ECRB-based optimal parameter encoding under secrecy constraints
IEEE Transactions on Signal Processing
Institute of Electrical and Electronics Engineers
3556 - 3570
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In this paper, optimal deterministic encoding of a scalar parameter is investigated in the presence of an eavesdropper. The aim is to minimize the expectation of the conditional Cramér-Rao bound at the intended receiver while keeping the mean-squared error (MSE) at the eavesdropper above a certain threshold. First, optimal encoding functions are derived in the absence of secrecy constraints for any given prior distribution on the parameter. Next, an optimization problem is formulated under a secrecy constraint and various solution approaches are proposed. Also, theoretical results on the form of the optimal encoding function are provided under the assumption that the eavesdropper employs a linear minimum mean-squared error (MMSE) estimator. Numerical examples are presented to illustrate the theoretical results and to investigate the performance of the proposed solution approaches.