This paper introduces hybrid automatic repeat request with incremental redundancy (HARQ-IR) to boost the reliability of short packet communications. The finite blocklength information theory and correlated decoding events tremendously preclude the analysis of average block error rate (BLER). Fortunately, the recursive form of average BLER motivates us to calculate its value through the trapezoidal approximation and Gauss-Laguerre quadrature. Moreover, the asymptotic analysis is performed to derive a simple expression for the average BLER at high signal-to-noise ratio (SNR). Then, we study the maximization of long term average throughput (LTAT) via power allocation meanwhile ensuring the power and the BLER constraints. For tractability, the asymptotic BLER is employed to solve the problem through geometric programming (GP). However, the GP-based solution underestimates the LTAT at low SNR due to a large approximation error in this case. Alternatively, we also develop a deep reinforcement learning (DRL)-based framework to learn power allocation policy. In particular, the optimization problem is transformed into a constrained Markov decision process, which is solved by integrating deep deterministic policy gradient (DDPG) with subgradient method. The numerical results finally demonstrate that the DRL-based method outperforms the GP-based one at low SNR, albeit at the cost of increasing computational burden.

翻译：本文引入混合自动重传请求与增量冗余（HARQ-IR）以提升短包通信的可靠性。有限块长信息论与相关译码事件极大阻碍了平均误块率（BLER）的分析。值得庆幸的是，平均BLER的递归形式促使我们通过梯形近似和高斯-拉盖尔求积法计算其值。此外，我们进行了渐近分析，推导出高信噪比（SNR）下平均BLER的简洁表达式。随后，通过功率分配研究长期平均吞吐量（LTAT）的最大化，同时保证功率和BLER约束。为便于处理，利用渐近BLER通过几何规划（GP）求解问题。然而，基于GP的解在低SNR时因近似误差较大而低估了LTAT。为此，我们还开发了基于深度强化学习（DRL）的框架来学习功率分配策略。具体而言，将优化问题转化为约束马尔可夫决策过程，通过结合深度确定性策略梯度（DDPG）与次梯度法求解。数值结果最终表明，尽管增加了计算负担，但基于DRL的方法在低SNR时优于基于GP的方法。