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：本文在利用可变长度停止反馈（VLSF）编码远程监控马尔可夫源的背景下，研究了错误信息时效性（AoII）。借助近期关于非渐近信道编码速率的成果，我们考虑基数较小的信源，其中反馈是非即时性的，因为传输信息与反馈消息的长度相当。我们重点关注反馈序列（即反馈传输的时刻），并推导出AoII最优和延迟最优的反馈序列。我们的结果展示了反馈序列对AoII的影响，表明较低的平均延迟并不一定对应较低的平均AoII。我们讨论了研究结果的意义，并提出了编码方案设计的可能方向。