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

25th Annual International Laser Physics Workshop

Reznichenko, A.V.^1,2 ; Terekhov, I.S.^1,2 ; Turitsyn, S.K.^2,3

Theory Department, Budker Institute of Nuclear Physics of Siberian Branch Russian, Academy of Sciences, Novosibirsk

630090, Russia^1

Novosibirsk State University, Novosibirsk

630090, Russia^2

Aston Institute of Photonics Technologies, Aston University, Aston Triangle, Birmingham

B4 7ET, United Kingdom^3

关键词: Additive Gaussian noise;    Conditional probability density;    Jensen's inequality;    Non-linear optical fibers;    Nonlinear correction;    Normalization factors;    Perturbative expansion;    Small nonlinearities;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/826/1/012026/pdf
DOI  :  10.1088/1742-6596/826/1/012026

来源: IOP

【 摘 要 】

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.