Nonlinear Inverse Synthesis and Eigenvalue Division Multiplexing in Optical Fiber Channels

Abstract

We scrutinize the concept of integrable nonlinear communication channels, resurrecting and extending the idea of eigenvalue communications in a novel context of nonsoliton coherent optical communications. Using the integrable nonlinear Schrödinger equation as a channel model, we introduce a new approach-the nonlinear inverse synthesis method-for digital signal processing based on encoding the information directly onto the nonlinear signal spectrum. The latter evolves trivially and linearly along the transmission line, thus, providing an effective eigenvalue division multiplexing with no nonlinear channel cross talk. The general approach is illustrated with a coherent optical orthogonal frequency division multiplexing transmission format. We show how the strategy based upon the inverse scattering transform method can be geared for the creation of new efficient coding and modulation standards for the nonlinear channel.

Nonlinear Inverse Synthesis for Optical Links With Distributed Raman Amplification

“…However, the usage of mapping given by Eq. (14), utilized in the series of previous works on the NIS method [17,[25][26], ensures the exact convergence of the nonlinear quantities to the respective linear analogs in the low power limit, which simplifies the system design and checks.…”

“…The evolution of such special nonlinear modes in the fiber channel is essentially linear, which means that the nonlinearity-induced cross-talk between these modes is effectively absent during the propagation (without signal corruption due to noise). Therefore, the parameters of nonlinear modes can be effectively used to encode and transmit information in fiber channel without suffering from nonlinear crosstalk [15][16][17][18][19]. This general idea was first introduced by Hasegawa and Nyu in [12] and was termed there as "eigenvalue communication".…”

“…However, the NFDM method requires considerable optimization of the pulse shapes for the purpose of maximizing the resulting spectral efficiency (SE) [24]. The second approach based on the modulation of the continuous part of the nonlinear spectrum, has been proposed in [17] and assessed in detail in [25,26] (for ideal Raman amplification and EDFA-based optical links) -and was termed there as the nonlinear inverse synthesis (NIS) method. Finally we note that there already exists a very recent study where both the continuous and discrete parts of the nonlinear spectrum have been used simultaneously [27].…”

First Experimental Demonstration of Nonlinear Inverse Synthesis Transmission over Transoceanic Distances

“…Finally, the output signal after INFT was downsampled to 25 Gs/s before being loaded into the arbitrary waveform generator (AWG) with 6 bits DAC resolution and fed through a linear amplifier to drive an IQ modulator. As explained in [4,7,8], the INFT maps the linear spectrum of the input signal to the continuous part of the nonlinear spectrum of the output signal. Since the OFDM waveform was used as the input signal of the INFT block, the continuous part of the nonlinear spectrum of the output signal was directly modulated by QPSK data.…”

Implications of information theory in optical fibre communications

“…Unfortunately, this linear multiplexing technique inevitably suffers from interference (crosstalk) between the channels owing to channel nonlinearity, which appears to limit the data transmission rates that can be achieved in such systems. A recently proposed nonlinear frequency division multiplexing (NFDM) approach [21][22][23][24] exploits the properties of the so-called nonlinear Fourier transform, to decompose the ideal nonlinear Schrödinger channel into parallel noninteracting subchannels, much as the ordinary (linear) Fourier transform decomposes a linear time-invariant channel into non-interacting subchannels. (A single-channel version of the idea of modulating information in this manner was termed 'eigenvalue communication' in [25].)…”