A Kashin Approach to the Capacity of the Discrete Amplitude Constrained Gaussian Channel

@inproceedings{Farrell2010AKA,
  title={A Kashin Approach to the Capacity of the Discrete Amplitude Constrained Gaussian Channel},
  author={Brendan Farrell and Peter Jung and Heinrich-Hertz Lehrstuhl},
  year={2010}
}
We derive an explicit lower bound on the capacity of the discrete amplitude–constrained Gaussian channel by proving the existence of tight frames that permit redundant vector representations with small coefficients. Our method encodes the information in subspaces that are optimal in terms of the power to amplitude ratio. In a recent paper, Lyubarskii and Vershynin discuss how the work of Kashin (1977) implies the existence of such representations, and they term them Kashin respresentations. We… CONTINUE READING

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