Maximum Zero-Outage Secrecy Capacity of Fading Wiretap Channels with Finite Alphabets

When a transmitted signal encounters slow fading and the support of the fading gain contains zero, an outage event will happen inevitably, if the transmitter has no knowledge of the channel state. This will deteriorate the system performance metrics such as latency due to re-transmissions caused by the outages. For scenarios like this, we use the outage probability or the outage capacity to measure the system performance. In this work, we investigate the possibility of achieving a positive zero-outage secrecy capacity (ZOSC) for a wiretap channel with fading gains from finite alphabet sets. In particular, we investigate the minimum secrecy outage probability with respect to all possible joint distributions of the fading gains, given their marginal distributions. We propose a systematic scheme to calculate the minimum secrecy outage probability by solving linear programming problems. From this, the maximum ZOSC of the considered wiretap channel model directly follows. Interestingly, we find that scenarios with a ZOSC of zero for independent fading can support a positive ZOSC when the fading links are dependent.

I. Introduction

Modern communication systems frequently transmit sensitive data wirelessly, e.g. in 5G systems and beyond [1]. Therefore, it is very important to ensure that the transmitted information is not intercepted by potential eavesdroppers. Besides cryptog-raphy, physical layer security is one promising alternative to achieve secure data transmission [2]. This approach uses the physical properties of the wireless channel but does not rely on shared keys. It is well-known that there exists a specific class of channel codes that fulfill the strong secrecy constraint over Gaussian wiretap channel (GWTC), when there is perfect channel-state information at the transmitter (CSI-T). In contrast, for a slow-fading GWTC with only statistical CSI-T, an outage event will occur when either the legitimate receiver or the eavesdropper experience a fading channel [3]. For such a system, the appropriate performance metrics are (secrecy) outage probability and the -(secrecy)-outage capacity, i.e., the maximum rate at which one can communicate with at most (secrecy) outages.