Optimal parameter encoding based on worst case fisher information under a secrecy constraint

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.