Secrecy Capacity Scaling in Large Cooperative Wireless Networks

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 $α\geq 2$. As long as $n_e^2(\log(n_e))^γ=o(n_l)$, for some positive $γ$, we show 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 (i) the source using Wyner randomized encoder and a serial (multi-stage) block Markov scheme, to cooperate with the relays and (ii) 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 $n_e^{\fracα{2}+1}(\log(n_e))^{γ+δ(\fracα{2}+1)}=o(n_l)$ holds, for some positive $γ,δ$. Finally, we study the improvement (to the detriment of legitimate nodes) the eavesdroppers achieve in terms of the information leakage rate in a large cooperative network in case of collusion. We show that again the zero-cost secure communication is possible, if $n_e^{(2+\frac{2}α)}(\log n_e)^γ=o(n_l)$ holds, for some positive $γ$; i.e., in case of collusion slightly fewer eavesdroppers can be tolerated compared to the non-colluding case.

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