Chen Yu, Tavakkolnia Iman, Alvarado Alex, Safari Majid
Institute for Digital Communication, School of Engineering, University of Edinburgh, Edinburgh EH9 3FD, UK.
Information and Communication Theory Lab, Signal Processing Systems Group, Department of Electrical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands.
Entropy (Basel). 2020 Aug 15;22(8):899. doi: 10.3390/e22080899.
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.
光纤通信系统在非线性状态下的容量限制尚未得到充分理解。在本文中，我们研究了调幅一阶孤子传输的容量，将其定义为所谓的时间尺度互信息的最大值。这样的定义使我们能够将孤子脉冲宽度对其幅度的依赖性直接纳入容量公式。最初考虑基于非中心卡方分布的常用无记忆信道模型。通过应用方差归一化变换，该信道可近似为单位方差加性高斯白噪声（AWGN）模型。基于对近似AWGN信道的数值容量分析，确定了容量逼近输入分布的一般形式。这些最优分布是离散的，包括一个零处的质量点（关符号）和有限数量的几乎均匀分布在远离零处的质量点。利用这种输入分布的一般形式，确定了容量的一种新颖的闭式近似，它与数值结果显示出良好的匹配。最后，基于考虑单孤子和孤子序列传输的非线性薛定谔方程的分步模拟，建立了失配容量界。这放宽了无记忆信道的初始假设，以显示孤子间相互作用和戈登 - 豪斯效应的影响。我们的结果表明，孤子间相互作用效应在较高孤子幅度时变得越来越显著，并且与戈登 - 豪斯效应引起的定时抖动相比，将成为主要的损伤。
