Calculation of mutual information for nonlinear optical fiber communication channel at large SNR within path-integral formalism

A.V. Reznichenko; Ivan S. Terekhov; Sergei K. Turitsyn

doi:10.1088/1742-6596/826/1/012026

Calculation of mutual information for nonlinear optical fiber communication channel at large SNR within path-integral formalism

A.V. Reznichenko, Ivan S. Terekhov, Sergei K. Turitsyn

Research output: Contribution to journal › Article › peer-review

Abstract

Using the path-integral technique we calculate the mutual information for the fiber optical channel modelled by the nonlinear Schrö dinger equation with additive Gaussian noise. At large signal-to-noise ratio (SNR) we present the mutual information through the path-integral which is convenient for the perturbative expansion both in nonlinearity and dispersion. In the leading order in 1/SNR we demonstrate that the mutual information is determined through the averaged logarithm of the normalization factor Λ of the conditional probability density function P[Y|X]. In the limit of small noise and small nonlinearity we derive analytically the first nonzero nonlinear correction to the mutual information for the channel. For the arbitrary nonlinearity we restrict the mutual information by the low bound obtained from the Jensen's inequality and analyze the bound for the case of large dispersion.

Original language	English
Article number	012026
Number of pages	10
Journal	Journal of Physics: Conference Series
Volume	826
Issue number	1
DOIs	https://doi.org/10.1088/1742-6596/826/1/012026
Publication status	Published - 20 Apr 2017
Event	25th Annual International Laser Physics Workshop (LPHYS 2016) - Elite Plaza Business Center & Best Western Congress Hotel, Yerevan, Armenia Duration: 10 Jul 2016 → 15 Jul 2016 http://www.lasphys.com/workshops/

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Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by IOP Publishing Ltd.

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10.1088/1742-6596/826/1/012026Licence: CC BY 3.0

Nonlinear optical fiber communication channel at large SNR within path-integral formalism
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by IOP Publishing Ltd.
Final published version, 525 KBLicence: CC BY 3.0

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title = "Calculation of mutual information for nonlinear optical fiber communication channel at large SNR within path-integral formalism",

abstract = "Using the path-integral technique we calculate the mutual information for the fiber optical channel modelled by the nonlinear Schr{\"o} dinger equation with additive Gaussian noise. At large signal-to-noise ratio (SNR) we present the mutual information through the path-integral which is convenient for the perturbative expansion both in nonlinearity and dispersion. In the leading order in 1/SNR we demonstrate that the mutual information is determined through the averaged logarithm of the normalization factor Λ of the conditional probability density function P[Y|X]. In the limit of small noise and small nonlinearity we derive analytically the first nonzero nonlinear correction to the mutual information for the channel. For the arbitrary nonlinearity we restrict the mutual information by the low bound obtained from the Jensen's inequality and analyze the bound for the case of large dispersion.",

author = "A.V. Reznichenko and Terekhov, {Ivan S.} and Turitsyn, {Sergei K.}",

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AU - Reznichenko, A.V.

AU - Terekhov, Ivan S.

AU - Turitsyn, Sergei K.

N1 - Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by IOP Publishing Ltd.

PY - 2017/4/20

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N2 - Using the path-integral technique we calculate the mutual information for the fiber optical channel modelled by the nonlinear Schrö dinger equation with additive Gaussian noise. At large signal-to-noise ratio (SNR) we present the mutual information through the path-integral which is convenient for the perturbative expansion both in nonlinearity and dispersion. In the leading order in 1/SNR we demonstrate that the mutual information is determined through the averaged logarithm of the normalization factor Λ of the conditional probability density function P[Y|X]. In the limit of small noise and small nonlinearity we derive analytically the first nonzero nonlinear correction to the mutual information for the channel. For the arbitrary nonlinearity we restrict the mutual information by the low bound obtained from the Jensen's inequality and analyze the bound for the case of large dispersion.

AB - Using the path-integral technique we calculate the mutual information for the fiber optical channel modelled by the nonlinear Schrö dinger equation with additive Gaussian noise. At large signal-to-noise ratio (SNR) we present the mutual information through the path-integral which is convenient for the perturbative expansion both in nonlinearity and dispersion. In the leading order in 1/SNR we demonstrate that the mutual information is determined through the averaged logarithm of the normalization factor Λ of the conditional probability density function P[Y|X]. In the limit of small noise and small nonlinearity we derive analytically the first nonzero nonlinear correction to the mutual information for the channel. For the arbitrary nonlinearity we restrict the mutual information by the low bound obtained from the Jensen's inequality and analyze the bound for the case of large dispersion.

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Calculation of mutual information for nonlinear optical fiber communication channel at large SNR within path-integral formalism

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