A Gaussian input is not too bad

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Abstract

We consider the problem of choosing a robust input for communicating over an input constrained additive-noise channel where the noise distribution is arbitrary. We show that the mutual information rate achievable using a white Gaussian input never incurs a loss of more than half a bit per sample with respect to the power constrained capacity. For comparison, for the family of colored Gaussian noise channels a white Gaussian input loses at most log (e) / 2e ≈ 0.265 bit per sample with respect to the optimum water-pouring solution. For general input constraints, we derive a formula for choosing the best input in the min-max capacity loss (bound) sense. The bound on the capacity loss is tight for pulse position modulation (PPM) in the presence of a bursty jammer.

Original languageEnglish
Pages (from-to)1362-1367
Number of pages6
JournalIEEE Transactions on Information Theory
Volume50
Issue number6
DOIs
StatePublished - Jun 2004

Keywords

  • Gaussian codebook
  • Min-max rate loss
  • Unknown channels
  • White versus water-pouring spectrum

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