On Secrecy Capacity Scaling in Wireless Networks (0908.0898v2)

Abstract: This work 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 $\lambda$ and $\lambda_e$, respectively. It is shown that, as long as $\lambda_e/\lambda=o((\log n)^{-2})$, almost all of the nodes achieve a perfectly secure rate of $\Omega(\frac{1}{\sqrt{n}})$ 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 multi-hop forwarding scheme where randomization is added in every hop to ensure maximal ambiguity at the eavesdropper(s). Secondly, 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 pre-coding, 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.

• The paper demonstrates that secure communication can achieve a per-node throughput of Ω(1/√n) in path loss models using multi-hop forwarding with randomization.
• The paper employs ergodic interference alignment and secrecy pre-coding to secure a constant positive rate even without precise eavesdropper channel state information.
• The paper shows that achievable secrecy rates hold under eavesdropper collusion when the density of eavesdroppers is sufficiently constrained.

On Secrecy Capacity Scaling in Wireless Networks

The paper "On Secrecy Capacity Scaling in Wireless Networks" investigates the achievable secure communication rates between source-destination pairs in wireless networks subject to eavesdropping. The authors, O. Ozan Koyluoglu, C. Emre Koksal, and Hesham El Gamal, present an in-depth paper of two fundamental channel models: the static path loss model and the ergodic fading model. This work focuses on understanding how secrecy constraints can impact the scalability and capacity of wireless networks.

Key Contributions

1. Secrecy in Path Loss Models: The paper presents an analysis of secure communications in wireless networks characterized by a path loss model. Nodes in the network, including both legitimate users and eavesdroppers, are distributed according to Poisson point processes. The network's capacity is evaluated under the assumption that the density of eavesdroppers is low relative to legitimate users, specifically as $\lambda_e/\lambda=o((\log n)^{-2})$. They employ a multi-hop forwarding scheme incorporating randomization at each hop, ensuring that eavesdroppers receive maximally ambiguous signals. The findings suggest that achieving a secure rate does not compromise the per-node throughput, which is $\Omega(1/\sqrt{n})$ for both extended and dense network scenarios.
2. Ergodic Fading Models and Interference Alignment: For networks influenced by ergodic fading models, the paper uses ergodic interference alignment coupled with secrecy pre-coding to guarantee a secure communication rate. This approach demonstrates that even without detailed eavesdropper CSI, the strategy can secure a constant positive secret rate. For sufficiently large networks, the secure throughput per node benefits from an increase in legitimate users. This model also explores the impact of eavesdropper collusion and presents bounds on achieveable rates even in such adverse conditions.
3. Collusion and Dependence on Eavesdropper Distribution: The paper extends its analysis to scenarios where eavesdroppers may collude, showing that established secrecy rates can still be achieved within certain constraints on eavesdropper density. In extended networks with path loss models, the results hold if the eavesdropper intensity is reduced slightly beyond $\lambda_e=O((\log n)^{-2})$.

Implications and Future Work

The authors have delivered a comprehensive framework for analyzing the secrecy capacity of wireless networks in the face of eavesdropping. The identifying feature of this work lies in its demonstration that secrecy constraints do not inherently limit the scaling of network capacity, provided that appropriate network strategies, such as those involving percolation theory and interference alignment, are employed. The theoretical contribution spans both practical application, in terms of realizing secure communications without additional overhead, and foundational understanding of network behavior under security threats.

Future research directions could explore optimizing the trade-offs between system complexity and achievable secret rates. Additionally, a deeper examination into practical implementations of the proposed multi-hop and interference alignment strategies in real-world network deployments could enhance the current theoretical models. Given the assumptions regarding node distributions and the models used for collusion handling, further work could investigate different node distributions and dynamic collusion scenarios to extend the applicability of the findings.