Secrecy Capacity Scaling in Large Cooperative Wireless Networks
This addresses security scaling for wireless networks, offering a theoretical foundation for zero-cost secure communication, though it is incremental by extending prior work to cooperative relaying.
The paper tackles the problem of secure communication in large wireless networks with eavesdroppers, showing that unbounded secure aggregate rate (zero-cost secure communication) is achievable under certain conditions on the numbers of legitimate nodes and eavesdroppers, even with collusion.
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.