Secure Degrees of Freedom of One-hop Wireless Networks
arXiv:1209.5370 · doi:10.1109/TIT.2014.2315801
Abstract
We study the secure degrees of freedom (d.o.f.) of one-hop wireless networks by considering four fundamental Gaussian network structures: wiretap channel, broadcast channel with confidential messages, interference channel with confidential messages, and multiple access wiretap channel. The secure d.o.f. of the canonical Gaussian wiretap channel with no helpers is zero. It has been known that a strictly positive secure d.o.f. can be obtained in the Gaussian wiretap channel by using a helper which sends structured cooperative signals. We show that the exact secure d.o.f. of the Gaussian wiretap channel with a helper is 1/2. Our achievable scheme is based on real interference alignment and cooperative jamming, which renders the message signal and the cooperative jamming signal separable at the legitimate receiver, but aligns them perfectly at the eavesdropper preventing any reliable decoding of the message signal. Our converse is based on two key lemmas. The first lemma quantifies the secrecy penalty by showing that the net effect of an eavesdropper on the system is that it eliminates one of the independent channel inputs. The second lemma quantifies the role of a helper by developing a direct relationship between the cooperative jamming signal of a helper and the message rate. We extend this result to the case of M helpers, and show that the exact secure d.o.f. in this case is M/(M+1). We then generalize this approach to more general network structures with multiple messages. We show that the sum secure d.o.f. of the Gaussian broadcast channel with confidential messages and M helpers is 1, the sum secure d.o.f. of the two-user interference channel with confidential messages is 2/3, the sum secure d.o.f. of the two-user interference channel with confidential messages and M helpers is 1, and the sum secure d.o.f. of the K-user multiple access wiretap channel is K(K-1)/(K(K-1)+1).
Submitted to IEEE Transactions on Information Theory, Sept. 2012
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- Physical Layer Security-Aware Routing and Performance Tradeoffs in Ad Hoc Networks
- Secure Degrees of Freedom Regions of Multiple Access and Interference Channels: The Polytope Structure
- A Joint Typicality Approach to Algebraic Network Information Theory
- MIMO Wiretap Channel under Receiver Side Power Constraints with Applications to Wireless Power Transfer and Cognitive Radio
- Energy-Efficient Secrecy in Wireless Networks Based on Random Jamming
- Secure Degrees of Freedom of the Gaussian Wiretap Channel with Helpers and No Eavesdropper CSI: Blind Cooperative Jamming
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- Adding a Helper Can Totally Remove the Secrecy Constraints in Interference Channel
- Blind MIMOME Wiretap Channel with Delayed CSIT
- Secure Degrees of Freedom of Multi-user Networks: One-Time-Pads in the Air via Alignment
- On the Optimality of Secure Communication Without Using Cooperative Jamming
- On the Secrecy Capacity of a MIMO Gaussian Wiretap Channel with a Cooperative Jammer
- Compute-and-Forward Can Buy Secrecy Cheap
- Optimal Secure GDoF of Symmetric Gaussian Wiretap Channel with a Helper
- Secure Communication over Interference Channel: To Jam or Not to Jam?
- Towards an Algebraic Network Information Theory: Simultaneous Joint Typicality Decoding
- On the Deterministic Sum-Capacity of the Multiple Access Wiretap Channel
- Towards Scalable Security in Interference Channels With Arbitrary Number of Users
- Preserving Confidentiality in The Gaussian Broadcast Channel Using Compute-and-Forward