  In applications such as remote estimation and monitoring, update packets are
transmitted by power-constrained devices using short-packet codes over wireless
networks. Therefore, networks need to be end-to-end optimized using information
freshness metrics such as age of information under transmit power and
reliability constraints to ensure support for such applications. For
short-packet coding, modelling and understanding the effect of block codeword
length on transmit power and other performance metrics is important. To
understand the above optimization for short-packet coding, we consider the
optimal tradeoff problem between age of information and transmit power under
reliability constraints for short packet point-to-point communication model
with an exogenous packet generation process. In contrast to prior work, we
consider scheduling policies that can possibly adapt the block-length or
transmission time of short packet codes in order to achieve the optimal
tradeoff. We characterize the tradeoff using a semi-Markov decision process
formulation. We also obtain analytical upper bounds as well as numerical,
analytical, and asymptotic lower bounds on the optimal tradeoff. We show that
in certain regimes, such as high reliability and high packet generation rate,
non-adaptive scheduling policies (fixed transmission time policies) are
close-to-optimal. Furthermore, in a high-power or in a low-power regime,
non-adaptive as well as state-independent randomized scheduling policies are
order-optimal. These results are corroborated by numerical and simulation
experiments. The tradeoff is then characterized for a wireless point-to-point
channel with block fading as well as for other packet generation models
(including an age-dependent packet generation model).
