  In recent years, extensive research has been conducted to explore the
utilization of machine learning algorithms in various direct-detected and
self-coherent short-reach communication applications. These applications
encompass a wide range of tasks, including bandwidth request prediction, signal
quality monitoring, fault detection, traffic prediction, and digital signal
processing (DSP)-based equalization. As a versatile approach, machine learning
demonstrates the ability to address stochastic phenomena in optical systems
networks where deterministic methods may fall short. However, when it comes to
DSP equalization algorithms, their performance improvements are often marginal,
and their complexity is prohibitively high, especially in cost-sensitive
short-reach communications scenarios such as passive optical networks (PONs).
They excel in capturing temporal dependencies, handling irregular or nonlinear
patterns effectively, and accommodating variable time intervals. Within this
extensive survey, we outline the application of machine learning techniques in
short-reach communications, specifically emphasizing their utilization in
high-bandwidth demanding PONs. Notably, we introduce a novel taxonomy for
time-series methods employed in machine learning signal processing, providing a
structured classification framework. Our taxonomy categorizes current time
series methods into four distinct groups: traditional methods, Fourier
convolution-based methods, transformer-based models, and time-series
convolutional networks. Finally, we highlight prospective research directions
within this rapidly evolving field and outline specific solutions to mitigate
the complexity associated with hardware implementations. We aim to pave the way
for more practical and efficient deployment of machine learning approaches in
short-reach optical communication systems by addressing complexity concerns.
