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Optimal Linear Joint Source-Channel Coding with Delay Constraint

Johannesson, Erik LU ; Rantzer, Anders LU ; Bernhardsson, Bo LU 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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organization
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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
id
a29c71c1-4de9-429d-923b-5652e7d86bbc (old id 2430825)
date added to LUP
2012-04-02 15:25:30
date last changed
2016-04-16 11:51:04
@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},
  keyword      = {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},
  year         = {2012},
}