Abstract

It is known that for a slow fading Gaussian wiretap channel without channel state information at the transmitter and with statistically independent fading channels, the outage probability of any given target secrecy rate is non-zero, in general. This implies that the so-called zero-outage secrecy capacity (ZOSC) is zero and we cannot transmit at any positive data rate reliably and confidentially. When the fading legitimate and eavesdropper channels are statistically dependent, this conclusion changes significantly. Our work shows that there exist dependency structures for which positive zero-outage secrecy rates (ZOSR) are achievable. In this paper, we are interested in the characterization of these dependency structures and we study the system parameters in terms of the number of observations at legitimate receiver and eavesdropper as well as average channel gains for which positive ZOSR are achieved. First, we consider the setting that there are two paths from the transmitter to the legitimate receiver and one path to the eavesdropper. We show that by introducing a proper dependence structure among the fading gains of the three paths, we can achieve a zero secrecy outage probability (SOP) for some positive secrecy rate. In this way, we can achieve a non-zero ZOSR. We conjecture that the proposed dependency structure achieves maximum ZOSR. To better understand the underlying dependence structure, we further consider the case where the channel gains are from finite alphabets and systematically and globally solve the ZOSC. In addition, we apply the rearrangement algorithm to solve the ZOSR for continuous channel gains. The results indicate that the legitimate link must have an advantage in terms of the number of antennas and average channel gains to obtain positive ZOSR. The results motivate further studies into the optimal dependency structures.

Highlights

  • With the rise of new technologies and applications, e.g., in the context of 6G [1], more sensitive data are transmitted wirelessly

  • A natural question will be: can we extend the concept of zero-outage capacity, to the wiretap channel, namely, the zero-outage secrecy capacity (ZOSC)? By definition, zero-outage secrecy rate (ZOSR) is the secrecy rate of any achievable scheme which guarantees zero outage probability and ZOSC is the largest

  • Our focus is on the ZOSC and we are interested in the question: is it possible to obtain a positive ZOSC for certain dependent fading channels? If yes, under what conditions and what are the values for common fading models?

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Summary

Introduction

With the rise of new technologies and applications, e.g., in the context of 6G [1], more sensitive data are transmitted wirelessly. For a point-to-point transmission without eavesdropper, it was shown in [18,19] that it is possible to have a positive zero-outage capacity with multiple dependent fading channels. Please note that the ZOSC is an important performance metric because it describes the transmission rate of data which is guaranteed to be delivered reliably and confidentially for every channel use, i.e., for every set of channels to the legitimate receiver and to the eavesdropper. It is not possible to apply the results from [18] and it is unclear, if the counter- and co-monotonicity of the dependence structure among the channel gains is optimal These huge discrepancies are our main motivation to investigate the model considered in this paper and the unique value of this work distinguished from the previous ones. Logarithms, if not stated otherwise, are assumed to be with respect to the natural base

System Model
Problem Formulation
Mathematical Background
Conclusions and Future Work
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