Scaling laws for secrecy capacity in 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 and n_e eavesdroppers, and path loss exponent α ≥ 2. As long as n_e²(log(n_e))^γ = o(n_l) holds for some positive γ, we show one can obtain unbounded secure aggregate rate. This means zero-cost secure communication, given a fixed total power constraint for the entire network. We achieve this result with (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^{α/2 + 1} (log(n_e))^{γ+δ(α/2+1)} = o(n_l) holds, for some positive γ, δ.