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arXiv:1704.01238

Finite State Multiple-Access Wiretap Channel with Delayed Feedback

Bin Dai, Zheng Ma, Ming Xiao, Xiaohu Tang, Pingzhi Fan

Published Apr 5, 2017• 2 citations
arXivHTMLPDF

Abstract

Recently, it has been shown that the time-varying multiple-access channel (MAC) with perfect channel state information (CSI) at the receiver and delayed feedback CSI at the transmitters can be modeled as the finite state MAC (FS-MAC) with delayed state feedback, where the time variation of the channel is characterized by the statistics of the underlying state process. To study the fundamental limit of the secure transmission over multi-user wireless communication systems, we re-visit the FS-MAC with delayed state feedback by considering an external eavesdropper, which we call the finite state multiple-access wiretap channel (FS-MAC-WT) with delayed feedback. The main contribution of this paper is to show that taking full advantage of the delayed channel output feedback helps to increase the secrecy rate region of the FS-MAC-WT with delayed state feedback, and the results of this paper are further illustrated by a degraded Gaussian fading example.

DOI
10.48550/arxiv.1704.01238

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Recently, it has been shown that the time-varying multiple-access channel (MAC) with perfect channel state information (CSI) at the receiver and delayed feedback CSI at the transmitters can be modeled as the finite state MAC (FS-MAC) with delayed state feedback, where the time variation of the channel is characterized by the statistics of the underlying state process. To study the fundamental limit of the secure transmission over multi-user wireless communication systems, we re-visit the FS-MAC with delayed state feedback by considering an external eavesdropper, which we call the finite state multiple-access wiretap channel (FS-MAC-WT) with delayed feedback. The main contribution of this paper is to show that taking full advantage of the delayed channel output feedback helps to increase the secrecy rate region of the FS-MAC-WT with delayed state feedback, and the results of this paper are further illustrated by a degraded Gaussian fading example.
Recently, it has been shown that the time-varying multiple-access channel (MAC) with perfect channel state information (CSI) at the receiver and delayed feedback CSI at the transmitters can be modeled as the finite state MAC (FS-MAC) with delayed state feedback, where the time variation of the channel is characterized by the statistics of the underlying state process. To study the fundamental limit of the secure transmission over multi-user wireless communication systems, we re-visit the FS-MAC with delayed state feedback by considering an external eavesdropper, which we call the finite state multiple-access wiretap channel (FS-MAC-WT) with delayed feedback. The main contribution of this paper is to show that taking full advantage of the delayed channel output feedback helps to increase the secrecy rate region of the FS-MAC-WT with delayed state feedback. Moreover, by a degraded Gaussian fading example, we show the effects of feedback delay and channel memory on the secrecy sum rate of the FS-MAC-WT with delayed feedback.
Recently, the finite state Markov channel (FSMC) with an additional eavesdropper and delayed feedback from the legitimate receiver to the transmitter has been shown to be a useful model for the physical layer security of the practical mobile wireless communication systems. In this paper, we extend this model to a multiple-access situation (up-link of the wireless communication systems), which we call the finite state multiple-access wiretap channel (FS-MAC-WT) with delayed feedback. To be specific, the FS-MAC-WT is a channel with two inputs (transmitters) and two outputs (a legitimate receiver and an eavesdropper). The channel depends on a state which undergoes a Markov process, and the state is entirely known by the legitimate receiver and the eavesdropper. The legitimate receiver intends to send his channel output and the perfectly known state back to the transmitters through noiseless feedback channels after some time delay. The main contribution of this paper is to provide inner and outer bounds on the secrecy capacity region of this new model. The capacity results are further explained via a degraded Gaussian fading example, and from this example we see that sending the legitimate receiver's channel output back to the transmitters helps to enhance the security of the FS-MAC-WT with only delayed state feedback.
In recent years, the finite state Markov channel (FSMC) in the presence of an eavesdropper has been shown to be a useful model for the physical layer security of the practical mobile wireless communication systems. In this paper, we extend this model to a multiple-access situation (up-link of the wireless communication systems), which we call the finite state multiple-access wiretap channel (FS-MAC-WT) with delayed state feedback. To be specific, the FS-MAC-WT consists of two transmitters, a legitimate receiver and an eavesdropper. The channel transition probability depends on a state which undergoes a Markov process, and the state is perfectly known by the legitimate receiver and the eavesdropper. The legitimate receiver intends to send the state back to the transmitters through noiseless feedback channels after some time delay. The main contribution of this paper is to provide inner and outer bounds on the secrecy capacity region of this new model, and these results are further explained via a degraded Gaussian fading example.
Viswanathan has shown that the practical mobile communication system can be modeled as the finite state Markov channel (FSMC) with delayed feedback, where the receiver perfectly knows the channel state information (CSI) which undergoes a Markov process, and the receiver sends the CSI and his own channel output back to the transmitter after some time delay. Viswanathan found that the delayed feedback of the channel output does not help to increase the capacity of the FSMC with only delayed state feedback. Does this still holds when an additional eavesdropper is considered? In order to answer this question, in this paper, we study the finite state Markov wiretap channel (FSM-WC) with delayed feedback, where the CSI is perfectly known by the legitimate receiver and the eavesdropper, and the legitimate receiver sends the CSI and his own channel output back to the transmitter after some time delay. Inner and outer bounds on the secrecy capacity of this model are provided, and we show that these bounds meet if the eavesdropper's received channel output is a degraded version of the legitimate receiver's. Furthermore, we find that the legitimate receiver's delayed channel output feedback helps to enhance the secrecy capacity of the degraded FSM-WC with only delayed state feedback.
The finite state Markov channel (FSMC) has been shown to be a useful model for the time-varying fading channels. In this paper, we study the security issue in the wireless communication systems by considering the FSMC with an eavesdropper, which we call the finite state Markov wiretap channel (FSM-WC). More specifically, the FSM-WC is a channel with one input (the transmitter) and two outputs (the legitimate receiver and the eavesdropper). The transition probability of the FSM-WC is controlled by a channel state which takes values in a finite set, and it undergoes a Markov process. We assume that the state is perfectly known by the legitimate receiver and the eavesdropper, and through a noiseless feedback channel, the legitimate receiver sends the state back to the transmitter after some time delay. Measuring the eavesdropper's uncertainty about the transmitted message by equivocation, we provide inner and outer bounds on the capacity-equivocation region of this novel model, and show that these bounds meet (the capacity-equivocation region is determined) if the channel output for the eavesdropper is a degraded version of that for the legitimate receiver. The capacity results of this paper are further explained via degraded Gaussian and Gaussian fading examples.
The finite-state Markov channel (FSMC), where the channel transition probability is controlled by a state undergoing a Markov process, is a useful model for the mobile wireless communication channel. In this paper, we investigate the security issue in the mobile wireless communication systems by considering the FSMC with an eavesdropper, which we call the finite-state Markov wiretap channel (FSM-WC). We assume that the state is perfectly known by the legitimate receiver and the eavesdropper, and through a noiseless feedback channel, the legitimate receiver sends his received channel output and the state back to the transmitter after some time delay. Inner and outer bounds on the capacity-equivocation regions of the FSM-WC with delayed state feedback and with or without delayed channel output feedback are provided in this paper, and we show that these bounds meet if the eavesdropper's received symbol is a degraded version of the legitimate receiver's. The above-mentioned results are further explained via a degraded Gaussian fading example.