C n .

UR - http://hdl.handle.net/10754/670695

UR - https://ieeexplore.ieee.org/document/8006786

UR - http://www.scopus.com/inward/record.url?scp=85034048081&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2017.8006786

DO - 10.1109/ISIT.2017.8006786

M3 - Conference contribution

AN - SCOPUS:85034048081

SN - 9781509040964

SP - 1534

EP - 1538

BT - 2017 IEEE International Symposium on Information Theory (ISIT)

PB - IEEE

ER -