The problem of real-time remote tracking and reconstruction of a two-state Markov process is considered here. A transmitter sends samples from an observed information source to a remote monitor over an unreliable wireless channel. The receiver, in turn, performs an action according to the state of the reconstructed source. We propose a state-aware randomized stationary sampling and transmission policy which accounts for the importance of different states of the information source, and their impact on the goal of the communication process. We then analyze the performance of the proposed policy, and compare it with existing goal-oriented joint sampling and transmission policies, with respect to a set of performance metrics. Specifically, we study the real-time reconstruction error, the cost of actuation error, the consecutive error, and a new metric, coined importance-aware consecutive error. In addition, we formulate and solve a constrained optimization problem that aims to obtain the optimal sampling probabilities that minimize the average cost of actuation error. Our results show that in the scenario of constrained sampling generation, the optimal state-aware randomized stationary policy outperforms all other sampling policies for fast evolving sources, and, under certain conditions, for slowly varying sources. Otherwise, a semantics-aware policy performs better only when the source is slowly varying.

翻译：本文研究了双状态马尔可夫过程的实时远程跟踪与重建问题。发射机通过不可靠无线信道将观测信息源的样本发送至远程监控端，接收机根据重建信源的状态执行相应动作。我们提出了一种状态感知的随机平稳采样与传输策略，该策略考虑了信息源不同状态的重要性及其对通信过程目标的潜在影响。随后，我们从一组性能指标角度分析了所提策略的性能，并将其与现有面向目标的联合采样与传输策略进行了比较。具体而言，我们研究了实时重建误差、执行错误代价、连续错误率，以及一种新型指标——重要性感知连续错误率。此外，我们构建并求解了一个约束优化问题，旨在获得使平均执行错误代价最小化的最优采样概率。结果表明，在受限采样生成场景下，所提最优状态感知随机平稳策略在快速演变信源中优于所有其他采样策略；在特定条件下，该策略对慢速变化信源同样表现更优。否则，语义感知策略仅在信源缓慢变化时表现更佳。