On the Capacity of Amplitude Modulated Soliton Communication over Long Haul Fibers

Abstract

The capacity limits of fiber-optic communication systems in the nonlinear regime are not yet well understood. In this paper, we study the capacity of amplitude modulated first-order soliton transmission, defined as the maximum of the so-called time-scaled mutual information. Such definition allows us to directly incorporate the dependence of soliton pulse width to its amplitude into capacity formulation. The commonly used memoryless channel model based on noncentral chi-squared distribution is initially considered. Applying a variance normalizing transform, this channel is approximated by a unit-variance additive white Gaussian noise (AWGN) model. Based on a numerical capacity analysis of the approximated AWGN channel, a general form of capacity-approaching input distributions is determined. These optimal distributions are discrete comprising a mass point at zero (off symbol) and a finite number of mass points almost uniformly distributed away from zero. Using this general form of input distributions, a novel closed-form approximation of the capacity is determined showing a good match to numerical results. Finally, mismatch capacity bounds are developed based on split-step simulations of the nonlinear Schro¨dinger equation considering both single soliton and soliton sequence transmissions. This relaxes the initial assumption of memoryless channel to show the impact of both inter-soliton interaction and Gordon–Haus effects. Our results show that the inter-soliton interaction effect becomes increasingly significant at higher soliton amplitudes and would be the dominant impairment compared to the timing jitter induced by the Gordon–Haus effect.

SPAD-Based Optical Wireless Communication with Signal Pre-Distortion and Noise Normalization

“…[14] and fibre optical communication systems [15], [17]. In this section, we will briefly introduce the SPAD-based system with SQRT.…”

“…Let's firstly consider the design of VNT at the receiver. The VNT is applied to random variables with certain relationships between the variance and mean to generate approximately Gaussian random variables with variance independent of the mean [13], [15], [17], [25] 1 . Defining the relationship between the mean and variance of the received SPAD signal given in (37) as σ 2 m =…”

“…1 Note that the convergence to Gaussian random variables is shown for the random variables with original gamma distribution [25], Gaussian distribution [13], noncentral chi-squared distribution [17], and an unknown distribution [15]. f 2 (µ m ), the function f (x) can be expressed as…”

“…In [13], the signalling in the square-root domain is proposed which can transform the signal-dependent noise into signal-independent one to simplify the decoding process and improve the BER performance. Such transformation has been further applied to SPAD-based OWC systems [9] and optical fibre communication [15]- [17]. In addition, in [14] an improved constellation and decoding threshold design for such signal dependent channel is obtained by solving the optimization problem aiming at minimizing the error probabilities.…”

SPAD-Based Optical Wireless Communication With Signal Pre-Distortion and Noise Normalization

“…In [13], the signalling in the square-root domain is proposed which can transform the signal-dependent noise into signalindependent one to simplify the decoding process and improve the BER performance. Such transformation has been further applied to SPAD-based OWC systems [9] and optical fibre communication [15]- [17]. In addition, in [14] an improved constellation and decoding threshold design for such signal dependent channel is obtained by solving an optimization problem aiming at minimizing the error probabilities.…”