Coding and Information Theory for Fiber-Optic Communications

光纤通信的编码和信息论

• 批准号: RGPIN-2016-06488
• 负责人: Kschischang, Frank
• 金额: $ 5.61万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=616343
• 关键词: Coding; Information; Theory; Fiber; Optic

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.

我们生活在一个互联互通的社会，数字信息在地球仪上不断交换。这些信息的绝大多数至少在其行程的一部分由光纤承载。长距离光纤通信的发展是一个令人着迷的发明故事，其中各种技术进步（单模光纤、高效激光发射器和调制器、光放大器、波分多路复用方案、相干信号检测和数字信号处理的发展）随着时间的推移使商业系统的信息承载能力不断提高。 许多自然的问题立即出现。这种进步能无限期地持续下去吗？还是光纤承载信息的能力最终会受到限制？如果是这样的话，我们离实现这一极限还有多远？现有的传输方案是否可以得到改进，以更接近最终极限，同时满足实现复杂性约束？这些都是激励这项工作的研究问题。 回答这些问题的方法主要是基于一种称为非线性傅里叶变换（NFT）的数学工具，它首先由数学家和物理学家在20世纪70年代发明。在光纤中的脉冲传播是由一个称为非线性薛定谔方程（NLSE）的偏微分方程控制的，这是一个非常好的近似。NFT对NLSE的作用与普通傅立叶变换对线性时不变系统的作用相同：它将时域中复杂的卷积运算变为频域中简单的乘法运算。我们的关键思想是在传播波的非线性光谱中对通过光纤传输的信息进行编码，这是一种从光纤一端到另一端完全保留的特征。这种技术，我们称之为非线性频分复用，可以看作是一个模拟的正交频分复用通常用于线性信道。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，而不需要在发射机或接收机处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空间和时间离散版本的NLSE称为土田离散化，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光谱域中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）进行优化。