Secure Degrees of Freedom of One-hop Wireless Networks
This work addresses secure communication in wireless networks, providing exact theoretical bounds for multiple fundamental network models, which is incremental but important for information theory and network security.
The paper tackles the problem of secure communication in one-hop wireless networks by deriving exact secure degrees of freedom for various Gaussian network structures, such as the wiretap channel with a helper achieving 1/2 and with M helpers achieving M/(M+1), and other configurations like the broadcast channel with confidential messages achieving sum secure d.o.f. of 1.
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).