We consider a block fading wiretap channel, where a transmitter attempts to send messages securely to a receiver in the presence of a hybrid half-duplex adversary, which arbitrarily decides to either jam or eavesdrop the transmitter-to- receiver channel. We provide bounds to the secrecy capacity for various possibilities on receiver feedback and show special cases where the bounds are tight. We show that, without any feedback from the receiver, the secrecy capacity is zero if the transmitter-to-adversary channel stochastically dominates the effective transmitter-to-receiver channel. However, the secrecy capacity is non-zero even when the receiver is allowed to feed back only one bit at the end of each block. Our novel achievable strategy improves the rates proposed in the literature for the non-hybrid adversarial model. We also analyze the effect of multiple adversaries and delay constraints on the secrecy capacity. We show that our novel time sharing approach leads to positive secrecy rates even under strict delay constraints.
We consider a block fading wiretap channel, where a transmitter attempts to send messages securely to a receiver in the presence of a hybrid half-duplex adversary, which arbitrarily decides to either jam or eavesdrop the transmitter-to- receiver channel. We provide bounds to the secrecy capacity for various possibilities on receiver feedback and show special cases where the bounds are tight. We show that, without any feedback from the receiver, the secrecy capacity is zero if the transmitter-to-adversary channel stochastically dominates the effective transmitter-to-receiver channel. However, the secrecy capacity is non-zero even when the receiver is allowed to feed back only one bit at the end of each block. Our novel achievable strategy improves the rates proposed in the literature for the non-hybrid adversarial model. We also analyze the effect of multiple adversaries and delay constraints on the secrecy capacity. We show that our novel time sharing approach leads to positive secrecy rates even under strict delay constraints.
We consider a block fading wiretap channel, where a transmitter attempts to send messages securely to a receiver in the presence of a hybrid half-duplex adversary, which arbitrarily decides to either jam or eavesdrop the transmitter-to-receiver channel. We provide bounds to the secrecy capacity for various possibilities on receiver feedback and show special cases where the bounds are tight. We show that, without any feedback from the receiver, the secrecy capacity is zero if the transmitter-to-adversary channel stochastically dominates the effective transmitter-to-receiver channel. However, the secrecy capacity is nonzero even when the receiver is allowed to feed back only one bit at the end of each block. Our novel achievable strategy improves the rates proposed in the literature for the nonhybrid adversarial model. We also analyze the effect of multiple adversaries and delay constraints on the secrecy capacity. We show that our novel time sharing approach leads to positive secrecy rates even under strict delay constraints.
In this paper, we investigate the ergodic secrecy capacity of a block-fading wiretap channel with limited channel knowledge at the transmitter. We consider that the legitimate receiver, the eavesdropper, and the transmitter are equipped with multiple antennas and that the receiving nodes are aware of their respective channel matrices. On the other hand, the transmitter is only provided by a B-bit feedback of the main channel state information. The feedback bits are sent by the legitimate receiver, at the beginning of each fading block, over an error-free public link with limited capacity. The statistics of the main and the eavesdropper channel state information are known at all nodes. Assuming an average transmit power constraint, we establish upper and lower bounds on the ergodic secrecy capacity. Then, we present a framework to design the optimal codebooks for feedback and transmission. In addition, we show that the proposed lower and upper bounds coincide asymptotically, as the capacity of the feedback link becomes large, i.e., B→∞, hence fully characterizing the ergodic secrecy capacity in this case. Besides, we analyze the asymptotic behavior of the presented secrecy rates, at high signal-to-noise ratio, and evaluate the gap between the bounds.
We study the secret message capacity of an ergodic block fading wiretap channel with partial channel state information at the transmitter and perfect channel state information at the receivers. We consider that in addition to the statistics of the main and the eavesdropper channel state information (CSI), the sender is provided by the legitimate receiver with a q-bit feedback, at the beginning of each coherence block, through an error-free feedback channel, with capacity q bits. We establish upper and lower bounds on the secrecy capacity. We show that a positive secrecy rate is achievable even when the feedback is at the end of each coherence block and q = 1. We also show that the lower and the upper bounds coincide asymptotically as q → ∞. Finally, asymptotic analysis at high Signal-to-Noise Ratio (SNR) are presented where it is found that the capacity is bounded at high-SNR and present a simple suboptimal scalar quantizer that is capacity achieving, without the need of any numerical optimization, as q → ∞. When applied to Rayleigh fading channels, we show that, at high-SNR, a 4-bit feedback achieves 90% of the secrecy capacity when perfect main CSI is available at the transmitter.
We study the secret message capacity of an ergodic block fading wiretap channel with partial channel state information at the transmitter and perfect channel state information at the receivers, under both a short term power constraint (STPC) and a long term power constraint (LTPC). We consider that in addition to the statistics of the main and the eavesdropper channel state information (CSI), the sender is provided by the legitimate receiver with a q-bit feedback, at the beginning of each coherence block, through an error-free public channel, with capacity q bits. We establish upper and lower bounds on the secrecy capacity. We show that the lower and the upper bounds coincide asymptotically as q → ∞. When applied to Rayleigh fading channels, we show that, a 4-bit feedback achieves about 90% of the secrecy capacity when perfect main CSI is available at the transmitter. Finally, asymptotic analysis at high and low Signal-to-Noise Ratio (SNR) is presented. It is found that the capacity is bounded at high-SNR, whereas at asymptotically low-SNR, the lower bounds and the upper bound scale linearly with SNR under STPC. Furthermore, subject to LTPC, the capacity at low-SNR is equal to the capacity of the main channel without secrecy constraint and with perfect CSI at both the transmitter and the receiver, under a mild condition on the fading statistics. We also show that a positive secrecy rate is achievable even when the feedback is at the end of each coherence block and q=1.
In this paper, we investigate the problem of secure broadcasting over block-fading channels with limited channel knowledge at the transmitter. More particularly, we analyze the effect of having imperfect channel state information (CSI) via a finite rate feedback on the throughput of a broadcast channel where the transmission is intended for multiple legitimate receivers in the presence of an eavesdropper. First, we partially characterize the ergodic secrecy capacity of the system when the source broadcasts the same information to all the receivers, i.e., common message transmission. Then, we look at the independent messages case, where the transmitter broadcasts multiple independent messages to the legitimate receivers. For this case, we present lower and upper bounds on the ergodic secrecy sum-capacity. In both scenarios, we show that the proposed lower and upper bounds coincide asymptotically as the capacity of the feedback links becomes large, hence, fully characterizing the secrecy capacity in this case.
We study the ergodic secrecy capacity of a block- fading wiretap channel when there are multiple antennas at the transmitter, the legitimate receiver and the eavesdropper. We consider that the receivers are aware of their respective channel matrices while the transmitter is only provided by a B-bits feedback of the main channel state information. The feedback bits are sent by the legitimate receiver, at the beginning of each fading block, over an error free public link with limited capacity. Assuming an average transmit power constraint, we provide an upper and a lower bounds on the ergodic secrecy capacity. Then, we present a framework to design the optimal codebooks for feedback and transmission. In addition, we show that the proposed lower and upper bounds coincide asymptotically as the capacity of the feedback link becomes large; hence, fully characterizing the secrecy capacity in this case.