On the Secure Degrees-of-Freedom of Partially Connected Networks with no CSIT

In this work, we focus on the partially connected interference network with confidential messages, and study the secure degrees of freedom with no channel state information at the transmitters (CSIT). Prior works on fully connected interference networks with full CSIT have shown that the secure degrees of freedom scales linearly with the number of users. With no CSIT, however, the secure degrees of freedom of fully connected networks collapses to zero. In this work, we show that partial connectivity, a widely prevalent property of wireless networks, can be leveraged to provide secrecy even with no CSIT. We present a systematic approach to first understand the feasibility of secure communication in a partially connected network and develop achievable schemes for a class of regular partially connected networks. Finally, we also provide novel information theoretic outer bounds on the secure degrees of freedom for this class of regular partially connected networks, and approximately characterize the secure degrees of freedom.