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端发送状态更新。我们考虑了一组联合采样与传输策略（包括一种语义感知策略），并针对相关指标研究其性能。具体而言，我们探究了实时重构误差及其方差、连续误差、记忆代价误差以及驱动代价误差。此外，我们提出一种随机平稳采样与传输策略，并推导出上述所有指标的闭式表达式。随后，我们构建一个在采样代价约束下最小化实时重构误差的优化问题。结果表明，在采样生成受限场景下，当信源快速演化时，最优随机平稳策略优于所有其他采样策略；反之，语义感知策略性能最优。