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Optimal Linear Joint Source-Channel Coding with Delay Constraint

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Author

Summary, in English

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.

Publishing year

2012

Language

English

Publication/Series

IEEE Transactions on Information Theory

Document type

Journal article

Publisher

IEEE - Institute of Electrical and Electronics Engineers Inc.

Topic

  • Mathematics
  • Computer Vision and Robotics (Autonomous Systems)
  • Control Engineering

Keywords

  • Analog transmission
  • causal coding
  • delay constraint
  • joint source-channel coding
  • MSE distortion
  • remote source
  • signal-to-noise ratio (SNR).

Status

Submitted

Project

  • LCCC

Research group

  • LCCC

ISBN/ISSN/Other

  • ISSN: 0018-9448