In this article, we consider the satellite Internet of Things (IoT) system, in which the IoT device observes physical processes and transmits the status updates to the monitor node over an error-prone channel with nontrivial propagation delay. The freshness of status updates is characterized by Age of Information (AoI), a novel metric that is defined as the time that elapsed since the freshest received status update was generated. Channel coding is used to combat the burst channel errors and feedback is available through hybrid automatic repeat request (HARQ) protocols. By adopting both the simple-HARQ and incremental redundancy HARQ (IR-HARQ) transmission schemes, we study the age-optimal redundancy allocation problems under the constraint of reliability. As we put special interests on the satellite-IoT scenarios in which the propagation delays are nonnegligible, there exists a threshold of the propagation delay only below which using retransmissions is beneficial to AoI. However, the characterization of such a threshold has received little attention in the literature. By formulating and solving the age-optimal redundancy allocation problems for the adopted HARQ schemes, explicit expressions of the optimal codeword length for each transmission round are derived, and then the threshold of the propagation delay for beneficial retransmissions is obtained. Extensive numerical analysis is conducted to show the effects of propagation delay and channel state on the redundancy allocation results and the optimal AoI. The threshold is also demonstrated by numerical analysis. The results shed important light on the age-optimal HARQ design for freshness-critical satellite-IoT systems in the presence of nontrivial propagation delay.

中文翻译：

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关键性卫星物联网系统的年龄最优HARQ设计

在本文中，我们考虑了卫星物联网（IoT）系统，其中IoT设备观察物理过程并将状态更新通过易错的信道以不重要的传播延迟传输到监视节点。状态更新的新鲜度以信息时代（AoI）为特征，信息时代（AoI）被定义为自从收到最新的状态更新以来经过的时间。信道编码用于解决突发信道错误，并且可以通过混合自动重发请求（HARQ）协议获得反馈。通过采用简单HARQ和增量冗余HARQ（IR-HARQ）传输方案，我们研究了可靠性约束下的年龄最优冗余分配问题。由于我们对传播延迟不可忽略的卫星物联网场景特别感兴趣，因此存在一个传播延迟阈值，只有在此阈值以下，使用重传对AoI有利。然而，这种阈值的表征在文献中很少受到关注。通过针对所采用的HARQ方案制定和求解年龄最优冗余分配问题，得出每个传输回合的最佳码字长度的明确表达式，然后获得有益重传的传播延迟阈值。进行了广泛的数值分析，以显示传播延迟和信道状态对冗余分配结果和最佳AoI的影响。该阈值也通过数值分析得到证明。