TY - JOUR

T1 - New Approaches to Coding Information using Inverse Scattering Transform

AU - Frumin, L. L.

AU - Gelash, A. A.

AU - Turitsyn, S. K.

PY - 2017/5/31

Y1 - 2017/5/31

N2 - Remarkable mathematical properties of the integrable nonlinear Schrödinger equation (NLSE) can offer advanced solutions for the mitigation of nonlinear signal distortions in optical fiber links. Fundamental optical soliton, continuous, and discrete eigenvalues of the nonlinear spectrum have already been considered for the transmission of information in fiber-optic channels. Here, we propose to apply signal modulation to the kernel of the Gelfand-Levitan-Marchenko equations that offers the advantage of a relatively simple decoder design. First, we describe an approach based on exploiting the general N-soliton solution of the NLSE for simultaneous coding of N symbols involving 4×N coding parameters. As a specific elegant subclass of the general schemes, we introduce a soliton orthogonal frequency division multiplexing (SOFDM) method. This method is based on the choice of identical imaginary parts of the N-soliton solution eigenvalues, corresponding to equidistant soliton frequencies, making it similar to the conventional OFDM scheme, thus, allowing for the use of the efficient fast Fourier transform algorithm to recover the data. Then, we demonstrate how to use this new approach to control signal parameters in the case of the continuous spectrum.

AB - Remarkable mathematical properties of the integrable nonlinear Schrödinger equation (NLSE) can offer advanced solutions for the mitigation of nonlinear signal distortions in optical fiber links. Fundamental optical soliton, continuous, and discrete eigenvalues of the nonlinear spectrum have already been considered for the transmission of information in fiber-optic channels. Here, we propose to apply signal modulation to the kernel of the Gelfand-Levitan-Marchenko equations that offers the advantage of a relatively simple decoder design. First, we describe an approach based on exploiting the general N-soliton solution of the NLSE for simultaneous coding of N symbols involving 4×N coding parameters. As a specific elegant subclass of the general schemes, we introduce a soliton orthogonal frequency division multiplexing (SOFDM) method. This method is based on the choice of identical imaginary parts of the N-soliton solution eigenvalues, corresponding to equidistant soliton frequencies, making it similar to the conventional OFDM scheme, thus, allowing for the use of the efficient fast Fourier transform algorithm to recover the data. Then, we demonstrate how to use this new approach to control signal parameters in the case of the continuous spectrum.

KW - NONLINEAR FOURIER-TRANSFORM

KW - EFFICIENT NUMERICAL-METHOD

KW - MATRICES

KW - WAVES

UR - http://www.scopus.com/inward/record.url?scp=85020170968&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.118.223901

DO - 10.1103/PhysRevLett.118.223901

M3 - Article

C2 - 28621991

AN - SCOPUS:85020170968

VL - 118

SP - 223901

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 22

M1 - 223901

ER -