In the past decade, the emergence of beyond fifth generation (B5G) wireless networks has necessitated the timely updating of system states in Internet of Things (IoT) and cyber-physical systems, where Age of Information (AoI) has been a well-concentrated metric. However, the content-agnostic nature of AoI reflects its limitation of characterizing the significance of status update messages, which induces various variants for AoI including Age of Incorrect Information (AoII). AoII is a goal-oriented significance (etymological meaning of “semantics”) metric that could overcome such shortcomings, and thus analyzing AoII performance can be a potential approach of realizing semantic communications. Nevertheless, AoII analysis of practical coded status update system under finite blocklength (FBL) regime is still in its nascent stages. To the best of our knowledge, our study represents the first analysis of AoII for FBL regime. We explicitly obtain the average AoII expressions for different transmission schemes including Automatic Repeat reQuest (ARQ), Hybrid ARQ (HARQ), and non-ARQ transmission schemes. Moreover, we theoretically prove that non-ARQ scheme outperforms ARQ schemes in terms of AoII, and numerically compare AoII performance between non-ARQ and HARQ schemes by formulating and solving the AoII-optimal block assignment problem. Extensive simulation results show the superiority of AoII-optimal transmission schemes.
