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。有限码长信息理论及相关解码事件极大地阻碍了平均块错误率（BLER）的分析。幸运的是，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数值。此外，我们进行了渐近分析，以推导高信噪比（SNR）下平均BLER的简化表达式。随后，我们研究了通过功率分配实现长期平均吞吐量（LTAT）最大化，同时确保功率和BLER约束。为便于处理，采用渐近BLER通过几何规划（GP）求解该问题。然而，基于GP的解法在低SNR情况下因较大的近似误差而低估了LTAT。作为替代，我们还开发了一种基于深度强化学习（DRL）的框架来学习功率分配策略。具体而言，优化问题被转化为受约束的马尔可夫决策过程，通过将深度确定性策略梯度（DDPG）与次梯度方法相结合来求解。数值结果最终表明，尽管计算负担增加，基于DRL的方法在低SNR下优于基于GP的方法。