We study real-time reconstruction and actuation for two binary Markov sources that share a wireless multi-packet reception (MPR) channel. Each sensor follows a stationary randomized sampling policy, and the receiver maintains source estimates using the most recently decoded updates. We derive closed-form expressions for the steady-state real-time reconstruction error (RTE) and the cost of actuation error (CAE) as functions of the source transition probabilities and the effective update probabilities. We then characterize these update probabilities under randomized sampling, linking the physical-layer MPR model to task-oriented reconstruction and actuation metrics. Using these expressions, we formulate a sampling-constrained optimization problem with a weighted-error objective. The resulting analysis reveals how source dynamics, semantic weights, and MPR coupling affect the allocation of sampling resources. Numerical results show that optimized randomized sampling outperforms random, greedy, and time-sharing baselines.

翻译：针对共享无线多包接收(MPR)信道的两路二值马尔可夫源，研究其实时重构与驱动问题。每个传感器采用平稳随机采样策略，接收端利用最新解码更新维持源状态估计。本文推导了稳态实时重构误差(RTE)与驱动误差成本(CAE)关于源状态转移概率和有效更新概率的闭式表达式。进而刻画随机采样下这些更新概率的特征，将物理层MPR模型与面向任务的驱动和重构度量建立关联。基于上述表达式，构建了以加权误差为目标的采样约束优化问题。分析结果揭示了源动态特性、语义权重及MPR耦合效应对采样资源分配的影响机制。数值结果表明，优化随机采样策略优于随机调度、贪婪算法和时分复用等基线方案。