On Properties of the Support of Capacity-Achieving Distributions for Additive Noise Channel Models With Input Cost Constraints

@article{Fahs2018OnPO,
  title={On Properties of the Support of Capacity-Achieving Distributions for Additive Noise Channel Models With Input Cost Constraints},
  author={Jihad Fahs and Ibrahim C. Abou-Faycal},
  journal={IEEE Transactions on Information Theory},
  year={2018},
  volume={64},
  pages={1178-1198}
}
We study the classical problem of characterizing the channel capacity and its achieving distribution in a generic fashion. We derive a simple relation between three parameters: the input–output function, the input cost function, and the noise probability density function, one which dictates the type of the optimal input. In layman terms, we prove that the support of the optimal input is bounded whenever the cost grows faster than a “cutoff” growth rate equal to the logarithm of the inverse of… CONTINUE READING