On SDoF of Multi-Receiver Wiretap Channel With Alternating CSIT

TL;DR

This paper investigates the secure degrees of freedom (SDoF) in a multi-receiver MISO wiretap channel with alternating channel state information at the transmitter (CSIT), revealing that joint encoding across states enhances secure communication rates.

Contribution

It characterizes the SDoF region for various CSIT state combinations and demonstrates the benefits of joint encoding over separate encoding, extending results to broadcast channels.

Findings

Alternating CSIT provides synergistic SDoF gains.

Joint encoding across states outperforms separate encoding.

Results apply to both wiretap and broadcast channels.

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 the state of the channel which is available to each receiver is conveyed either perfectly ($P$) or with delay ($D$) to the transmitter. Denoting by $S_1$, $S_2$, and $S_3$ the 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., $(S_1,S_2,S_3) \in \{P,D\}^3$. We denote by $\lambda_{S_1 S_2 S_3}$ the fraction of time during which the state $S_1S_2S_3$ occurs. Under these assumptions, we first consider the Gaussian MISO wiretap channel and characterize the secure degrees of freedom (SDoF). Next, we consider the general multi-receiver setup and characterize the SDoF region of fixed hybrid states $PPD$, $PDP$, and $DDP$. We then focus our attention on the symmetric case in which $\lambda_{PDD}=\lambda_{DPD}$. For this case, we establish bounds on SDoF region. The analysis reveals that alternating CSIT allows synergistic gains in terms of SDoF; and shows that, by opposition to encoding separately over different states, joint encoding across the states enables strictly better secure rates. Furthermore, we specialize our results for the two receivers channel with an external eavesdropper to the two-user broadcast channel. We show that, the synergistic gains in terms of SDoF by alternating CSIT is not restricted to multi-receiver wiretap channels; and, can also be harnessed under broadcast setting.