AI 中文总结
该研究针对MPR信道上的二元马尔可夫源，提出通过重建/驱动误差评估通信性能的方法，将优化问题简化为有限一维搜索，量化独立随机化的损失，得出MPR能力需结合可靠并发接收才有效的结论。
AI 中文摘要
本文研究在具有多分组接收（MPR）能力的共享无线信道上，两个二元马尔可夫源的实时重建与远程驱动问题。与许多丢弃同时传输的基于碰撞的现有公式不同，我们利用MPR技术，通过重建和驱动误差而非原始传输速率来评估通信性能。我们考虑两个观测源的传感器，旨在找到在每个传感器采样约束下，最小化加权实时重建误差（RTE）或等效于所考虑二元源的加权驱动误差（CAE）的采样策略。我们首先根据有效更新概率获得RTE和CAE的闭式表达式。当传感器独立随机化时，MPR诱导的更新率映射变为双线性，且约束优化问题为非凸。我们利用可实现更新率区域的几何特性，证明对帕累托最优独立随机化策略的搜索可简化为对有限集的一维边界分支搜索，且存在闭式候选解。作为基准，我们允许传感器联合动作间的时间共享，并证明最多两种帕累托极端模式即足够，且用此基准量化独立随机化造成的损失。数值结果表明，仅具备MPR能力并不足够；仅当对两个源的并发接收均可靠时，联合解码才能提升面向任务的目标；否则，避免同时传输的策略可达到同等效果。
英文摘要
This paper studies the real-time reconstruction and remote actuation of two binary Markov sources over a shared wireless channel with multi-packet reception (MPR). Unlike many existing collision-based formulations that discard simulta- neous transmissions, we exploit MPR and evaluate communica- tion through reconstruction and actuation errors rather than raw delivery rates. We consider two sensors observing the sources and aim to find sampling policies that minimize the weighted real- time reconstruction error (RTE), or equivalently the weighted cost of actuation error (CAE) for the considered binary sources, under per-sensor sampling constraints. We first obtain closed- form expressions for the RTE and CAE in terms of the effective update probabilities. When the sensors randomize independently, the MPR-induced update-rate map becomes bilinear, and the constrained optimization is nonconvex. We exploit the geometry of the achievable update-rate region to show that the search over Pareto-efficient independently randomized policies reduces to a finite set of one-dimensional boundary-branch searches with closed-form candidates. As a benchmark, we allow time sharing among joint sensor actions, and we prove that at most two Pareto- extreme modes are sufficient, and use this benchmark to quantify the loss caused by independent randomization. Numerical results reveal that MPR capability alone is not sufficient; simultaneous decoding improves the task-oriented objective only when con- current reception is reliable for both sources; otherwise, policies that avoid simultaneous transmissions can be equally effective.
