TY - GEN
T1 - Secret-key agreement with public discussion over multi-antenna transmitters with amplitude constraints
AU - Rezki, Zouheir
AU - Alouini, Mohamed Slim
N1 - Publisher Copyright:
© 2017 IEEE.
PY - 2017/8/9
Y1 - 2017/8/9
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.
KW - Discrete input
KW - Information-theoretic security
KW - Karush-Kuhn-Tucker (KKT) conditions
KW - Secret-key agreement
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
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 1534
EP - 1538
BT - 2017 IEEE International Symposium on Information Theory, ISIT 2017
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2017 IEEE International Symposium on Information Theory, ISIT 2017
Y2 - 25 June 2017 through 30 June 2017
ER -