  Delivering timely status updates in a timeliness-critical communication
system is of paramount importance to assist accurate and efficient decision
making. Therefore, the topic of analyzing Age of Information has aroused new
research interest. This paper contributes to new results in this area by
systematically analyzing the AoI of two types of Hybrid Automatic Repeat
reQuest (HARQ) techniques that have been newly standardized in the Release-16
5G New Radio (NR) specifications, namely reactive HARQ and proactive HARQ.
Under a code-based status update system with non-trivial coding delay,
transmission delay, propagation delay, decoding delay, and feedback delay, we
derive unified closed-form average AoI and average Peak AoI expressions for
reactive HARQ and proactive HARQ, respectively. Based on the obtained explicit
expressions, we formulate an AoI minimization problem to investigate the
age-optimal codeblock assignment strategy in the finite block-length (FBL)
regime. Through case studies and analytical results, we provide comparative
insights between reactive HARQ and proactive HARQ from a perspective of
freshness of information. The numerical results and optimization solutions show
that proactive HARQ draws its strength from both age performance and system
robustness, thus enabling the potential to provide new system advancement of a
freshness-critical status update system.
