Privacy-aware retransmission strategy design for remote state estimation under hybrid ARQ

This paper investigates a privacy-aware transmission control strategy for a hybrid automatic repeat request (HARQ)-based remote state estimation system. In this framework, packet reliability increases with the number of retransmissions owing to HARQ combining. When a transmission failure occurs, the sensor decides whether to retransmit the previously failed local estimate or to transmit current local estimate. This decision induces a trade-off between reliability and timeliness, as retransmissions improve success probability but degrade freshness. In addition, as the number of retransmissions increases, an external eavesdropper may intercept multiple transmissions and gradually accumulate information about the system state, which increases privacy leakage risk. This introduces a coupled trade-off among transmission reliability, information timeliness, and privacy preservation. By quantifying the privacy leakage of each transmission through mutual information and characterizing the estimation performance via the remote estimation mean-squared error (MSE), we formulate the sensor’s transmission decision problem as a Markov decision process (MDP). Within this framework, an optimal transmission policy is obtained that minimizes a long-term performance criterion combining the remote estimation MSE and the cumulative privacy leakage. Furthermore, a sufficient condition for the existence of a stationary and deterministic optimal policy that stabilizes the remote estimation system is provided. To provide important insight into the organization of the optimal policy, the structural property of the optimal solution is derived, under which the remaining state variables exhibit a threshold behavior when the local state variable is fixed. Moreover, a closed-form suboptimal policy is obtained. A simulation example is provided to validate the accuracy of the theoretical results presented in this work.