Opportunistic Secrecy with a Strict Delay Constraint

arXiv:0907.3341v1 [cs.IT] 20 Jul 2009 1 Opportunistic Secrecy with a Strict Delay Constraint Karim Khalil, O. Ozan Koyluoglu, Hesham El Gamal, and Moustafa Youssef Abstract We investigate the delay limited secrecy capacity of the flat fading channel under two different assumptions on the available transmitter channel state information (CSI). The first scenario assumes perfect prior knowledge of both the main and eavesdropper channel gains. Here, upper and lower bounds on the delay limited secrecy capacity are derived, and shown to be tight in the high signal-to-noise ratio (SNR) regime. In the second scenario, only the main channel CSI is assumed to be available at the transmitter where, remarkably, we establish the achievability of a non-zero delay-limited secure rate, for a wide class of channel distributions, with a high probability. In the two cases, our achievability arguments are based on a novel two-stage key-sharing approach that overcomes the secrecy outage phenomenon observed in earlier works. I. INTRODUCTION Many wireless applications are limited by different forms of delay constraints. These applications range from the most basic voice communication to the more demanding multimedia streaming. However, due to its broadcast nature, the wireless channel is vulnerable to eavesdropping and other security threats. Therefore, techniques that satisfy both the delay limitation and the confidentiality requirement are of definite interest. This motivates our analysis of the fundamental (information theoretic) limits of secure communication over fading channels subject to strict deadlines. Recent works on information theoretic security have been largely inspired by the wire-tap channel model of Wyner [1]. In this seminal work, Wyner established the achievability of non-zero secrecy capacity when the wiretapper channel is a degraded version of the main one, by exploiting the noise to create an advantage for the legitimate receiver. More recently, the effect of fading on the secrecy capacity was studied in [2] in the ergodic setting. The main insight offered by this work is the achievability of a non-zero secrecy capacity, by opportunistically This work is submitted to the IEEE Transactions on Information Theory. Karim Khalil and Moustafa Youssef are with the Wireless Intelligent Networks Center (WINC), Nile University, Cairo, Egypt. Email: {kareem.makarem,mayoussef}@nileu.edu.eg. O. Ozan Koyluoglu and Hesham El Gamal are with the Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH 43210 USA. Email: {koyluogo,helgamal}@ece.osu.edu. This work is supported in part by an NPRP grant from the QNRF, the Egyptian NTRA, and the National Science Foundation (NSF). The material in this paper was presented in part at the IEEE International Symposium on Information Theory, Seoul, Korea in July 2009. October 30, 2018 DRAFT 2 exploiting the multi-path channel fluctuations, even when the eavesdropper channel is better than the legitimate one on the average. On the other side, delay limited transmission over fading channels has been well studied in different network settings and using various traffic models. For example, in [3], the delay limited capacity notion was introduced and the optimal power control policies were characterized in several interesting scenarios. In [4], the strict delay limitation of [3] was relaxed by allowing for buffering the packets at the transmitter. In this setup, the asymptotic behavior of the power-delay trade-off curve was characterized yielding valuable insights on the structure of the optimal resource allocation strategies [4]. More recently, the scheduling problem of data transmission over a finite delay horizon assuming perfect CSI was considered in [5]. Our work can be viewed as a generalization of [3] whereby a secrecy constraint is imposed on the problem. The delay limited transmission of secure data over fading channels was considered previously in [6]. In that work, the authors attempted to send the secure information using binning techniques inspired by the wiretap channel results. The drawback of this approach is that it fails to secure the information in the particular instants where the eavesdropper channel gain is larger than that of the main channel. This results in the so-called secrecy outage phenomenon (as defined in [6]). Unfortunately, in the delay limited setting, the secrecy outage can not be made to vanish by increasing the transmission power, since it does not offer a relative advantage to the legitimate receiver, leading to the conclusion that the delay limited secure rate achieved by this approach is equal to zero for most channel distributions of interest [6]. This obstacle is overcome by our two-stage approach. Here, the delay sensitive data is secured via Vernam’s one time pad approach [7] (see also [8]) using a private key, which was shared secretly by the two legitimate nodes during previous transmissions. Since the key packets are

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