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).

翻译：在远程估计与监控等应用中，更新数据包由功率受限设备通过无线网络采用短包编码传输。因此，网络需在发射功率与可靠性约束下，利用信息年龄等信息新鲜度指标进行端到端优化，以确保对此类应用的支持。对于短包编码而言，建模并理解码块长度对发射功率及其他性能指标的影响至关重要。为探究短包编码的上述优化问题，我们考虑在存在外生数据包生成过程的短包点对点通信模型中，基于可靠性约束实现信息年龄与发射功率的最优权衡。与先前研究不同，我们考虑可通过自适应调整短包码的码块长度或传输时间的调度策略以达到最优权衡。我们利用半马尔可夫决策过程模型刻画此权衡关系，并推导了最优权衡的解析上界，以及数值、解析和渐近下界。研究表明，在特定场景（如高可靠性与高数据包生成率）下，非自适应调度策略（固定传输时间策略）接近最优。此外，在高功率或低功率区域中，非自适应及状态无关的随机化调度策略均为阶数最优。上述结论通过数值与仿真实验得到验证。此外，我们还针对具有块衰落的无线点对点信道及其他数据包生成模型（包括年龄相关数据包生成模型）刻画了此权衡关系。