Performance Bounds of Joint Detection with Kalman Filtering and Channel Decoding for Wireless Networked Control Systems
🤖 AI Summary
This work addresses the unclear performance limits of joint detection in wireless networked control systems, particularly the absence of theoretical bounds that jointly account for system interference, quantization intervals, and weight distributions. The authors model joint detection as maximum a posteriori (MAP) decoding, leveraging Kalman filter estimates of control outputs to inform prior probabilities for decoding. They introduce, for the first time, an infinite-state Markov chain to characterize the packet loss process and derive upper and lower bounds on MAP performance that explicitly incorporate interference and quantization effects. Through pairwise error probability analysis and a polar code–CRC concatenated design, simulations demonstrate that a (64,16) polar code with a 16-bit CRC achieves a 3.0 dB gain over finite-blocklength normal approximations at a block error rate of 10⁻³, with performance approaching the derived theoretical upper bound as SNR increases.
Application Category
📝 Abstract
The joint detection uses Kalman filtering (KF) to estimate the prior probability of control outputs to assist channel decoding. In this paper, we regard the joint detection as maximum a posteriori (MAP) decoding and derive the lower and upper bounds based on the pairwise error probability considering system interference, quantization interval, and weight distribution. We first derive the limiting bounds as the signal-to-noise ratio (SNR) goes to infinity and the system interference goes to zero. Then, we construct an infinite-state Markov chain to describe the consecutive packet losses of the control systems to derive the MAP bounds. Finally, the MAP bounds are approximated as the bounds of the transition probability from the state with no packet loss to the state with consecutive single packet loss. The simulation results show that the MAP performance of $\left(64,16\right)$ polar code and 16-bit CRC coincides with the limiting upper bound as the SNR increases and has $3.0$dB performance gain compared with the normal approximation of the finite block rate at block error rate $10^{-3}$.
Problem
Research questions and friction points this paper is trying to address.
Wireless Networked Control Systems
Joint Detection
Kalman Filtering
Channel Decoding
Performance Bounds
Innovation
Methods, ideas, or system contributions that make the work stand out.
Joint Detection
MAP Decoding
Performance Bounds
Infinite-State Markov Chain
Polar Codes
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