In this work, we study the problem of real-time tracking and reconstruction of an information source with the purpose of actuation. A device monitors an $N$-state Markov process and transmits status updates to a receiver over a wireless erasure channel. We consider a set of joint sampling and transmission policies, including a semantics-aware one, and we study their performance with respect to relevant metrics. Specifically, we investigate the real-time reconstruction error and its variance, the consecutive error, the cost of memory error, and the cost of actuation error. Furthermore, we propose a randomized stationary sampling and transmission policy and derive closed-form expressions for all aforementioned metrics. We then formulate an optimization problem for minimizing the real-time reconstruction error subject to a sampling cost constraint. Our results show that in the scenario of constrained sampling generation, the optimal randomized stationary policy outperforms all other sampling policies when the source is rapidly evolving. Otherwise, the semantics-aware policy performs the best.

翻译：本文研究了以驱动为目的的信息源实时跟踪与重构问题。设备监测一个$N$状态马尔可夫过程，并通过无线擦除信道向接收器传输状态更新。我们考虑了一组联合采样与传输策略（包括语义感知策略），并研究了它们在与相关指标下的性能。具体而言，我们探究了实时重构误差及其方差、连续误差、记忆误差成本以及驱动误差成本。此外，我们提出了一种随机静态采样与传输策略，并推导了上述所有指标的闭式表达式。随后，我们构建了一个优化问题，旨在采样成本约束下最小化实时重构误差。结果表明，在采样生成受限的场景中，当信源快速演化时，最优随机静态策略优于所有其他采样策略；反之，语义感知策略表现最佳。