Coding and Information Theory for Fiber-Optic Communications

我们生活在一个互联的社会中，数字信息在全球范围内不断交换。这些信息中的绝大多数至少有一部分是由光纤传输的。长途光纤通信的发展是一个引人入胜的发明故事，其中各种技术的进步（单模光纤的发展，高效的激光发射机和调制器，光放大器，波分复用方案，相干信号检测和数字信号处理）随着时间的推移，商业系统的信息承载能力不断提高。许多自然的问题马上就产生了。这种进展能否无限期地持续下去，还是光纤的承载能力最终会受到限制？如果是这样，我们离达到这个终极极限还有多远？是否可以改进现有的传输方案以更接近最终极限，同时满足实现复杂性约束？这些都是激发这项工作的研究问题。回答这些问题的方法集中在一个叫做非线性傅立叶变换（NFT）的数学工具上，这个工具最早是由数学家和物理学家在20世纪70年代发明的。脉冲在光纤中的传播，在一个很好的近似上，是由一个叫做非线性薛定谔方程（NLSE）的偏微分方程控制的。NFT对NLSE的作用就像普通傅里叶变换对线性时不变系统的作用一样：它把时域上复杂的卷积运算变成频域上简单的乘法运算。我们的关键思想是在传播波的非线性频谱中对光纤传输的信息进行编码，这一特征从光纤的一端到另一端完全保留下来。这种技术，我们称之为非线性频分复用，可以看作是线性信道中常用的正交频分复用的模拟。与大多数其他光纤数据传输方案不同，该技术无条件地处理色散和非线性，而不需要在发送端或接收端使用额外的补偿方法。***利用NFT的特性，我们希望能够理解光纤的最终信息承载能力。我们计划研究最近发现的NLSE的空间和时间离散版本，称为Tsuchida离散化，这是nft兼容的，我们希望从中获得重要的见解。我们还计划研究非线性谱域的光学和数字信号处理技术。我们的研究结果将指导我们设计新的通信方案，这些方案直接针对所有光纤信道损伤（包括线性和非线性）的弹性进行优化

We live in a connected society where digital information is continuously exchanged across the globe. The vast majority of this information is carried by optical fibres for at least part of their journey. The development of long-haul fibre-optic communications is a fascinating story of invention in which various technological advances (the development of single-mode fibre, efficient laser transmitters and modulators, optical amplifiers, wavelength-division multiplexing schemes, coherent signal detection and digital signal processing have, over time yielded steady improvements in the information-carrying capacity of commercial systems.*** Many natural questions arise immediately. Can this progress continue indefinitely, or are optical fibres ultimately limited in their capacity to carry information? If so, how close are we to achieving this ultimate limit? Can existing transmission schemes be improved to approach the ultimate limit more closely, while satisfying implementation-complexity constraints? These are the research questions that motivate this work.*** The approach taken to answer these questions is centred upon a mathematical tool called the nonlinear Fourier transform (NFT), first devised by mathematicians and physicists in the 1970s. Pulse propagation in optical fibres is, to a very good approximation, governed by a partial differential equation called the nonlinear Schroedinger equation (NLSE). The NFT does for the NLSE what the ordinary Fourier transform does for linear time-invariant systems: it changes a complicated convolution operation in the time domain to a simple multiplication operation in the frequency domain. Our key idea is to encode information for transmission over optical fibres in the nonlinear spectrum of the propagating wave, a feature that is entirely preserved from one end of the fibre to the other. This technique, which we have termed nonlinear frequency division multiplexing, can be viewed as an analogue of orthogonal frequency-division multiplexing commonly used in linear channels. Unlike most other fibre-optic data transmission schemes, this technique deals with both dispersion and nonlinearity unconditionally without the need for additional compensation methods at the transmitter or receiver.***Using the properties of the NFT, we hope to achieve an understanding of the ultimate information-carrying capacity of optical fibres. We plan to study a recently-discovered spatially and temporally discrete version of the NLSE called the Tsuchida Discretization, which is NFT-compatible and from which we hope to gain significant insights. We also plan to study optical and digital signal processing techniques in the nonlinear spectral domain. Our research results will guide us in the design of new communication schemes that are directly optimized for resilience against all fibre-optic channel impairments, both linear and nonlinear.**