Coding is an essential technology for efficient fiber-optic communications and secure quantum communications. In particular, low-density parity-check (LDPC) coding is favoured due to its strong error correction capability and high-throughput implementation feasibility. In fiber-optic communications, it has been realized that advanced high-order modulation formats and soft-decision forward error correction (FEC) such as LDPC codes are the key technologies for the next-generation high-speed optical communications. Therefore, energy-efficient LDPC coding in combination with advanced modulation formats is an important topic that needs to be studied for fiber-optic communications. In secure quantum communications, large-alphabet quantum key distribution (QKD) is becoming attractive recently due to its potential in improving the efficiency of key exchange. To recover the carried information bits, efficient information reconciliation is desirable, for which the use of LDPC coding is essential. In this dissertation, we first explore different efficient LDPC coding schemes for optical transmission of polarization-division multiplexed quadrature-amplitude modulation (QAM) signals. We show that high energy efficiency can be achieved without incurring extra overhead and complexity. We then study the transmission performance of LDPC-coded turbo equalization for QAM signals in a realistic fiber link as well as that of pragmatic turbo equalizers. Further, leveraging the polarization freedom of light, we expand the signal constellation into a four-dimensional (4D) space and evaluate the performance of LDPC-coded 4D signals in terms of transmission reach. Lastly, we study the security of a proposed weak-coherent-state large-alphabet QKD protocol and investigate the information reconciliation efficiency based on LDPC coding.

[pt] A comunicação por fibras ópticas utiliza diversos modelos herdados dos sistemas de telecomunicações tradicionais. Recentemente, a necessidade de maior controle sobre o fluxo de dados tem atraído muita atenção para as vantagens da comunicação óptica adaptativa. Num sistema de comunicação adaptativo, o fluxo de dados pode ser alterado em função de variações na qualidade do canal ou simplesmente pela necessidade de racionalizar a utilização dos recursos disponíveis. A interoperação entre redes pressiona pela necessidade de uma rede elástica e a expectativa é que este tipo de rede permita o controle sobre vários níveis da estrutura de comunicação. Nesta tese, a análise deste tema se concentra na camada física da rede óptica, em que a elasticidade pode ser obtida através de diferentes técnicas de modulação e multiplexação. A camada física de uma rede óptica adaptativa deve responder a variações e restrições do meio de transmissão. O consumo de energia, por exemplo, é um requisito cada vez mais presente nos projetos das redes de comunicação e a relevância deste requisito tende a aumentar na medida em que as redes ópticas aumentam sua capilaridade. O principal objetivo desta tese é analisar uma solução de comunicação óptica adaptativa que atenda aos requisitos básicos de uma rede elástica. O sistema de comunicação em análise é baseado em modulações realizadas no espaço de sinais de quatro dimensões, também conhecidas como modulações 4D. A perspectiva adotada privilegia a polarização da portadora óptica. A vantagem em adotar esta perspectiva, reside no fato de que ela permite a construção de modulações multidimensionais utilizando os fibrados de Hopf. Conforme será observado, o uso dos fibrados de Hopf em conjunto com o conceito matemático denominado vértice embutido de politopos, potencializa as soluções de engenharia para o problema da comunicação óptica adaptativa. / [en] Fiber-optic communications use several models inherited from traditional telecommunications systems. Recently, the need to improve the control over the data flow has attracted attention to the advantages of adaptive optical communication. In adaptive systems, the data flow can be altered due to changes in the channel quality or simply to rationalize the use of available resources. Interoperation between networks further presses on the need for an elastic network and the expectation is that this type of network will allow control over various levels of the communication structure. In this thesis, the analysis of this theme focuses on the physical layer of the optical network, where elasticity can be obtained through different modulation and multiplexing techniques. The physical layer of an adaptive optical network must respond to variations and restrictions of the transmission medium. Energy consumption, for example, is a requirement that is increasingly present in communication network projects and the relevance of this requirement tends to increase as optical networks expands in capillarity. The main objective of this thesis is to analyze an adaptive optical communication solution that meets the basic requirements of an elastic network. The communication system under analysis is based on the four-dimensional signal space modulations, also known as 4D modulations. The perspective adopted favors the polarization of the optical carrier. The advantage in adopting this perspective resides in the fact that it allows the construction of multidimensional modulations using Hopf bundles. As will be observed, the use of Hopf bundles in conjunction with the mathematical concept called embedded vertex polytopes, improves the engineering solutions to the problem of adaptive optical communication.