In this work, fundamental limits and optimal mechanisms of privacy-preserving data release that aims to minimize the privacy leakage under utility constraints of a set of multiple tasks are investigated. While the private feature to be protected is typically determined and known by the sanitizer, the target task is usually unknown. To address the lack of information on the specific task, utility constraints laid on a set of multiple possible tasks are considered. The mechanism protects the specific privacy feature of the to-be-released data while satisfying utility constraints of all possible tasks in the set. First, the single-letter characterization of the rate-leakage-distortion region is derived, where the utility of each task is measured by a distortion function. It turns out that the minimum privacy leakage problem with log-loss distortion constraints and the unconstrained released rate is a non-convex optimization problem. Second, focusing on the case where the raw data consists of multiple independent components, we show that the above non-convex optimization problem can be decomposed into multiple parallel privacy funnel (PF) problems with different weightings. We explicitly derive the optimal solution to each PF problem when the private feature is a component-wise deterministic function of a data vector. The solution is characterized by a leakage-free threshold: when the utility constraint is below the threshold, the minimum leakage is zero; once the required utility level is above the threshold, the privacy leakage increases linearly. Finally, we show that the optimal weighting of each privacy funnel problem can be found by solving a linear program (LP). A sufficient released rate to achieve the minimum leakage is also derived. Numerical results are shown to illustrate the robustness of our approach against the task non-specificity.

Privacy-preserving data release mechanisms aiming to minimize the privacy leakage under utility constraints of nonspecific tasks are studied through the lens of information theory. While the private feature to be protected is typically determined and known by the users who release their data, the specific task where the release data is utilized is usually unknown. To address the lack of information of the specific task, utility constraints laid on a set of multiple possible tasks are considered. The mechanism protects the privacy of a given feature of the to-be-released data while satisfying utility constraints of all possible tasks in the set. First, the single-letter characterization of the privacy-utility tradeoff region is derived. Characterization of the minimum privacy under log-loss utility constraints turns out to be a non-convex optimization problem involving mutual information in the objective function and the constraints. Second, focusing on the case where the raw data consists of multiple independent components, we show that the above optimization problem can be decomposed into multiple parallel privacy funnel (PF) problems [1] with different weightings. We explicitly derive the optimal solution to each PF problem when the private feature is a deterministic function of a data component. The solution is characterized by the leakage-free threshold, and the minimum leakage is zero while the utility constraint is below the threshold. Once the utility requirement is above the threshold, the privacy leakage increases linearly. Finally, we show that the optimal weighting of each privacy funnel problem can be found by solving a linear program (LP). Numerical results are shown to illustrate the robustness of our approach.

This paper considers the joint design of training and data transmission in physical-layer secret communications, and examines the role of artificial noise (AN) in both of these phases. In particular, AN in the training phase is used to prevent the eavesdropper from obtaining accurate channel state information (CSI), whereas AN in the data transmission phase can be used to mask the transmission of confidential messages. By considering AN-assisted training and secrecy beamforming, we first derive bounds on the achievable secrecy rate and utilize them to obtain approximate secrecy rate expressions that are asymptotically tight at high SNR. By maximizing these expressions, power allocation policies between signal and AN in both training and data transmission phases are then proposed for conventional and AN-assisted training-based schemes, respectively. We show that the optimal AN power at high SNR should be non-vanishing with respect to the total power, and that AN usage can be more effective in the training phase than in the data transmission phase when the coherence time is large. However, at low SNR, we show that AN cannot be effectively utilized due to the lack of accurate CSI, and thus, one can often do better without. Numerical results are presented to verify our theoretical claims.

We consider the block Rayleigh fading multiple-input multiple-output (MIMO) wiretap channel with no prior channel state information (CSI) available at any of the terminals. The channel gains remain constant within a coherence interval of T symbols, and then change to another independent realization in the next coherence interval. The transmitter, the legitimate receiver, and the eavesdropper have nt, nr, and ne antennas, respectively. We determine the exact secure degrees of freedom (s.d.o.f.) of this system when T ≥ 2min(nt,nr). We show that, in this case, the s.d.o.f. is exactly equal to (min(nt,nr)-ne)+(T -min(nt,nr))/T. The first term in this expression can be interpreted as the eavesdropper with ne antennas taking away ne antennas from both the transmitter and the legitimate receiver. The second term can be interpreted as a fraction of the s.d.o.f. being lost due to the lack of CSI at the legitimate receiver. In particular, the fraction loss, min(nt,nr)/T, can be interpreted as the fraction of channel uses dedicated to training the legitimate receiver for it to learn its own CSI. We prove that this s.d.o.f. can be achieved by employing a constant norm channel input, which can be viewed as a generalization of discrete signalling to multiple dimensions.

Discriminatory channel estimation (DCE) is a secrecy-enhancing training and channel estimation technique previously proposed in the literature to enhance the effective channel quality difference between the main and the eavesdropper channels (i.e., the channels experienced by the legitimate receiver and the eavesdropper, respectively) in the channel estimation phase. In the past, this was achieved by developing techniques to first provide the transmitter with preliminary estimates of the main channel and by then emitting training signals that embed AN in the null space of the estimated main channel to disrupt the channel estimation at the eavesdropper. Extending upon previous works on DCE, this work proposes a general AN design that does not rely on the availability of the null space of the estimated main channel and, thus, does not require the transmitter to have more antennas than the receiver. In particular, the AN covariance matrix, the pilot signal power, and the linear estimator are jointly determined to minimize the channel estimation error at the receiver subject to a constraint below on the channel estimation error at the eavesdropper. The design is obtained by adopting an alternating optimization approach where the AN and pilot signals at the transmitter and the estimator at the receiver are optimized in turn until no further decrease in channel estimation error is observed. The effectiveness of the proposed scheme is demonstrated through computer simulations.

We consider the block Rayleigh fading multiple-input multiple-output (MIMO) wiretap channel with no prior channel state information (CSI) available at any of the terminals. The channel gains remain constant in a coherence time of T symbols, and then change to another independent realization. The transmitter, the legitimate receiver and the eavesdropper have nt, nrand neantennas, respectively. We determine the exact secure degrees of freedom (s.d.o.f.) of this system when T ≥ 2 min(nt, nr). We show that, in this case, the s.d.o.f. is exactly (min(nt, nr) − ne)+(T − min(nt, nr))/T. The first term can be interpreted as the eavesdropper with neantennas taking away neantennas from both the transmitter and the legitimate receiver. The second term can be interpreted as a fraction of s.d.o.f. being lost due to the lack of CSI at the legitimate receiver. In particular, the fraction loss, min(nt, nr)/T, can be interpreted as the fraction of channel uses dedicated to training the legitimate receiver for it to learn its own CSI. We prove that this s.d.o.f. can be achieved by employing a constant norm channel input, which can be viewed as a generalization of discrete signalling to multiple dimensions.

In this paper, we consider the joint design of training and data transmission signals for wiretap channels where the transmitter is to send a secrect massage to the receiver without being intercepted by the eavesdropper. The celebrated secrecy beamforming scheme, which may or may not be assisted by artificial-noise (AN), is adopted in the data transmission phase to achieve this task. The achievable secrecy rate for practical systems with channel estimation error is first derived. Based on the achievable secrecy rate, we find the optimal tradeoff between the energy used for training and data signals. The optimal solutions in the low and high energy regimes are characterized analytically. We show that AN does not provide any advantages in the low energy regime, while it may have significant impact in the high energy regime. Numerical results are presented to verify our theoretical claims.