Secrecy Capacity Scaling in Large Cooperative Wireless Networks

Abstract

We investigate large wireless networks subject to security constraints. In contrast to point-to-point, interference-limited communications considered in prior works, we propose active cooperative relaying-based schemes. We consider a network with $n_{l}$ legitimate nodes, $n_{e}$ eavesdroppers, and path loss exponent $\alpha \geq 2$ . As long as $n_{e}^{2}\big (\log (n_{e})\big )^{\gamma }=o(n_{l})$ , for some positive $\gamma $ , we show that one can obtain unbounded secure aggregate rate. This means zero-cost secure communication, given fixed total power constraint for the entire network. We achieve this result through: 1) the source using Wyner randomized encoder and a serial (multi-stage) block Markov scheme, to cooperate with the relays and 2) the relays acting as a virtual multi-antenna to apply beamforming against the eavesdroppers. Our simpler parallel (two-stage) relaying scheme can achieve the same unbounded secure aggregate rate when $n_{e}^{\alpha /{2}+1}\big (\log (n_{e})\big )^{\gamma +\delta ({\alpha }/{2}+1)}=o(n_{l})$ holds, for some positive $\gamma ,\delta $ . Finally, we study the improvement (to the detriment of legitimate nodes) that the eavesdroppers achieve in terms of the information leakage rate in a large cooperative network in the case of collusion . We show that again the zero-cost secure communication is possible, if $n_{e}^{(2+{2}/{\alpha })}\big (\log n_{e}\big )^{\gamma }=o(n_{l})$ holds, for some positive $\gamma $ ; that is, in the case of collusion slightly fewer eavesdroppers can be tolerated compared with the non-colluding case.