TY - JOUR

T1 - Optimal input signal distribution for a nonlinear optical fiber channel with small Kerr nonlinearity

AU - Reznichenko, A. V.

AU - Chernykh, A. I.

AU - Sedov, E. V.

AU - Terekhov, I. S.

N1 - Funding Information:
Acknowledgment. The work of A.V. Reznichenko was supported by the Ministry of Education and Science of the Russian Federation. The work of I.S. Terekhov and E.V. Sedov was supported by the RSF.
Funding Information:
Funding. Russian Science Foundation (17-72-30006).
Publisher Copyright:
© 2022 Optica Publishing Group.

PY - 2022/3

Y1 - 2022/3

N2 - We consider the information channel described by the Schrödinger equation with additive Gaussian noise. We introduce the model of the input signal and the model of the output signal receiver. For this channel, using perturbation theory for the small nonlinearity parameter, we calculate the first three terms of the expansion of the conditional probability density function in the nonlinearity parameter. At a large signal-to-noise power ratio, we calculate the conditional entropy, output signal entropy, and mutual information in the leading and next-to-leading order in the nonlinearity parameter and in the leading order in the parameter 1/SNR. Using the mutual information, we find the optimal input signal distribution and channel capacity in the leading and next-to-leading order in the nonlinearity parameter. Finally, we present the method of the construction of the input signal with the optimal statistics for the given shape of the signal.

AB - We consider the information channel described by the Schrödinger equation with additive Gaussian noise. We introduce the model of the input signal and the model of the output signal receiver. For this channel, using perturbation theory for the small nonlinearity parameter, we calculate the first three terms of the expansion of the conditional probability density function in the nonlinearity parameter. At a large signal-to-noise power ratio, we calculate the conditional entropy, output signal entropy, and mutual information in the leading and next-to-leading order in the nonlinearity parameter and in the leading order in the parameter 1/SNR. Using the mutual information, we find the optimal input signal distribution and channel capacity in the leading and next-to-leading order in the nonlinearity parameter. Finally, we present the method of the construction of the input signal with the optimal statistics for the given shape of the signal.

UR - http://www.scopus.com/inward/record.url?scp=85125436520&partnerID=8YFLogxK

UR - https://www.elibrary.ru/item.asp?id=48185888

UR - https://www.mendeley.com/catalogue/c6aa186c-9340-3aee-9e62-e83ef1f9e0cc/

U2 - 10.1364/JOSAB.445376

DO - 10.1364/JOSAB.445376

M3 - Article

AN - SCOPUS:85125436520

VL - 39

SP - 810

EP - 820

JO - Journal of the Optical Society of America B: Optical Physics

JF - Journal of the Optical Society of America B: Optical Physics

SN - 0740-3224

IS - 3

ER -