Inference-Aware State Reconstruction for Industrial Metaverse Under Synchronous/Asynchronous Short-Packet Transmission

We consider a real-time state reconstruction system for industrial metaverse. The time-varying physical process states in real space are captured by multiple sensors via wireless links, and then reconstructed in virtual space. In this paper, we use the spatial-temporal correlation of the sensor data of interest to infer the real-time data of the target sensor to reduce the mean squared error (MSE) of reconstruction for industrial metaverse under short-packet transmission (SPT). Both synchronous and asynchronous transmission modes for multiple sensors are considered. It is proved that the average reconstruction MSE and average block error probability (BLEP) have a positive correlation under inference with synchronous transmission scheme, whereas they have a negative correlation under inference with asynchronous transmission scheme in certain conditions. Additionally, the average reconstruction MSE decreases monotonically with the mean squared spatial correlation (MSSC), which characterizes the global spatial correlation level. With a high BLEP or long transmission period, even under weak MSSC, the inference scheme still significantly reduces the average reconstruction MSE compared to the no inference case. Moreover, closed-form MSSC thresholds are derived for the superiority regions of the inference with synchronous transmission and inference with asynchronous transmission schemes, respectively. Adaptations of blocklength and time shift of asynchronous transmission are conducted to minimize the average reconstruction MSE. Simulation results show that the two inference schemes outperform the no inference case, with an average MSE reduction of more than 50%.