Minimizing Age of Incorrect Information for Unreliable Channel with Power Constraint

Age of Incorrect Information (AoII) is a newly introduced performance metric that is adaptable to a variety of communication goals. It has advantages over both the traditional performance metrics and the recently introduced metric - Age of Information (AoI). However, the fundamental nature of AoII has been elusive so far. In this work, we consider the AoII in a system where a transmitter sends updates about a multi-state Markovian source to a remote receiver through an unreliable channel. The communication goal is to minimize AoII subject to a power constraint. We cast the problem into a Constrained Markov Decision Process (CMDP) and prove that the optimal policy is a mixture of two deterministic threshold policies. Afterward, by leveraging the notion of Relative Value Iteration (RVI) and the structural properties of threshold policy, we propose an efficient algorithm to find the threshold policies as well as the mixing coefficient. Lastly, numerical results are laid out to highlight the effects of system parameters on the performance of AoII-optimal policy.