Performance Bounds of Joint Detection with Kalman Filtering and Channel Decoding for Wireless Networked Control Systems

TL;DR

This paper derives theoretical bounds for joint detection in wireless control systems using Kalman filtering and channel decoding, highlighting the performance limits and benefits of specific coding schemes.

Contribution

It introduces new bounds for MAP decoding in joint detection, considering system interference and packet loss, and validates them through simulations.

Findings

MAP bounds match the limiting upper bound at high SNR

Polar codes with CRC achieve 3.0 dB gain at BER 10^{-3}

Bounds effectively describe packet loss behavior in control systems

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 $10^{-3}$.