arXiv subjects

A. V. Reznichenko

Publications and source records attributed to A. V. Reznichenko.

12 recordsLinked to original sources

arXiv2023

Path-integral approach to mutual information calculation for nonlinear communication channel with small second dispersion at large signal-to-noise power ratio

We consider the information fiber optical channel modeled by the nonlinear Schrodinger equation with additive Gaussian noise. Using path-integral approach and perturbation theory for the small dimensionless parameter of the second dispersion, we calculate the conditional probability density functional in the leading and next-to-leading order in the dimensionless second dispersion parameter associated with the input signal bandwidth. Taking into account specific filtering of the output signal by the output signal receiver, we calculate the mutual information in the leading and next-to-leading order in the dispersion parameter and in the leading order in the parameter signal-to-noise ratio (SNR). Further, we find the explicit expression for the mutual information in case of the modified Gaussian input signal distribution taking into account the limited frequency bandwidth of the input signal.

cs.IT↗

arXiv2021

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

We consider the information channel described by 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 large signal-to-noise power ratio we calculate the conditional entropy, the output signal entropy, and the mutual information in the leading and next-to-leading order in the nonlinearity parameter and in the leading order in the parameter $1/\mathrm{SNR}$. 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.

cs.IT↗

arXiv2018

Investigation of Nonlinear Communication Channel with Small Dispersion via Stochastic Correlator Approach

We consider the optical fiber channel modelled by the nonlinear Schrödinger equation with additive white Gaussian noise and with large signal-to-noise ratio. For the small dispersion case we present the approach to analyze the stochastic nonlinear Schrödinger equation. Taking into account the averaging procedure (frequency filtering) of the output signal detector we find the first corrections in small dispersion parameter to the correlators of the input signal recovered by the backward propagation. These correlators are the important ingredients for the calculation of the channel capacity and the optimal input signal distribution. We assert that the information channel characteristics essentially depend on the procedures of the output signal filtering and the recovery of the transmitted signal.

cs.IT↗

arXiv2018

The $\log\log$ growth of channel capacity for nondispersive nonlinear optical fiber channel in intermediate power range. Extension of the model

In our previous paper [Phys. Rev. E 95, 062122 (2017)] we considered the optical channel modelled by the nonlinear Schrödinger equation with zero dispersion and additive Gaussian noise. We found per-sample channel capacity rof this model. In the present paper we extend per-sample model by introducing the initial signal dependence on time and the output signal detection procedure. The proposed model is a closer approximation of the realistic communication link than the per-sample model where there is no dependence of the initial signal on time. For the proposed model we found the correlators of the output signal both analytically and numerically. Using these correlators we built the conditional probability density function. Then we calculated an entropy of the output signal, a conditional entropy, and the mutual information. Maximizing the mutual information we found the optimal input signal distribution, channel capacity? and their dependence on the shape or the initial signal in the time domain for the intermediate power range.

cs.IT↗

arXiv2016

Next-to-leading order corrections to capacity for nondispersive nonlinear optical fiber channel in intermediate power region

We consider the optical fiber channel modelled by the nonlinear Shrödinger equation with zero dispersion and additive Gaussian noise. Using Feynman path-integral approach for the model we find corrections to conditional probability density function, output signal distribution, conditional and output signal entropies, and the channel capacity at large signal-to-noise ratio. We demonstrate that the correction to the channel capacity is positive for large signal power. Therefore, this correction increases the earlier calculated capacity for a nondispersive nonlinear optical fiber channel in the intermediate power region.

cs.IT↗

arXiv2016

Mutual information in nonlinear communication channel. Preliminary analytical results in large SNR and small nonlinearity limit

Applying perturbation theory to the path-integral representation for the mutual information of the nonlinear communication channel described by the nonlinear Shrödinger equation (NLSE) with the additive Gaussian noise we analyze the analytical expression for the mutual information at large signal-to-noise ratio ($\mathrm{SNR}$) and small nonlinearity. We classify all possible corrections to the mutual information in nonlinearity parameter and demonstrate that all singular in $\mathrm{SNR}$ terms vanish in the final result. Furthermore our analytical result demonstrates that the corrections to Shannon's contribution to the mutual information in the leading order in $\mathrm{SNR}$ are of order of squared nonlinearity parameter. We outline the way for the calculation of these corrections in the further investigations.

cs.IT↗

arXiv2016

Calculation of mutual information for nonlinear communication channel at large SNR

Using the path-integral technique we examine the mutual information for the communication channel modelled by the nonlinear Schrödinger equation with additive Gaussian noise. The nonlinear Schrödinger equation is one of the fundamental models in nonlinear physics, and it has a broad range of applications, including fiber optical communications --- the backbone of the Internet. At large signal-to-noise ratio ($\mathrm{SNR}$) we present the mutual information through the path-integral which is convenient for the perturbative expansion in nonlinearity. In the limit of small noise and small nonlinearity we derive analytically the first nonzero nonlinear correction to the mutual information for the channel.

cs.IT↗

arXiv2016

Optimal input signal distribution and per-sample mutual information for nondispersive nonlinear optical fiber channel at large SNR

We consider a model nondispersive nonlinear optical fiber channel with additive white Gaussian noise at large $\mathrm{SNR}$ (signal-to-noise ratio) in the intermediate power region. Using Feynman path-integral technique we for the first time find the optimal input signal distribution maximizing the channel's per-sample mutual information. The finding of the optimal input signal distribution allows us to improve previously known estimates for the channel capacity. The output signal entropy, conditional entropy, and per-sample mutual information are calculated for Gaussian, half-Gaussian and modified Gaussian input signal distributions. We explicitly show that in the intermediate power regime the per-sample mutual information for the optimal input signal distribution is greater than the per-sample mutual information for the Gaussian and half-Gaussian input signal distributions.

cs.IT↗

arXiv2015

Gluon Reggeization in Yang-Mills Theories

The proof of the multi-Regge form of multiple production amplitudes in the next-to-leading logarithmic approximation is presented for Yang-Mills theories with fermions and scalars in any representations of the colour group and with any Yukawa-type interaction. Explicit expressions for the Reggeized gauge boson trajectory, the Reggeon vertices and the impact factors are given. Fulfilment of the bootstrap conditions is proved.

hep-th↗

arXiv2015

Effective vertex of quark production in collision of Reggeized quark and gluon

We calculated the effective vertex of the quark production in the collision of Reggeized quark and Reggeized gluon in the next-to-leading order (NLO). The vertex in question is the missing component of the multi-Regge NLO amplitudes with the quark and gluon exchanges in $t_i$ channels. The calculation allows us to develop the bootstrap approach to the quark Reggeization proof within next-to-leading logarithmic approximation.

hep-ph↗

arXiv2006

Proof of the multi-Regge form of QCD amplitudes with gluon exchanges in the NLA

The multi--Regge form of QCD amplitudes with gluon exchanges is proved in the next-to-leading approximation. The proof is based on the bootstrap relations, which are required for the compatibility of this form with the s-channel unitarity. We show that the fulfillment of all these relations ensures the Reggeized form of energy dependent radiative corrections order by order in perturbation theory. Then we prove that all these relations are fulfilled if several bootstrap conditions on the Reggeon vertices and trajectory hold true. Now all these conditions are checked and proved to be satisfied.

hep-ph↗

arXiv2003

Radiative Corrections to QCD Amplitudes in Quasi-Multi-Regge Kinematics

Radiative corrections to QCD amplitudes in the quasi-multi-Regge kinematics are interesting in particular since the Reggeized form of these amplitudes is used in the derivation of the NLO BFKL. This form is a hypothesis which must be at least carefully checked, if not proved. We calculate the radiative corrections in the one-loop approximation using the s-channel unitarity. Compatibility of the Reggeized form of the amplitudes with the s-channel unitarity requires fulfillment of the set of nonlinear equations for the Reggeon vertices. We show that these equations are satisfied.

hep-ph↗