Upper Bound on the Capacity of the Nonlinear Schr\"odinger Channel

Mansoor I. Yousefi; Gerhard Kramer; Frank R. Kschischang

Upper Bound on the Capacity of the Nonlinear Schr\"odinger Channel

Information Theory 2015-04-01 v2 math.IT

Authors: Mansoor I. Yousefi , Gerhard Kramer , Frank R. Kschischang

Abstract

It is shown that the capacity of the channel modeled by (a discretized version of) the stochastic nonlinear Schr\"odinger (NLS) equation is upper-bounded by $\log(1+\text{SNR})$ with $\text{SNR}=\mathcal P_0/\sigma^2(z)$ , where $\mathcal P_0$ is the average input signal power and $\sigma^2(z)$ is the total noise power up to distance $z$ . The result is a consequence of the fact that the deterministic NLS equation is a Hamiltonian energy-preserving dynamical system.

Keywords

channel capacity nonlinear Schrödinger channel capacity upper bound stochastic NLS equation Hamiltonian system energy preservation signal-to-noise ratio

Cite

@article{arxiv.1502.06455,
  title  = {Upper Bound on the Capacity of the Nonlinear Schr\"odinger Channel},
  author = {Mansoor I. Yousefi and Gerhard Kramer and Frank R. Kschischang},
  journal= {arXiv preprint arXiv:1502.06455},
  year   = {2015}
}

Comments

To be presented at the 14th Canadian Workshop on Information Theory (CWIT), St. John's, NL, Canada, July 6-9, 2015. This is the final version submitted to the CWIT 2015

Upper Bound on the Capacity of the Nonlinear Schr\"odinger Channel

Abstract

Keywords

Cite

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