Variable-Length Stop-Feedback Coding for Minimum Age of Incorrect Information

We study the average Age of Incorrect Information (AoII) in the context of remote monitoring of a symmetric Markov source using variable-length stop-feedback (VLSF) coding. We consider sources with small cardinality, where feedback is non-instantaneous, as the transmitted information and feedback may have comparable lengths. We leverage recent results on the non-asymptotic achievable channel coding rate to derive optimal feedback sequences, i.e. the times of feedback transmissions, in terms of either AoII or delay. Our results showcase the impact of the feedback sequence and SNR on the AoII, revealing that a lower average delay does not necessarily correspond to a lower average AoII. We discuss implications and suggest directions for efficient coding scheme design.