They currently serve the majority of fiber broadband subscribers worldwide and an ongoing demand for bandwidth has led to recent standardization efforts that enabled 50 Gb/s line rate transmission [1], while the research community is investigating the technologies that will enable PONs beyond 100 Gb/s [2]. One possibility for achieving 100 Gb/s is the use of higher-order modulation formats in intensity-modulation and direct-detection (IM/DD) links. However, this comes at the cost of an increased signal-to-noise ratio (SNR) requirement and lower tolerance to non-linearities in the channel. In a PON, the semiconductor optical amplifiers (SOAs) used to improve the receiver sensitivity suffer from non-linear gain saturation and the electro-absorption modulator (EAM) responsible for modulating the intensity of the optical signal has a non-linear transfer function.

This is mostly due to the success of neural networks (NNs) and in particular the technique of deep learning [1]. Deep learning and the accompanying software tools have also found their way into optical communications and are now indispensable tools in the field; ML is now commonly used in all parts of fiber-optical communication networks [2]. ML is already widely used for parameter estimation in optical networks, with the goal of configuring optical network links. Due to their capacity as universal function approximators, ML algorithms and in particular NNs are also often used in the physical layer to replace suboptimal or overly complex digital signal processing (DSP) algorithms in the receiver or transmitter. The use of ML to replace parts of the transmitter or receiver, e.g., as DSP algorithms or to support forward error correction (FEC) decoding, still poses many research challenges, despite the benefits we already see. In particular, standard out-of-the-box ML solutions typically have higher computational complexity than conventional, optimized algorithms. Due to the enormous data rates at which optical communication systems operate, complexity is a major concern. The parallel structure of NNs can lead to straightforward parallelization (as in the ubiquitous graphics processing unit (GPU) implementations), which makes them attractive for implementation in optical transceivers. A future challenge will be the development of ultra-low-complexity hardware platforms with low power dissipation that can be used in highly integrated, high-speed optical transceivers.

To satisfy the growing throughput demand of data-intensive applications, the performance of optical communication systems increased dramatically in recent years. With higher throughput, more advanced equalizers are crucial, to compensate for impairments caused by inter-symbol interference (ISI). The latest research shows that artificial neural network (ANN)-based equalizers are promising candidates to replace traditional algorithms for high-throughput communications. On the other hand, not only throughput but also flexibility is a main objective of beyond-5G and 6G communication systems. A platform that is able to satisfy the strict throughput and flexibility requirements of modern communication systems are field programmable gate arrays (FPGAs). Thus, in this work, we present a high-performance FPGA implementation of an ANN-based equalizer, which meets the throughput requirements of modern optical communication systems. Further, our architecture is highly flexible since it includes a variable degree of parallelism (DOP) and therefore can also be applied to low-cost or low-power applications which is demonstrated for a magnetic recording channel. The implementation is based on a cross-layer design approach featuring optimizations from the algorithm down to the hardware architecture, including a detailed quantization analysis. Moreover, we present a framework to reduce the latency of the ANN-based equalizer under given throughput constraints. As a result, the bit error ratio (BER) of our equalizer for the optical fiber channel is around four times lower than that of a conventional one, while the corresponding FPGA implementation achieves a throughput of more than 40 GBd, outperforming a high-performance graphics processing unit (GPU) by three orders of magnitude for a similar batch size.

In this work, we present a high-throughput field programmable gate array (FPGA) demonstrator of an artificial neural network (ANN)-based equalizer. The equalization is performed and illustrated in real-time for a 30 GBd, two-level pulse amplitude modulation (PAM2) optical communication system.

We investigate the application of the factor graph framework for blind joint channel estimation and symbol detection on time-variant linear inter-symbol interference channels. In particular, we consider the expectation maximization (EM) algorithm for maximum likelihood estimation, which typically suffers from high complexity as it requires the computation of the symbol-wise posterior distributions in every iteration. We address this issue by efficiently approximating the posteriors using the belief propagation (BP) algorithm on a suitable factor graph. By interweaving the iterations of BP and EM, the detection complexity can be further reduced to a single BP iteration per EM step. In addition, we propose a data-driven version of our algorithm that introduces momentum in the BP updates and learns a suitable EM parameter update schedule, thereby significantly improving the performance-complexity tradeoff with a few offline training samples. Our numerical experiments demonstrate the excellent performance of the proposed blind detector and show that it even outperforms coherent BP detection in high signal-to-noise scenarios.

Since PONs are primarily used for fiber-to-the-home (FTTH), the end-user transceivers must be cheap and power efficient while covering the increasing demand of data rates. For this reasons, they typically rely on intensity-modulation and direct-detection (IM/DD) of the optical signal. Current research is focusing on data rates beyond recent 50G-PON standardization efforts [1], i.e., towards PONs which are capable of delivering 100 Gbit/s [2]. Since cost-effective hardware hinders increasing the symbol rate, the focus shifts towards higherorder modulation formats such as 4-ary pulse amplitude modulation (PAM4). However, compared to conventional on-off-keying (OOK), which is used until 50G-PON, multi-level modulation formats are more prone to nonlinerities and, due to its reduced signal-to-noise ratio (SNR) tolerance, require optical amplification. The utilized low-cost semiconductor optical amplifiers (SOA) distort the signal at high received optical power (ROP) due to nonlinear gain saturation, which reduces the dynamic range [3].

We gratefully acknowledge support from the Simons Foundation and member institutions. Our automated source to PDF conversion system has failed to produce PDF for the paper: 2312.12909 . Return to the abstract for an alternative link to the source, or to find an email address to contact the author. For help regarding the automated source to PDF system, please contact help@arxiv.org

In recent years, communication engineers put strong emphasis on artificial neural network (ANN)-based algorithms with the aim of increasing the flexibility and autonomy of the system and its components. In this context, unsupervised training is of special interest as it enables adaptation without the overhead of transmitting pilot symbols. In this work, we present a novel ANN-based, unsupervised equalizer and its trainable field programmable gate array (FPGA) implementation. We demonstrate that our custom loss function allows the ANN to adapt for varying channel conditions, approaching the performance of a supervised baseline. Furthermore, as a first step towards a practical communication system, we design an efficient FPGA implementation of our proposed algorithm, which achieves a throughput in the order of Gbit/s, outperforming a high-performance GPU by a large margin.

Message passing on factor graphs is a powerful framework for probabilistic inference, which finds important applications in various scientific domains. The most wide-spread message passing scheme is the sum-product algorithm (SPA) which gives exact results on trees but often fails on graphs with many small cycles. We search for an alternative message passing algorithm that works particularly well on such cyclic graphs. Therefore, we challenge the extrinsic principle of the SPA, which loses its objective on graphs with cycles. We further replace the local SPA message update rule at the factor nodes of the underlying graph with a generic mapping, which is optimized in a data-driven fashion. These modifications lead to a considerable improvement in performance while preserving the simplicity of the SPA. We evaluate our method for two classes of cyclic graphs: the 2x2 fully connected Ising grid and factor graphs for symbol detection on linear communication channels with inter-symbol interference. To enable the method for large graphs as they occur in practical applications, we develop a novel loss function that is inspired by the Bethe approximation from statistical physics and allows for training in an unsupervised fashion.

We propose a novel method to optimize the structure of factor graphs for graph-based inference. As an example inference task, we consider symbol detection on linear inter-symbol interference channels. The factor graph framework has the potential to yield low-complexity symbol detectors. However, the sum-product algorithm on cyclic factor graphs is suboptimal and its performance is highly sensitive to the underlying graph. Therefore, we optimize the structure of the underlying factor graphs in an end-to-end manner using machine learning. For that purpose, we transform the structural optimization into a clustering problem of low-degree factor nodes that incorporates the known channel model into the optimization. Furthermore, we study the combination of this approach with neural belief propagation, yielding near-maximum a posteriori symbol detection performance for specific channels.