Stabilizing Error Correction Codes for Controlling LTI Systems over Erasure Channels

TL;DR

This paper introduces (k,k') stabilizing codes designed for control over erasure channels, ensuring system stability with fewer transmissions, and demonstrates their effectiveness through theoretical analysis and simulations.

Contribution

The paper presents a novel class of delayless stabilizing codes tailored for LTI systems over erasure channels, combining independent encodings and multiple descriptions.

Findings

Codes guarantee stability with any k' received symbols

Significant performance gains over repetition codes

Theoretical efficiency validated by simulation results

Abstract

We propose (k,k') stabilizing codes, which is a type of delayless error correction codes that are useful for control over networks with erasures. For each input symbol, k output symbols are generated by the stabilizing code. Receiving any k' of these outputs guarantees stability. Thus, the system to be stabilized is taken into account in the design of the erasure codes. Our focus is on LTI systems, and we construct codes based on independent encodings and multiple descriptions. The theoretical efficiency and performance of the codes are assessed, and their practical performances are demonstrated in a simulation study. There is a significant gain over other delayless codes such as repetition codes.