离散块长下的开环传输：年龄最优调度的表征
Open-Loop Transmission with Discrete Blocklengths: Characterization of AoI-Optimal Schedules
AI总结：
本文针对无反馈的状态更新系统，研究离散块长下的开环传输调度，通过马尔可夫决策过程推导最优调度条件，证实非平凡调度对平均指数AoI增益显著，且可应用于LDPC码本的年龄最优传输场景。
AI中文摘要：
本文研究由监测物理过程的信源和接收端组成的通用状态更新系统，状态更新传输时存在一组离散的块长-错误概率元组，典型示例为采用固定调制与编码方案集的通信系统。假设不存在确认反馈信道，研究状态更新系统的确定性调度构造问题。平均信息年龄（AoI）和平均指数AoI是衡量信息新鲜度的合适性能指标，研究发现静态块长通常次优：对于平均AoI，使用非平凡周期调度的增益相对较小；但对于平均指数AoI，增益显著。基于此，本文证明了存在两个块长时的单块长最优性条件，为此采用类Dinkelbach方法将问题重构为无限状态瞬态平均成本马尔可夫决策过程，并应用精细边界技术推导最优性条件；作为对偶分析，研究平稳随机策略以验证非平凡确定性调度优于最优恒定调度的参数区域，还提供了超过两个传输长度情况的扩展分析。数值结果表明，推导的条件覆盖了大部分参数空间，且短块长恒定调度的最优性条件虽是充分条件，也可能是必要条件；作为示例，将结果应用于使用小型LDPC码本的年龄最优传输问题，验证了其实际适用性。
英文摘要：
In this paper, we consider a general status update system, consisting of a source at which a physical process is monitored and a receiver. For transmission of status updates, a discrete set of blocklength error probability tuples is available. A typical example is a communication system with a fixed set of modulation and coding schemes. We assume that no feedback channel for acknowledgments exists and thus investigate the problem of constructing deterministic schedules for the status updating system. The average Age of Information (AoI) and average exponential AoI are appropriate performance metrics to capture the freshness of information. Interestingly, a static blocklength is shown to be suboptimal in general. While for the average AoI the gains that can be achieved by using a non-trivial periodic schedule are relatively small, they are significant for the average exponential AoI. Motivated by this, we prove conditions for single-blocklength optimality when two blocklengths are available. To achieve this, we use a Dinkelbach-like approach to reformulate the problem as an infinite-state transient average-cost Markov Decision Process and apply careful bounding techniques to derive the optimality conditions. As a converse, we analyze stationary randomized policies to certify the parameter regions where a non-trivial deterministic schedule outperforms the best constant schedule. Extensions to the case with more than two transmission lengths are provided. Numerical results show that the derived conditions cover a large portion of the parameter space and suggest that the optimality conditions for a constant schedule with the shorter blocklength, while sufficient, may also be necessary. As an example, we apply the results to the problem of age-optimal transmission with a small LDPC codebook, which illustrates the practical applicability.
