Real-Time Reconstruction and Actuation Error Analysis for Markov Sources over MPR Channels

2026-05-15

AI Summary

This work addresses the problem of real-time state reconstruction and actuation control for two binary Markov sources sharing a wireless multi-packet reception (MPR) channel. The authors propose a stochastic sampling policy that maintains state estimates based on the most recently decoded updates and derive closed-form expressions for the steady-state reconstruction and actuation errors, explicitly linking physical-layer MPR characteristics to task-oriented semantic error metrics. Building upon this analytical foundation, they formulate a constrained optimization problem with weighted error objectives to investigate how source dynamics, semantic priorities, and channel coupling jointly govern optimal sampling resource allocation. Numerical experiments demonstrate that the proposed strategy significantly outperforms baseline approaches, including random, greedy, and time-division multiplexing schemes.

Abstract

We study real-time reconstruction and actuation for two binary Markov sources that share a wireless multi-packet reception (MPR) channel. Each sensor follows a stationary randomized sampling policy, and the receiver maintains source estimates using the most recently decoded updates. We derive closed-form expressions for the steady-state real-time reconstruction error (RTE) and the cost of actuation error (CAE) as functions of the source transition probabilities and the effective update probabilities. We then characterize these update probabilities under randomized sampling, linking the physical-layer MPR model to task-oriented reconstruction and actuation metrics. Using these expressions, we formulate a sampling-constrained optimization problem with a weighted-error objective. The resulting analysis reveals how source dynamics, semantic weights, and MPR coupling affect the allocation of sampling resources. Numerical results show that optimized randomized sampling outperforms random, greedy, and time-sharing baselines.

Problem

• real-time reconstruction
• actuation error
• Markov sources
• multi-packet reception
• wireless channel

Innovation

• real-time reconstruction
• actuation error
• multi-packet reception (MPR)
• Markov sources
• randomized sampling