On Interplay Between Network Topology and Alternating CSIT for Multi-Receiver Wiretap Channel

Abstract

We study the problem of secure transmission over a Gaussian multi-input single-output (MISO) two receiver channel with an external eavesdropper under the assumption that links connecting the transmitter to three receivers may have unequal strength statistically. In addition to this, the state of the channel to each receiver is conveyed either perfectly (${P}$) or with delay (${D}$) to the transmitter. Let $S_{1}, S_{2}$, and ${S}3$bethe channel state information at the transmitter (CSIT) of user 1, user 2, and eavesdropper, respectively. The overall CSIT can then alternate between eight possible states, i.e., $(S_{1},S_{2},S3) \in \{P,D\}^{3}$. We denote by $\lambda _{\mathrm {S}_{1}\mathrm {S}_{2}\mathrm {S}_{3}}$ the fraction of time during which the state $S_{1}S_{2}S_{3}$ occurs; and, focus on a two state topological setting of strong v.s. weak links with symmetric alternating CSIT, $\lambda _{PDD}=\lambda _{DPD}$. For this setting, we establish an inner bound on the Generalized Secure Degrees of Freedom (GSDoF) region with different topology states. The encoding scheme sheds light on the usage of both resources, i.e., alternating - topology and CSIT; and, shows that as opposed to coding independently over different states, joint encoding across the CSIT and topological states, enables strictly better secure rates.