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Optimal Linear Joint Source-Channel Coding with Delay Constraint

Johannesson, Erik LU ; Rantzer, Anders LU orcid ; Bernhardsson, Bo LU orcid and Ghulchak, Andrey LU (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)
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author
; ; and
organization
publishing date
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}},
}