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Secrecy Capacity with Leakage Constraints in Fading Channels

Zhi Chen, Pingyi Fan, Dapeng Oliver Wu, Khaled B. Letaief

Published Dec 1, 2010• 3 citations
Publisher

Abstract

The secure transmission of information over wireless systems in the presence of an eavesdropper has attracted much attention. In this paper, we consider the case that full CSI of the legitimate user but only the average channel gain of the eavesdropper is known at the transmitter. In such setting, some information will be inevitably leaked to the eavesdropper from the information-theoretic view and this was not quantitatively evaluated before. A secrecy transmission framework with leakage threshold is thereby proposed. The secrecy capacity satisfying this leakage probability constraints is derived along with an optimal power allocation strategy. For Rayleigh and Nakagami-m fading channels, numerical results indicate that our framework can work well with transmitter knowledge of only average channel gain of the eavesdropper.

DOI
10.1109/glocom.2010.5684361

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The secure transmission of information over wireless systems in the presence of an eavesdropper has attracted much attention. In this paper, we consider the case that full CSI of the legitimate user but only the average channel gain of the eavesdropper is known at the transmitter. In such setting, some information will be inevitably leaked to the eavesdropper from the information-theoretic view and this was not quantitatively evaluated before. A secrecy transmission framework with leakage threshold is thereby proposed. The secrecy capacity satisfying this leakage probability constraints is derived along with an optimal power allocation strategy. For Rayleigh and Nakagami-m fading channels, numerical results indicate that our framework can work well with transmitter knowledge of only average channel gain of the eavesdropper.
ABSTRACT Secure transmission of information over wireless channels in the presence of an eavesdropper has attracted much attention recently. Previous work assumes that a transmitter has perfect knowledge of the channel side information (CSI) of the legitimate channel and the eavesdropper's channel. To loosen this strong requirement, this paper considers the case where a transmitter has perfect knowledge of the CSI of the legitimate channel and only the average channel gain of the eavesdropper's channel. In this case, some information may be leaked to the eavesdropper because the eavesdropper's channel may have a higher gain than the legitimate channel. Hence, we propose, for the first time, to study leakage‐probability‐constrained secrecy capacity of a fading channel, that is, secrecy capacity under the constraint on leakage probability. We also propose an optimal power allocation strategy that maximizes leakage‐probability‐constrained secrecy capacity under average power constraint. Moreover, we study the impact of the bias of the average gain estimate of the eavesdropper's channel on leakage‐probability‐constrained secrecy capacity. Copyright © 2011 John Wiley & Sons, Ltd.
We consider the secure transmission of information over an ergodic fading channel in the presence of an eavesdropper. Our eavesdropper can be viewed as the wireless counterpart of Wyner's wiretapper. The secrecy capacity of such a system is characterized under the assumption of asymptotically long coherence intervals. We first consider the full channel state information (CSI) case, where the transmitter has access to the channel gains of the legitimate receiver and the eavesdropper. The secrecy capacity under this full CSI assumption serves as an upper bound for the secrecy capacity when only the CSI of the legitimate receiver is known at the transmitter, which is characterized next. In each scenario, the perfect secrecy capacity is obtained along with the optimal power and rate allocation strategies. We then propose a low-complexity on/off power allocation strategy that achieves near-optimal performance with only the main channel CSI. More specifically, this scheme is shown to be asymptotically optimal as the average signal-to-noise ratio (SNR) goes to infinity, and interestingly, is shown to attain the secrecy capacity under the full CSI assumption. Overall, channel fading has a positive impact on the secrecy capacity and rate adaptation, based on the main channel CSI, is critical in facilitating secure communications over slow fading channels.
We consider the secure transmission of information over an ergodic fading channel in the presence of an eavesdropper. Our eavesdropper can be viewed as the wireless counterpart of Wyner's wiretapper. The secrecy capacity of such a system is characterized under the assumption of asymptotically long coherence intervals. We first consider the full Channel State Information (CSI) case, where the transmitter has access to the channel gains of the legitimate receiver and the eavesdropper. The secrecy capacity under this full CSI assumption serves as an upper bound for the secrecy capacity when only the CSI of the legitimate receiver is known at the transmitter, which is characterized next. In each scenario, the perfect secrecy capacity is obtained along with the optimal power and rate allocation strategies. We then propose a low-complexity on/off power allocation strategy that achieves near-optimal performance with only the main channel CSI. More specifically, this scheme is shown to be asymptotically optimal as the average SNR goes to infinity, and interestingly, is shown to attain the secrecy capacity under the full CSI assumption. Remarkably, our results reveal the positive impact of fading on the secrecy capacity and establish the critical role of rate adaptation, based on the main channel CSI, in facilitating secure communications over slow fading channels.
We consider the secure transmission of information over an ergodic fading channel in the presence of an eavesdropper. Our eavesdropper can be viewed as the wireless counterpart of Wyner's wiretapper. The secrecy capacity of such a system is characterized under the assumption of asymptotically long coherence intervals. We analyze the full Channel State Information (CSI) case, where the transmitter has access to the channel gains of the legitimate receiver and eavesdropper, and the main channel CSI scenario, where only the legitimate receiver channel gain is known at the transmitter. In each scenario, the secrecy capacity is obtained along with the optimal power and rate allocation strategies. We then propose a low-complexity on/off power allocation strategy that achieves near-optimal performance with only the main channel CSI. More specifically, this scheme is shown to be asymptotically optimal as the average SNR goes to infinity, and interestingly, is shown to attain the secrecy capacity under the full CSI assumption. Remarkably, our results reveal the positive impact of fading on the secrecy capacity and establish the critical role of rate adaptation, based on the main channel CSI, in facilitating secure communications over slow fading channels.
Nakagami-m fading channel is chosen to analyze the secrecy capacity for fading channels since the Nakagami-m distribution can model fading conditions, which are more or less severe than that of Rayleigh and has the advantage of including Rayleigh as a special case. At first, secrecy capacity is defined in case of full channel state information (CSI) at the transmitter, where transmitter has access to both the main channel and eavesdropper channel gains. Secondly, secrecy capacity is defined with only main channel CSI at the transmitter. Then, optimal power allocation at the transmitter that achieves the secrecy capacity is derived for both the cases. Moreover, secrecy capacity is defined under open-loop transmission scheme, and the exact closed form analytical expression for the lower bound of ergodic secrecy capacity is derived for Nakagami-m fading single-input multiple-output (SIMO) channel. In addition, secrecy capacity is defined for the AWGN channel in order to realize the information-theoretic security of wireless channels with no fading. Finally, analytical expressions for the probability of non-zero secrecy capacity and secure outage probability are derived in order to investigate the secure outage performance of fading channels.