On Secrecy Capacity Scaling in Wireless Networks

• Published in: IEEE transactions on information theory 2012-05, Vol.58 (5), p.3000-3015
• Main Authors: Koyluoglu, O. O., Koksal, C. E., Gamal, H. E.
• Format: Article
• Language: English
• Subjects: Alignment; Ambiguity; Applied sciences; Capacity scaling; Coding theory; Electronic eavesdropping; Ergodic processes; Exact sciences and technology; Fading; information theoretic security; Information theory; Information, signal and communications theory; Interference; network information theory; Networks; Randomization; Receivers; Road transportation; Secret; secure throughput; Signal to noise ratio; Switching and signalling; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments); Transmitters; Wireless networks
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2012.2184692

This paper studies the achievable secure rate per source-destination pair in wireless networks. First, a path loss model is considered, where the legitimate and eavesdropper nodes are assumed to be placed according to Poisson point processes with intensities λ and λ e , respectively. It is shown that, as long as λ e /λ = o ((log n ) -2 ), almost all of the nodes achieve a perfectly secure rate of Ω(1/√ n ) for the extended and dense network models. Therefore, under these assumptions, securing the network does not entail a loss in the per-node throughput. The achievability argument is based on a novel multihop forwarding scheme where randomization is added in every hop to ensure maximal ambiguity at the eavesdropper(s). Second, an ergodic fading model with n source-destination pairs and n e eavesdroppers is considered. Employing the ergodic interference alignment scheme with an appropriate secrecy precoding, each user is shown to achieve a constant positive secret rate for sufficiently large n . Remarkably, the scheme does not require eavesdropper CSI (only the statistical knowledge is assumed) and the secure throughput per node increases as we add more legitimate users to the network in this setting. Finally, the effect of eavesdropper collusion on the performance of the proposed schemes is characterized.