In this paper we revisit the connections of the distributed hypothesis testing against independence (HT) problem with the Wyner-Ahlswede-Korner (WAK) problem and the identification systems (ID). We show that the strong converse for the WAK problem is equivalent to the strong converse for the HT problem via constructive and nonconstructive transformations of codes. As another consequence of the transformation we provide a new exponentially strong converse equivalence statement. Applying the same idea, we prove a new result that the epsilon-identification capacity of the ID problem is equal to the maximum epsilon-exponent of type II of error in the HT problem when both side compression is allowed.

In this work, necessary and sufficient conditions for empirical coordination of vector-valued Witsenhausen counter-example two terminal setups with non-classical information structure are derived. Vector-valued processing allows to involve coding in the design of the control strategies. Optimal characterizations are obtained for the non-causal encoding and causal decoding case as well as causal encoding and non-causal decoding case. Necessary and sufficient conditions are provided for the case with both non-causal encoding and decoding. The feasible set of target distributions can serve as optimization domain for characterizing the optimal average cost, in particular using Witsenhausen's cost function.

Privacy against an adversary (AD) that tries to detect the underlying privacy-sensitive data distribution is studied. The original data sequence is assumed to come from one of the two known distributions, and the privacy leakage is measured by the probability of error of the binary hypothesis test carried out by the AD. A management unit (MU) is allowed to manipulate the original data sequence in an online fashion while satisfying an average distortion constraint. The goal of the MU is to maximize the minimal type II probability of error subject to a constraint on the type I probability of error assuming an adversarial Neyman-Pearson test, or to maximize the minimal error probability assuming an adversarial Bayesian test. The asymptotic exponents of the maximum minimal type II probability of error and the maximum minimal error probability are shown to be characterized by a Kullback-Leibler divergence rate and a Chernoff information rate, respectively. Privacy performances of particular management policies, the memoryless hypothesis-aware policy and the hypothesis-unaware policy with memory, are compared. The proposed formulation can also model adversarial example generation with minimal data manipulation to fool classifiers. At last, the results are applied to a smart meter privacy problem, where the user's energy consumption is manipulated by adaptively using a renewable energy source in order to hide user's activity from the energy provider.

The trade-off of hypothesis tests on the correlated privacy hypothesis and utility hypothesis is studied. The error exponent of the Bayesian composite hypothesis test on the privacy or utility hypothesis can be characterized by the corresponding minimal Chernoff information rate. An optimal management protects the privacy by minimizing the error exponent of the privacy hypothesis test and meanwhile guarantees the utility hypothesis testing performance by satisfying a lower bound on the corresponding minimal Chernoff information rate. The asymptotic minimum error exponent of the privacy hypothesis test is shown to be characterized by the infimum of corresponding minimal Chernoff information rates subject to the utility guarantees.

We study the problem of securely estimating the states of an unstable dynamical system subject to non-stochastic disturbances. The estimator obtains all its information through an uncertain channel, which is subject to nonstochastic disturbances as well, and an eavesdropper obtains a disturbed version of the channel inputs through a second uncertain channel. An encoder observes and block encodes the states in such a way that, upon sending the generated codeword, the estimator's error is bounded and a security criterion is satisfied, thereby ensuring that the eavesdropper obtains as little state information as possible. Two security criteria are considered and discussed with the help of a numerical example. A sufficient condition on the uncertain wiretap channel, i.e., the pair formed by the uncertain channel from the encoder to the estimator and the uncertain channel from the encoder to the eavesdropper is derived, which ensures that a bounded estimation error and security are achieved. This condition is also shown to be necessary for a subclass of uncertain wiretap channels. To formulate the condition, the zero-error secrecy capacity of uncertain wiretap channels is introduced, i.e., the maximal rate at which data can be transmitted from the encoder to the estimator in such a way that the eavesdropper is unable to reconstruct the transmitted data. Finally, the zero-error secrecy capacity of uncertain wiretap channels is studied.

In this paper, we present a degradation-aware privacy control strategy for smart meters by taking into account the capacity fade and energy loss of the battery, which has not been included previously. The energy management strategy is designed by minimizing the weighted sum of both privacy loss and total energy storage losses, where the weightage is set using a trade-off parameter. The privacy loss is measured in terms of Bayesian risk of an unauthorized hypothesis test. By making first-order Markov assumptions, the stochastic parameters of energy loss and capacity fade of the energy storage system are modelled using degradation maps. Using household power consumption data from the ECO dataset, the proposed control strategy is numerically evaluated for different trade-off parameters. Results show that, by including the degradation losses in the design of the privacy-enhancing control strategy, significant improvement in battery life can be achieved, in general, at the expense of some privacy loss.

We study a hypothesis testing problem to decide whether or not an observation sequence is related to one of users in a database which contains compressed versions of users' data. Our main interest lies on the characterization of the exponent of the probability of the second kind of error when the number of users in the database grows exponentially. We show a lower bound on the error exponent and identify special cases where the bound is tight. Next, we study the -achievable error exponent and show a sub-region where the lower bound is tight.

In this work we consider a two-stage identification problem with pre-processing where the users' data and observation are Gaussian distributed. In the first stage the processing unit returns a list of compatible users using the information from the first storage layer and the pre-processed observation. Then, the refined search is performed in the second stage where the processing unit returns the exact user's identity and a corresponding reconstruction sequence. We provide a complete rate-distortion trade-off for the Gaussian setting.

The design of optimal energy management strategies that trade-off consumers' privacy and expected energy cost by using an energy storage is studied. The Kullback-Leibler divergence rate is used to assess the privacy risk of the unauthorized testing on consumers' behavior. We further show how this design problem can be formulated as a belief state Markov decision process problem so that standard tools of the Markov decision process framework can be utilized, and the optimal solution can be obtained by using Bellman dynamic programming. Finally, we illustrate the privacy-enhancement and cost-saving by numerical examples. 

This paper studies the optimal tradeoff between secrecy and non-secrecy rates of the MISO wiretap channels for different power constraint settings:sum power constraint only, per-antenna power constraints only and joint sum and per-antenna power constraints. The problem is motivated by the fact thatchannel capacity and secrecy capacity are generally achieved by different transmit strategies. First, a necessary and sufficient condition to ensure a positive secrecy capacity is shown. The optimal tradeoff between secrecy rate and transmission rate is characterized by a weighted rate sum maximization problem. Since this problem is not necessarily convex, equivalent problem formulations are introduced to derive the optimal transmit strategies. Under sum power constraint only, a closed-form solution is provided. Under per-antenna power constraints, necessary conditions to find the optimal power allocation are provided. Sufficient conditions are provided for the special case of two transmit antennas. For the special case of parallel channels, the optimal transmit strategies can deduced from an equivalent point-to-point channel problem. Lastly, the theoretical results are illustrated by numerical simulations.