Optimal Linear Joint Source-Channel Coding with Delay Constraint
(2012) In IEEE Transactions on Information Theory- Abstract
- The problem of joint source-channel coding is considered for a stationary remote (noisy) Gaussian source and a Gaussian channel. The encoder and decoder are assumed to be causal and their combined operations are subject to a delay constraint. It is shown that, under the mean-square error distortion metric, an optimal encoder-decoder pair from the linear and time-invariant (LTI) class can be found by minimization of a convex functional and a spectral factorization. The functional to be minimized is the sum of the well-known cost in a corresponding Wiener filter problem and a new term, which is induced by the channel noise and whose coefficient is the inverse of the channel's signal-to-noise ratio. This result is shown to also hold in the... (More)
- The problem of joint source-channel coding is considered for a stationary remote (noisy) Gaussian source and a Gaussian channel. The encoder and decoder are assumed to be causal and their combined operations are subject to a delay constraint. It is shown that, under the mean-square error distortion metric, an optimal encoder-decoder pair from the linear and time-invariant (LTI) class can be found by minimization of a convex functional and a spectral factorization. The functional to be minimized is the sum of the well-known cost in a corresponding Wiener filter problem and a new term, which is induced by the channel noise and whose coefficient is the inverse of the channel's signal-to-noise ratio. This result is shown to also hold in the case of vector-valued signals, assuming parallel additive white Gaussian noise channels. It is also shown that optimal LTI encoders and decoders generally require infinite memory, which implies that approximations are necessary.
A numerical example is provided, which compares the performance to the lower bound provided by rate-distortion theory. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/2430825
- author
- Johannesson, Erik LU ; Rantzer, Anders LU ; Bernhardsson, Bo LU and Ghulchak, Andrey LU
- organization
- publishing date
- 2012
- type
- Contribution to journal
- publication status
- submitted
- subject
- keywords
- Analog transmission, causal coding, delay constraint, joint source-channel coding, MSE distortion, remote source, signal-to-noise ratio (SNR).
- in
- IEEE Transactions on Information Theory
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- ISSN
- 0018-9448
- project
- LCCC
- language
- English
- LU publication?
- yes
- additional info
- Submitted to IEEE Transactions on Information Theory on March 28th 2012. month=March
- id
- a29c71c1-4de9-429d-923b-5652e7d86bbc (old id 2430825)
- date added to LUP
- 2016-04-04 13:55:11
- date last changed
- 2021-04-06 15:28:29
@article{a29c71c1-4de9-429d-923b-5652e7d86bbc, abstract = {{The problem of joint source-channel coding is considered for a stationary remote (noisy) Gaussian source and a Gaussian channel. The encoder and decoder are assumed to be causal and their combined operations are subject to a delay constraint. It is shown that, under the mean-square error distortion metric, an optimal encoder-decoder pair from the linear and time-invariant (LTI) class can be found by minimization of a convex functional and a spectral factorization. The functional to be minimized is the sum of the well-known cost in a corresponding Wiener filter problem and a new term, which is induced by the channel noise and whose coefficient is the inverse of the channel's signal-to-noise ratio. This result is shown to also hold in the case of vector-valued signals, assuming parallel additive white Gaussian noise channels. It is also shown that optimal LTI encoders and decoders generally require infinite memory, which implies that approximations are necessary.<br/><br> A numerical example is provided, which compares the performance to the lower bound provided by rate-distortion theory.}}, author = {{Johannesson, Erik and Rantzer, Anders and Bernhardsson, Bo and Ghulchak, Andrey}}, issn = {{0018-9448}}, keywords = {{Analog transmission; causal coding; delay constraint; joint source-channel coding; MSE distortion; remote source; signal-to-noise ratio (SNR).}}, language = {{eng}}, publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}}, series = {{IEEE Transactions on Information Theory}}, title = {{Optimal Linear Joint Source-Channel Coding with Delay Constraint}}, url = {{https://lup.lub.lu.se/search/files/6236590/2430827.pdf}}, year = {{2012}}, }