Secure degrees of freedom region of the Gaussian multiple access wiretap channel

摘要

[1] showed that the sum secure degrees of freedom (s.d.o.f.) of the K-user Gaussian multiple access (MAC) wiretap channel is K(K-1)/K(K-1);1. In this paper, we determine the entire s.d.o.f. region of the K-user Gaussian MAC wiretap channel. The converse follows from a middle step in the converse of [1]. The achievability follows from exploring the polytope structure of the converse region, determining its extreme points, and then showing that each extreme point can be achieved by an m-user MAC wiretap channel with K−m helpers, i.e., by setting K−m users' secure rates to zero and utilizing them as pure (structured) cooperative jammers. A byproduct of our result is that the sum s.d.o.f. is achieved only at one corner point of the s.d.o.f. region.