Coded Kalman Filtering Over Gaussian Channels with Feedback

Barron Han, Oron Sabag, Victoria Kostina, Babak Hassibi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

This paper investigates the problem of zero-delay joint source-channel coding of a vector Gauss-Markov source over a multiple-input mulitple-output (MIMO) additive white Gaussian noise (AWGN) channel with feedback. In contrast to the classical problem of causal estimation using noisy observations, we examine a system where the source can be encoded before transmission. An encoder, equipped with feedback of past channel outputs, observes the source state and encodes the information in a causal manner as inputs to the channel while adhering to a power constraint. The objective of the code is to estimate the source state with minimum mean square error at the infinite horizon. This work shows a fundamental theorem for two scenarios: for the transmission of an unstable vector Gauss-Markov source over either a multiple-input single-output (MISO) or a single-input multiple-output (SIMO) AWGN channel, finite estimation error is achievable if and only if the sum of the unstable eigenvalues of the state gain matrix is less than the Shannon channel capacity. We prove these results by showing an optimal linear innovations encoder that can be applied to sources and channels of any dimension and analyzing it together with the corresponding Kalman filter decoder.

Original languageAmerican English
Title of host publication2023 59th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2023
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9798350328141
DOIs
StatePublished - 2023
Event59th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2023 - Monticello, United States
Duration: 26 Sep 202329 Sep 2023

Publication series

Name2023 59th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2023

Conference

Conference59th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2023
Country/TerritoryUnited States
CityMonticello
Period26/09/2329/09/23

Keywords

  • feedback
  • joint source channel coding
  • Kalman filter
  • Shannon capacity

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Computational Theory and Mathematics
  • Computer Networks and Communications
  • Computer Science Applications
  • Computational Mathematics
  • Control and Optimization

Fingerprint

Dive into the research topics of 'Coded Kalman Filtering Over Gaussian Channels with Feedback'. Together they form a unique fingerprint.

Cite this