Optimal Parameter Encoding Based on Worst Case Fisher Information Under a Secrecy Constraint

Abstract

Abstract-In this letter, optimal deterministic encoding of a uniformly distributed scalar parameter is performed in the presence of an eavesdropper. The objective is to maximize the worst case Fisher information of the parameter at the intended receiver while keeping the mean-squared error (MSE) at the eavesdropper above a certain level. The eavesdropper is modeled to employ the linear minimum MSE estimator based on the encoded version of the parameter. First, the optimal encoding function is derived when there exist no secrecy constraints. Next, to obtain the solution of the problem in the presence of the secrecy constraint, the form of the encoding function that maximizes the MSE at the eavesdropper is explicitly derived for any given level of worst case Fisher information. Then, based on this result, a low-complexity algorithm is provided to calculate the optimal encoding function for the given secrecy constraint. Finally, numerical examples are presented.Index Terms-Fisher information, mean-squared error (MSE), optimization, parameter estimation, secrecy.

Estimation Theoretic Optimal Encoding Design for Secure Transmission of Multiple Parameters

“…and h i = h e,i /σ e,i . Based on (18) and (21), the generic optimization problem in (14) reduces to…”

“…In [17], the optimal deterministic encoding of scalar parameters is investigated based on the minimization of the expectation of conditional Cramér-Rao bound (ECRB) in order to guarantee a certain level of estimation accuracy at the intended receiver while keeping the estimation error at the eavesdropper above a certain level. In [18], a robust parameter encoding approach is developed and the optimization is based on the worst-case CRB (equivalently, the worst-case Fisher information) of the parameter in order to guarantee a certain level of estimation accuracy at the intended receiver.…”

“…In the estimation theoretic secrecy framework, Fisher information and Cramér-Rao bounds provide crucial metrics to evaluate performance of estimators and have been employed in various security problems [15]- [18]. Even though the CRB and the Fisher information for a given value of a parameter of interest have very clear interpretations as a measure of estimation efficiency, they are not directly applicable in the Bayesian framework.…”

“…Even though the optimal parameter encoding problem has been investigated for scalar parameters in [17] and [18] from a CRB-based optimization perspective, it is possible that the channel input can contain multiple parameters in many practical scenarios such as [11], [15], [19]- [22]. Estimation of multiple parameters is required in many applications such as in localization [26] and joint frequency and phase estimation [23].…”

“…Based on the preceding motivations, we focus on a secure multi-parameter transmission scenario in this study. Similarly to [17] and [18], the parameter is encoded using an encoding function prior to transmission. It is important to emphasize that the difference of the multiparameter scenario investigated in this manuscript from the single parameter case studied in [17] is not only based on the number of parameters.…”