Capacity-achieving probability measure for conditionally Gaussian channels with bounded inputs

  • Authors:
  • T. H. Chan;S. Hranilovic;F. R. Kschischang

  • Affiliations:
  • Dept. of Comput. Sci., Univ. of Regina, Sask., Canada;-;-

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2005

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Abstract

A conditionally Gaussian channel is a vector channel in which the channel output, given the channel input, has a Gaussian distribution with (well-behaved) input-dependent mean and covariance. We study the capacity-achieving probability measure for conditionally Gaussian channels subject to bounded-input constraints and average cost constraints. Many practical communication systems, including additive Gaussian noise channels, certain optical channels, fading channels, and interference channels fall within this framework. Subject to bounded-input constraint (and average cost constraints), we show that the channel capacity is achievable and we derive a necessary and sufficient condition for a probability measure to be capacity achieving. Under certain conditions, the capacity-achieving measure is proved to be discrete.