On the Per-Sample Capacity of Nondispersive Optical Fibers

• Published in: IEEE transactions on information theory Vol. 57; no. 11; pp. 7522 - 7541
• Main Authors: Yousefi, M. I., Kschischang, F. R.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.11.2011; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Amplitudes; Applied sciences; Channels; Communication channels; Differential equations; Dispersion; Dispersions; Exact sciences and technology; Fading; Fiber nonlinear optics; Fiber optic communications; Information theory; Information, signal and communications theory; Input output analysis; Mathematical model; Mathematical models; Modulation, demodulation; Noise; nonlinear Schrödinger equation; Nonlinearity; optical fiber; Optical fibers; path integral; Probability density function; Schrodinger equation; Signal and communications theory; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments); Fading channels; MIMO system; Lower bound; Input signal; Path integral; nonlinear Schrodinger equation; Rice fading; Non linear channel; Conditional probability; Non linear phenomenon; Schrödinger equation; Amplified spontaneous emission; Non linear equation; Statistical method; Modulation; Fokker Planck equation; Probability density function; Digital communication; Non linear effect; Peak power; Optical fiber; Signal to noise ratio; Information theory
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2011.2165793

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 × 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.