The Age of Incorrect Information (AoII) is studied within the context of remote monitoring a Markov source using variable-length stop-feedback (VLSF) coding. Leveraging recent results on the non-asymptotic channel coding rate, we consider sources with small cardinality, where feedback is non-instantaneous as the transmitted information and feedback message have comparable lengths. We focus on the feedback sequence, i.e. the times of feedback transmissions, and derive AoII-optimal and delay-optimal feedback sequences. Our results showcase the impact of the feedback sequence on the AoII, revealing that a lower average delay does not necessarily correspond to a lower average AoII. We discuss the implications of our findings and suggest directions for coding scheme design.

翻译：在远程监测马尔可夫源的背景下，研究了采用可变长度停止反馈（VLSF）编码的最小错误信息年龄（AoII）。借助非渐近信道编码速率的最新成果，我们考虑小基数信源，此时反馈并非瞬时完成，因为传输的信息与反馈消息具有相当的长度。我们聚焦于反馈序列（即反馈传输的时刻），推导出AoII最优与延迟最优的反馈序列。研究结果揭示了反馈序列对AoII的影响，表明较低的平均延迟并不必然对应较低的平均AoII。我们探讨了这些发现的启示，并为编码方案设计指明了方向。