Real-Time Reconstruction of Markov Sources over MPR Channels

2026-08-27

AI Summary

研究利用多包接收技术实时重构二元马尔可夫源，通过优化采样策略最小化加权实时重构误差或执行误差。

Abstract

This paper studies the real-time reconstruction and remote actuation of two binary Markov sources over a shared wireless channel with multi-packet reception (MPR). Unlike many existing collision-based formulations that discard simulta- neous transmissions, we exploit MPR and evaluate communica- tion through reconstruction and actuation errors rather than raw delivery rates. We consider two sensors observing the sources and aim to find sampling policies that minimize the weighted real- time reconstruction error (RTE), or equivalently the weighted cost of actuation error (CAE) for the considered binary sources, under per-sensor sampling constraints. We first obtain closed- form expressions for the RTE and CAE in terms of the effective update probabilities. When the sensors randomize independently, the MPR-induced update-rate map becomes bilinear, and the constrained optimization is nonconvex. We exploit the geometry of the achievable update-rate region to show that the search over Pareto-efficient independently randomized policies reduces to a finite set of one-dimensional boundary-branch searches with closed-form candidates. As a benchmark, we allow time sharing among joint sensor actions, and we prove that at most two Pareto- extreme modes are sufficient, and use this benchmark to quantify the loss caused by independent randomization. Numerical results reveal that MPR capability alone is not sufficient; simultaneous decoding improves the task-oriented objective only when con- current reception is reliable for both sources; otherwise, policies that avoid simultaneous transmissions can be equally effective.

Problem

• Real-Time Reconstruction
• Multi-Packet Reception (MPR)
• Markov Sources
• Reconstruction Error
• Actuation Error

Innovation

• Multi-Packet Reception (MPR)
• Real-Time Reconstruction Error (RTE)
• Cost of Actuation Error (CAE)
• Pareto-Efficient Policies
• Simultaneous Decoding