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The per-sample zero-dispersion channel model of the optical fiber is considered. It is shown that capacity is uniquely achieved by an input probability distribution that has continuous uniform phase and discrete amplitude that takes on finitely many values. This result holds when the channel is subject to general input cost constraints, that include a peak amplitude constraint and a joint average and peak amplitude constraint. [ABSTRACT FROM AUTHOR]

In the most general case, all three components—the discrete eigenvalues, the discrete spectral amplitudes, and the continuous spectrum—of the nonlinear Fourier transform of a signal can be independently modulated. This paper examines information transmission using only the discrete eigenvalues, and presents heuristic designs for multisoliton signal sets with spectral efficiencies greater than 3 b/s/Hz. The first design, called multieigenvalue position encoding, is based on an exhaustive search followed by pruning of the signal set to remove high pulsewidth or high bandwidth outliers. The second design, called trellis encoding, achieves comparable efficiencies to the fist method at much lower complexity. These multisoliton signals do not undergo any pulse broadening, but are significantly limited by bandwidth expansion if the system length is not much smaller than the dispersion length parameter. This limitation suggests that modulating the eigenvalues alone cannot address the problem of nonlinearity in commercial fiber transmission systems, and that our proposed methods are only meaningful when dispersion is very small and dominated by nonlinearity, e.g., close to the zero-dispersion wavelength at 1300 nm. [ABSTRACT FROM PUBLISHER]

The nonlinear Fourier transform (NFT), a powerful tool in soliton theory and exactly solvable models, is a method for solving integrable partial differential equations governing wave propagation in certain nonlinear media. The NFT decorrelates signal degrees-of-freedom in such models, in much the same way that the Fourier transform does for linear systems. In this three-part series of papers, this observation is exploited for data transmission over integrable channels, such as optical fibers, where pulse propagation is governed by the nonlinear Schrödinger equation. In this transmission scheme, which can be viewed as a nonlinear analogue of orthogonal frequency-division multiplexing commonly used in linear channels, information is encoded in the nonlinear frequencies and their spectral amplitudes. Unlike most other fiber-optic transmission schemes, this technique deals with both dispersion and nonlinearity directly and unconditionally without the need for dispersion or nonlinearity compensation methods. This paper explains the mathematical tools that underlie the method. [ABSTRACT FROM AUTHOR]

The capacity of the channel defined by the stochastic nonlinear Schrödinger equation, which includes the effects of the Kerr nonlinearity and amplified spontaneous emission noise, is considered in the case of zero dispersion. In the absence of dispersion, this channel behaves as a collection of parallel per-sample channels. The conditional probability density function of the nonlinear per-sample channels is derived using both a sum-product and a Fokker–Planck differential equation approach. It is shown that, for a fixed noise power, the per-sample capacity grows unboundedly with input signal. The channel can be partitioned into amplitude and phase subchannels, and it is shown that the contribution to the total capacity of the phase channel declines for large input powers. It is found that a 2-D distribution with a half-Gaussian profile on the amplitude and uniform phase provides a lower bound for the zero-dispersion optical fiber channel, which is simple and asymptotically capacity-achieving at high signal-to-noise ratios (SNRs). A lower bound on the capacity is also derived in the medium-SNR region. The exact capacity subject to peak and average power constraints is numerically quantified using dense multiple ring modulation formats. The differential model underlying the zero-dispersion channel is reduced to an algebraic model, which is more tractable for digital communication studies, and, in particular, it provides a relation between the zero-dispersion optical channel and a 2\,\times\,2 multiple-input multiple-output Rician fading channel. It appears that the structure of the capacity-achieving input distribution resembles that of the Rician fading channel, i.e., it is discrete in amplitude with a finite number of mass points, while continuous and uniform in phase. [ABSTRACT FROM AUTHOR]