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Low-complexity neural networks (NNs) have successfully been proposed for digital signal processing (DSP) in short-reach intensity-modulated directly detected optical links, where chromatic dispersion-induced impairments significantly limit the transmission distance. The NN-based equalizers are usually optimized independently from other DSP components, such as matched filtering. This approach may result in lower equalization performance. Alternatively, optimizing a NN equalizer to perform functionalities of multiple DSP blocks may increase transmission reach while keeping the complexity low with respect to the scenarios where DSP blocks that involve nonlinear equalizers are separated and optimized independently. In this work, we propose a low-complexity NN that performs samples-to-symbol equalization, meaning that the NN-based equalizer includes match filtering and downsampling. We compare it to a samples-to-sample equalization approach followed by match filtering and downsampling in terms of performance and computational complexity. Both approaches are evaluated using three different types of NNs combined with optical preprocessing. We numerically and experimentally show that the proposed samples-to-symbol equalization approach applied for 32 GBd on-off keying (OOK) signals outperforms the samples-domain alternative keeping the computational complexity low with respect to the sample-based approach. Additionally, the different types of NN-based equalizers are compared in terms of performance with respect to computational complexity.

Inter-symbol interference (ISI) induced by chromatic dispersion combined with square-law detection is a key impairment in intensity-modulated and directly detected (IM/DD) links. The ISI significantly degrades the link performance and limits fiber transmission reach. The IM/DD receivers cannot rely on equalizers with high inference phase computational complexity (CC) such as deep neural networks. However, high CC can be reduced by applying a low complexity reservoir computing (RC) combined with a multi-symbol equalization scheme. In this work, we numerically investigate the multi-symbol RC equalizer applied to a spectrally sliced receiver for 32-GBd PAM-4 transmission in single-mode fiber. We show that up to 17 sequential symbols can be equalized simultaneously while still achieving transmission performance of 68 km distance below the KP4 FEC threshold. The multi-symbol method can significantly reduce CC to a couple of hundred multiplications per symbol compared to a single-symbol. The RC equalization has a high potential for receiver-end integration due to its reduced CC and easy training.

We examine here what type of predictive modelling, classification, or regression, using neural networks (NN), fits better the task of soft-demapping based post-processing in coherent optical communications, where the transmission channel is nonlinear and dispersive. For the first time, we present possible drawbacks in using each type of predictive task in a machine learning context, considering the nonlinear coherent optical channel equalization/soft-demapping problem. We study two types of equalizers based on the feed-forward and recurrent NNs, for several transmission scenarios, in linear and nonlinear regimes of the optical channel. We point out that even though from the information theory perspective the cross-entropy loss (classification) is the most suitable option for our problem, the NN models based on the cross-entropy loss function can severely suffer from learning problems. The latter translates into the fact that regression-based learning is typically superior in terms of delivering higher Q-factor and achievable information rates. In short, we show by empirical evidence that loss functions based on cross-entropy may not be necessarily the most suitable option for training communication systems in practical scenarios when overfitting- and vanishing gradients-related problems come into play.