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The exponential growth of the demand for higher data rates is pushing scientists to find ways to improve the internet infrastructure, which crucially relies on optical fibres. The main obstacle to increasing transmission rates of optical fibre systems is presented by the fibre Kerr nonlinear effect, which impairs signal transmission as the transmitted power is increased. Fortunately, optical coherent detection, in combination with digital signal processing techniques, have enabled more sophisticated digital receivers, tailored to the optical fibre channel. This thesis describes a comprehensive study on the performance of two digital receiver-side techniques: digital back-propagation (DBP) and maximum likelihood sequence detection (MLSD). DBP is the most widespread digital technique to mitigate fibre nonlinearity at the receiver. The performance of DBP, is assessed for long-haul, wide-bandwidth systems, highlighting theoretical gains and practical limitations. Analytical models to predict DBP performance are discussed and compared to numerical results. The impact of polarisation-mode dispersion on the capability of DBP to remove nonlinear impairments is investigated. The principles of detection theory are discussed in the context of the optical fibre nonlinear channel. Following such principles, MLSD strategies are studied and their performance analysed for unrepeatered systems. A close to optimum receiver scheme, using the Viterbi algorithm, is proposed and investigated for the first time in a singlespan fibre system. Finally, information-theoretic tools are used to predict achievable information rates of both receiver schemes, when employed in combination with forward error correction codes. In particular, pragmatic coded modulation schemes were examined to assess the potential of off-the-shelf channel codes. Both receiving strategies analysed were demonstrated to significantly outperform conventional receivers optimised for the additive white Gaussian noise channel. The results of this thesis provide a useful insight on the properties of the optical fibre channel and on the design of receivers aiming to maximise information rates through it.