@article{7e47da0f953941a1b7457c25a5602e73,
title = "The Secrecy Capacity of Cost-Constrained Wiretap Channels",
abstract = "In many information-theoretic channel coding problems, adding an input cost constraint to the operational setup amounts to restricting the optimization domain in the capacity formula. This paper shows that, in contrast to common belief, such a simple modification does not hold for the cost-constrained (CC) wiretap channel (WTC). The secrecy-capacity of the discrete memoryless (DM) WTC without cost constraints is described by a single auxiliary random variable. For the CC DM-WTC, however, we show that two auxiliaries are necessary to achieve capacity. Specifically, we first derive the secrecy-capacity formula, proving the direct part via superposition coding. Then, we provide an example of a CC DM-WTC whose secrecy-capacity cannot be achieved using a single auxiliary. This establishes the fundamental role of superposition coding over CC WTCs.",
keywords = "Cost constraint, physical-layer security, secrecy-capacity, superposition coding, wiretap channel",
author = "Sreejith Sreekumar and Alexander Bunin and Ziv Goldfeld and Permuter, {Haim H.} and Shlomo Shamai",
note = "Funding Information: Manuscript received April 8, 2020; revised November 5, 2020; accepted November 13, 2020. Date of publication November 23, 2020; date of current version February 17, 2021. The work of Sreejith Sreekumar was supported by the Transdisciplinary Research in Principles of Data Science (TRIPODS) Center for Data Science National Science Foundation under Grant CCF-1740822. The work of Ziv Goldfeld was supported in part by the National Science Foundation under Grant CCF-1947801 and in part by the 2020 IBM Academic Award. The work of Haim H. Permuter was supported in part by the WIN Consortium via the Israel Ministry of Economy and Science, in part by the Deutsche Forschungsgemeinschaft (DFG) via the Deutsch-lsraelische Projektkooperation (DIP), in part by the Israel Science Foundation, and in part by the Cyber Center at Ben-Gurion University of the Negev. The work of Shlomo Shamai was supported in part by the WIN Consortium via the Israel Ministry of Economy and Science and in part by the European Union{\textquoteright}s Horizon 2020 Research and Innovation Programme under Grant 694630. (Corresponding author: Sreejith Sreekumar.) Sreejith Sreekumar and Ziv Goldfeld are with the School of Electrical and Computer Engineering, Cornell University, Ithaca, NY 14850 USA (e-mail: sreejithsreekumar@cornell.edu; goldfeld@cornell.edu). Publisher Copyright: {\textcopyright} 1963-2012 IEEE.",
year = "2021",
month = mar,
day = "1",
doi = "10.1109/TIT.2020.3039916",
language = "English",
volume = "67",
pages = "1433--1445",
journal = "IEEE Transactions on Information Theory",
issn = "0018-9448",
publisher = "Institute of Electrical and Electronics Engineers",
number = "3",
}