Inference-Aware Reconstruction for Short-Packet Transmission in Industrial Metaverse

Industrial metaverse aims to build an immersive virtual space that can interact with physical space in real-time. Accurate reconstruction of the time-varying physical processes in virtual space is crucial to the realization of industrial metaverse, especially under short-packet transmission (SPT). In this paper, we investigate the suitability of inferring the real-time data of a sensor from the spatially correlated sensor data for SPT in industrial metaverse, in the presence of transmission delay and error as well as imperfect spatial correlation among data. Closed-form expressions for the average mean squared error (MSE) with and without inference are derived. Also, a tight approximation for the average MSE with inference is presented. A closed-form threshold that the inference-aware reconstruction outperforms the case without inference is derived in terms of the average received SNR. Simulation results verify the analytical results and demonstrate that the inference-aware reconstruction enables an average MSE reduction of 32% over the case without inference, and is suitable to the scenarios with low average received SNR, long period, short blocklength and strong mean squared spatial correlation.