Secure Degrees of Freedom of One-Hop Wireless Networks

Abstract

We study the secure degrees of freedom (d.o.f.) of one-hop wireless networks\nby considering four fundamental Gaussian network structures: wiretap channel,\nbroadcast channel with confidential messages, interference channel with\nconfidential messages, and multiple access wiretap channel. The secure d.o.f.\nof the canonical Gaussian wiretap channel with no helpers is zero. It has been\nknown that a strictly positive secure d.o.f. can be obtained in the Gaussian\nwiretap channel by using a helper which sends structured cooperative signals.\nWe show that the exact secure d.o.f. of the Gaussian wiretap channel with a\nhelper is 1/2. Our achievable scheme is based on real interference alignment\nand cooperative jamming, which renders the message signal and the cooperative\njamming signal separable at the legitimate receiver, but aligns them perfectly\nat the eavesdropper preventing any reliable decoding of the message signal. Our\nconverse is based on two key lemmas. The first lemma quantifies the secrecy\npenalty by showing that the net effect of an eavesdropper on the system is that\nit eliminates one of the independent channel inputs. The second lemma\nquantifies the role of a helper by developing a direct relationship between the\ncooperative jamming signal of a helper and the message rate. We extend this\nresult to the case of M helpers, and show that the exact secure d.o.f. in this\ncase is M/(M+1). We then generalize this approach to more general network\nstructures with multiple messages. We show that the sum secure d.o.f. of the\nGaussian broadcast channel with confidential messages and M helpers is 1, the\nsum secure d.o.f. of the two-user interference channel with confidential\nmessages is 2/3, the sum secure d.o.f. of the two-user interference channel\nwith confidential messages and M helpers is 1, and the sum secure d.o.f. of the\nK-user multiple access wiretap channel is K(K-1)/(K(K-1)+1).\n