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We demonstrate multipath interference-penalty-free S-band transmission over two G.654.E-compliant fibres with cable cutoff up to 1530 nm. No SNR degradation was observed across various transmission distances and baud rates, Comment: 3 pages, 2 figures, OFC (Optical Fiber Communications Conference) 2025

Topology Bench is a comprehensive topology dataset designed to accelerate benchmarking studies in optical networks. The dataset, focusing on core optical networks, comprises publicly accessible and ready-to-use topologies, including (a) 105 georeferenced real-world optical networks and (b) 270,900 validated synthetic topologies. Prior research on real-world core optical networks has been characterised by fragmented open data sources and disparate individual studies. Moreover, previous efforts have notably failed to provide synthetic data at a scale comparable to our present study. Topology Bench addresses this limitation, offering a unified resource and represents a 61.5% increase in spatially-referenced real world optical networks. To benchmark and identify the fundamental nature of optical network topologies through the lens of graph-theoretical analysis, we analyse both real and synthetic networks using structural, spatial and spectral metrics. Our comparative analysis identifies constraints in real optical network diversity and illustrates how synthetic networks can complement and expand the range of topologies available for use. Currently, topologies are selected based on subjective criteria, such as preference, data availability, or perceived suitability, leading to potential biases and limited representativeness. Our framework enhances the generalisability of optical network research by providing a more objective and systematic approach to topology selection. A statistical and correlation analysis reveals the quantitative range of all of these graph metrics and the relationships between them. Finally, we apply unsupervised machine learning to cluster real-world topologies into distinctive groups using nine optimal graph metrics using K-means. We conclude the analysis by providing guidance on how to use such clusters to select a diverse set of topologies for future studies.

Using a recently developed fast integral ultrawideband Gaussian noise model, we quantify the achievable throughput under total optical power constraints for systems ranging from C-band to fully populated OESCLU bands using optimum launch powers, showing conditions when expanding bandwidth provides no additional throughput.

We experimentally investigated the performance of split nonlinearity compensation schemes for single and multi-channel WDM systems. We show that split NLC SNR gains of more than 0.4 dB at 5540 km can be achieved compared to transmitter- or receiver-side DBP alone when signal-ASE beating limits transmission performance., Comment: 2024 European Conference on Optical Communication (ECOC)

Ultra-wideband, field-deployed metropolitan fibre transmission is experimentally demonstrated, measuring a record 202.3 Tb/s GMI and 189.5 Tb/s after decoding with 20.9 dBm launch power and lumped amplification only. An experimentally-optimised 5 dB pre-tilt over the 15.6 THz optical bandwidth was applied to overcome ISRS., Comment: 3 pages plus 1 page reference, 6 figures, submit to ECOC 2024

The accuracy of a recently-developed closed-form GN nonlinear interference model is evaluated in experimental 1065 km S+C+L band WDM transmission with backward Raman pumping. The model accurately estimates the nonlinear interference and ASE with total SNR error of less than 0.6 dB., Comment: 3 pages plus 1 page reference, 4 figures, submitted to ECOC 2024

Per-channel launch power optimisation in a hybrid-amplified link with optimised pump powers and wavelengths is described. Compared to using the optimum spectrally uniform launch power, an average SNR gain of 0.13 dB is obtained against 0.56 dB for the same system operating with lumped amplifiers only., Comment: Submitted to 2024 European Conference on Optical Communication (ECOC2024)

We model the transmission of ultrawideband signals, including wavelength-dependent fibre parameters: dispersion, nonlinear coefficient and effective fibre core area. To that end, the inter-channel stimulated Raman scattering Gaussian noise integral model is extended to include these parameters. The integrals involved in this frequency-domain model are numerically solved in hyperbolic coordinates using a Riemann sum. The model implementation is designed to work on parallel GPUs and is optimised for fast computational time. The model is valid for Gaussian-distributed signals and is compared with the split-step Fourier method, for transmission over standard single-mode fibre (SSMF) in the O-band (wavelengths around the zero-dispersion wavelength), showing reasonable agreement. Further, we demonstrated SNR evaluation over an 80~km SSFM single-span transmission using 589x96 GBaud channels, corresponding to almost 59 THz optical bandwidth, fully populating the O, E, S, C, L and U bands (1260-1675 nm). The SNR evaluation is completed in just 3.6 seconds using four Nvidia V100 16GB PCIe GPUs. Finally, we used this model to find the optimum launch power profile for this system achieving 747 Tbps of potential throughput over 80 km fibre and demonstrating its suitability for UWB optimisation routines.

We generate and transmit 75-GHz-bandwidth OFDM signals over the air using three mutually frequency-locked lasers, achieving minimal frequency gap between the wireless W and D bands using optical-assisted approaches, resulting in 173.5 Gb/s detected capacity., Comment: 3 pages, 2 figures, conference submission

A closed-form expression that estimates the nonlinear interference of arbitrary modulation formats in Raman amplified links is presented. Accounting for any pumping schemes and inter-channel stimulated Raman scattering effect, the formula is applied to an optical bandwidth of 20~THz and validated using numerical simulations., Comment: To be presented at European Conference on Optical Communications (ECOC) 2023

A closed-form model for the nonlinear interference (NLI) in Raman amplified links is presented, the formula accounts for both forward (FW) and backward (BW) pumping schemes and inter-channel stimulated Raman scattering (ISRS) effect. The formula also accounts for an arbitrary number of pumps, wavelength-dependent fibre parameters, launch-power profiles, and is tested over a distributed Raman-amplified system setup. The formula is suitable for ultra-wideband (UWB) optical transmission systems and is applied in a signal with 13~THz optical bandwidth corresponding to transmission over the S-, C-, and L- band. The accuracy of the closed-form formula is validated through comparison with numerical integration of the Gaussian noise (GN) model and split-step Fourier method (SSFM) simulations in a point-to-point transmission link., Comment: arXiv admin note: text overlap with arXiv:2210.09067

A closed-form model for the nonlinear interference in distributed Raman amplified links is presented, the formula accounts for both forward and backward pumping.

This paper presents design methods for highly efficient optimisation of geometrically shaped constellations to maximise data throughput in optical communications. It describes methods to analytically calculate the information-theoretical loss and the gradient of this loss as a function of the input constellation shape. The gradients of the \ac{MI} and \ac{GMI} are critical to the optimisation of geometrically-shaped constellations. It presents the analytical derivative of the achievable information rate metrics with respect to the input constellation. The proposed method allows for improved design of higher cardinality and higher-dimensional constellations for optimising both linear and nonlinear fibre transmission throughput. Near-capacity achieving constellations with up to 8192 points for both 2 and 4 dimensions, with generalised mutual information (GMI) within 0.06 bit/2Dsymbol of additive white Gaussian noise channel (AWGN) capacity, are presented. Additionally, a design algorithm reducing the design computation time from days to minutes is introduced, allowing the presentation of optimised constellations for both linear AWGN and nonlinear fibre channels for a wide range of signal-to-noise ratios.

The relationship between topology and network throughput of arbitrarily-connected mesh networks is studied. Taking into account nonlinear channel properties, it is shown that throughput decreases logarithmically with physical network size with minor dependence on network ellipticity.

Space division multiplexing using multi-core fiber (MCF) is a promising solution to cope with the capacity crunch in standard single-mode fiber based optical communication systems. Nevertheless, the achievable capacity of MCF is limited by inter-core crosstalk (IC-XT). Many existing researches treat IC-XT as a static interference, however, recent research shows that IC-XT varies with time, wavelength and baud rate. This inherent stochastic feature requires a comprehensive characterization of the behaviour of MCF to its application in practical transmission systems and the theoretical understanding of IC-XT phenomenon. In this paper, we experimentally investigate the IC-XT behaviour of an 8-core trench-assisted MCF in a temperature-controlled environment, using popular modulation formats. We compare the measured results with the theoretical prediction to validate the analytical IC-XT models previously developed. Moreover, we explore the effects of the measurement configurations on the IC-XT accuracy and present an analysis on the IC-XT step distribution. Our results indicate that a number of transmission parameters have significant influence on the strength and volatility of IC-XT. Moreover, the averaging time of the power meter and the observation time window can affect the value of the observed IC-XT, the degrees of the effects vary with the type of the source signals., Comment: 14 pages

In this paper, we propose a geometric shaping (GS) strategy to design 8, 16, 32 and 64-ary modulation formats for the optical fibre channel impaired by both additive white Gaussian (AWGN) and phase noise. The constellations were optimised to maximise generalised mutual information (GMI) using a mismatched channel model. The presented formats demonstrate an enhanced signal-to-noise ratio (SNR) tolerance in high phase noise regimes when compared with their quadrature amplitude modulation (QAM) or AWGN-optimised counterparts. By putting the optimisation results in the context of the 400ZR implementation agreement, we show that GS alone can either relax the laser linewidth (LW) or carrier phase estimation (CPE) requirements of 400 Gbit/s transmission links and beyond. Following the GMI validation, the performance of the presented formats was examined in terms of post forward error correction (FEC) bit-error-rate (BER) for a soft decision (SD) extended Hamming code (128, 120), implemented as per the 400ZR implementation agreement. We demonstrate gains of up to 1.2 dB when compared to the 64-ary AWGN shaped formats., Comment: 10 pages, journal, R1

Fiber nonlinearities, that lead to nonlinear signal interference (NLI), are typically regarded as an instantaneous material response with respect to the optical field. However, in addition to an instantaneous part, the nonlinear fiber response consists of a delayed contribution, referred to as the Raman response. The imaginary part of its Fourier transform, referred to as the Raman gain spectrum, leads to inter-channel stimulated Raman scattering (ISRS). ISRS is a nonlinear effect that redistributes optical power from high to lower frequencies during propagation. However, as the nonlinear fiber response is causal, the Raman spectrum obeys the Kramers-Kronig relations resulting in the real part of the complex valued Raman spectrum. While the impact of the imaginary part (i.e. ISRS) is well studied, the direct implications of its associated real part on the NLI are unexplored. In this work, a theory is proposed to analytically quantify the impact of the real Raman spectrum on the nonlinear interference power. Starting from a generalized Manakov equation, an extension of the ISRS Gaussian Noise (GN) model is derived to include the real Raman spectrum and, thus, to account for the complete nonlinear Raman response. Accurate integral expressions are derived and approximations in closed-form are proposed. Different formulations for the case of single -and dual polarized signals are derived and novel analytical approximations of the real Raman spectrum are proposed. Moreover, it is analytically shown that the real Raman spectrum scales the strength of the instantaneous nonlinear distortions depending on the frequency separation of the interacting frequencies. A simple functional form is derived to assess the scaling of the NLI strength. The proposed theory is validated by numerical simulations over C-and C+L band, using experimentally measured fiber data.

The throughput gains of extending the optical transmission bandwidth to the S+C+L-band are quantified using a Gaussian Noise model that accounts for inter-channel stimulated Raman scattering (ISRS). The impact of potential ISRS mitigation strategies, such as dynamic gain equalization and power optimization, are investigated.

A closed-form formula for the nonlinear interference estimation of arbitrary modulation formats in ultra-wideband transmission systems is presented. Enabled by the proposed approach, the formula is applied to the entire S+C+L band (20 THz) and validated by numerical simulations with experimentally measured fibre data.

We investigate methods for experimental performance enhancement of auto-encoders based on a recurrent neural network (RNN) for communication over dispersive nonlinear channels. In particular, our focus is on the recently proposed sliding window bidirectional RNN (SBRNN) optical fiber autoencoder. We show that adjusting the processing window in the sequence estimation algorithm at the receiver improves the reach of simple systems trained on a channel model and applied "as is" to the transmission link. Moreover, the collected experimental data was used to optimize the receiver neural network parameters, allowing to transmit 42 Gb/s with bit-error rate (BER) below the 6.7% hard-decision forward error correction threshold at distances up to 70km as well as 84 Gb/s at 20 km. The investigation of digital signal processing (DSP) optimized on experimental data is extended to pulse amplitude modulation with receivers performing sliding window sequence estimation using a feed-forward or a recurrent neural network as well as classical nonlinear Volterra equalization. Our results show that, for fixed algorithm memory, the DSP based on deep learning achieves an improved BER performance, allowing to increase the reach of the system., Comment: Invited paper at the IEEE International Workshop on Signal Processing Systems (SiPS) 2020

We investigate end-to-end optimized optical transmission systems based on feedforward or bidirectional recurrent neural networks (BRNN) and deep learning. In particular, we report the first experimental demonstration of a BRNN auto-encoder, highlighting the performance improvement achieved with recurrent processing for communication over dispersive nonlinear channels., Comment: Invited paper at IEEE Photonics Conference (IPC), Special Symposium for Machine Learning in Photonic Systems (SS MLPS)

We propose a time-multiplexed DS-DBR/SOA-gated system to deliver low-power fast tuning across S-/C-/L-bands. Sub-ns switching is demonstrated, supporting 122$\times$50 GHz channels over 6.05 THz using AI techniques., Comment: 3 pages, 3 figures, conference

A linear regression algorithm is applied to a digital-supermode distributed Bragg reflector laser to optimise wavelength switching times. The algorithm uses the output of a digital coherent receiver as feedback to update the pre-emphasis weights applied to the laser section currents. This permits in-situ calculation without manual weight adjustments. The application of this optimiser to a representative subsection of channels indicates this commercially available laser can rapidly reconfigure over 6.05 THz, supporting 122 channels, in less than 10 ns., Comment: 4 pages, 9 figures, one algorithm, Letter

We introduce PULSE, a sub-microsecond optical circuit-switched data centre network architecture controlled by distributed hardware schedulers. PULSE is a flat architecture that uses parallel passive coupler-based broadcast and select networks. We employ a novel transceiver architecture, for dynamic wavelength-timeslot selection, to achieve a reconfiguration time down to O(100ps), establishing timeslots of O(10ns). A novel scheduling algorithm that has a clock period of 2.3ns performs multiple iterations to maximize throughput, wavelength usage and reduce latency, enhancing the overall performance. In order to scale, the single-hop PULSE architecture uses sub-networks that are disjoint by using multiple transceivers for each node in 64 node racks. At the reconfiguration circuit duration (epoch = 120 ns), the scheduling algorithm is shown to achieve up to 93% throughput and 100% wavelength usage of 64 wavelengths, incurring an average latency that ranges from 0.7-1.2 microseconds with best-case 0.4 microsecond median and 5 microsecond tail latency, limited by the timeslot (20 ns) and epoch size (120 ns). We show how the 4096-node PULSE architecture allows up to 260k optical channels to be re-used across sub-networks achieving a capacity of 25.6 Pbps with an energy consumption of 85 pJ/bit., Comment: 16 pages, 12 figures

We present the first experimental demonstration of learned time-domain digital back-propagation (DBP), in 64-GBd dual-polarization 64-QAM signal transmission over 1014 km. Performance gains were comparable to those obtained with conventional, higher complexity, frequency-domain DBP.

We perform an experimental end-to-end transceiver optimization via deep learning using a generative adversarial network to approximate the test-bed channel. Previously, optimization was only possible through a prior assumption of an explicit simplified channel model., Comment: accepted for publication at OFC 2020

The potential benefits of extending the optical fibre transmission bandwidth are studied. Even in the presence of Kerr nonlinearity and inter-channel stimulated Raman scattering, increasing the usable optical fibre bandwidth appears to be the most promising solution to increase system throughput.

In this paper, we apply deep learning for communication over dispersive channels with power detection, as encountered in low-cost optical intensity modulation/direct detection (IM/DD) links. We consider an autoencoder based on the recently proposed sliding window bidirectional recurrent neural network (SBRNN) design to realize the transceiver for optical IM/DD communication. We show that its performance can be improved by introducing a weighted sequence estimation scheme at the receiver. Moreover, we perform bit-to-symbol mapping optimization to reduce the bit-error rate (BER) of the system. Furthermore, we carry out a detailed comparison with classical schemes based on pulse-amplitude modulation and maximum likelihood sequence detection (MLSD). Our investigation shows that for a reference 42\,Gb/s transmission, the SBRNN autoencoder achieves a BER performance comparable to MLSD, when both systems account for the same amount of memory. In contrast to MLSD, the SBRNN performance is achieved without incurring a computational complexity exponentially growing with the processed memory., Comment: Invited paper at Allerton 2019 Conference on Communication, Control and Computing

The effect of Kerr-induced optical fiber nonlinearities in C-band (5 THz) EDFA and C+L-band (12.5 THz) Raman-amplified optical communication systems has been studied considering the impact of third-order fiber dispersion. The performance of digital nonlinearity compensation with single channel and 250-GHz bandwidth in both EDFA and Raman amplified systems has been investigated, respectively. The achievable information rates (AIRs) and optimum code rates in each individual transmission channel have been evaluated for the DP-64QAM, the DP-256QAM and the DP-1024QAM modulation formats, both with and without the use of the probabilistic shaping technique. It is found that, for all considered modulation formats, the signal-to-noise ratios, AIRs and code rates exhibit significantly asymmetric behavior about the central channel due to the presence of the third-order dispersion. This provides a new insight that the forward error correction schemes have to be optimized asymmetrically, on a per-channel basis, to maximize the overall throughput.

The recent advances in modelling nonlinear interference of systems operating beyond the C-band are discussed. Estimation accuracy as well as computational complexity of current approaches are compared and addressed.

A closed-form formula is derived, which corrects for the modulation format dependence of the Gaussian Noise (GN) model in the presence of inter-channel stimulated Raman scattering (ISRS). The analytical result enables a rapid estimate of the nonlinear interference (NLI) for arbitrary modulation formats and avoids the need for complex integral evaluations and split-step simulations. It is shown that the modulation format dependent NLI can be approximated by two contributions, one originating from a single span and one asymptotic contribution for a large number of spans. The asymptotic contribution is solved in closed-form for an arbitrary link function, making the result applicable for generic fiber systems using lumped, distributed or hybrid amplification schemes. The methodology is applied to the ISRS GN model and a modulation format correction formula in closed-form is derived which accounts for an arbitrary number of spans, inter-channel stimulated Raman scattering, arbitrary launch power distributions and wavelength dependent dispersion and attenuation. The proposed formula is validated by numerical simulations over the entire C+L band for multiple fiber types., Comment: Version 3: Typos have been corrected in Eq. (4), (15) and (16)

Transmission of 306x35 GBd, dual polarization, 64-ary geometrically shaped channels over 90x70 km of SMF was demonstrated, achieving a net throughput of 74.38 Tb/s. A combination of hybrid fiber spans and EDFA/Raman amplifiers enabled a continuous gain bandwidth of 10.8 THz.

There has been much interest in the non-linear frequency-division multiplexing (NFDM) transmission scheme in the optical fibre communication system. Up to date, most of the demonstrated NFDM schemes have employed only single polarisation for data transmission. Employing both polarisations can potentially double the data rate of NFDM systems. We investigate in simulation a dual-polarisation NFDM transmission with data modulation on the $b$-coefficient. First, a transformation that facilitates the dual-polarisation $b$-modulation was built upon an existing transformation. Second, the $q_c$- and $b$-modulation for dual-polarisation were compared in terms of Q-factor, spectral efficiency (SE), and correlation of sub-carriers. The correlation is quantified via information theoretic metrics, joint and individual entropy. The polarisation-multiplexed $b$-modulation system shows 1 dB Q-factor improvement over $q_c$-modulation system due to a weaker correlation of sub-carriers and less effective noise. Finally, the $b$-modulation system was optimised for high data rate, achieving a record net data rate of 400 Gbps (SE of 7.2 bit/s/Hz) over $12\times 80$ km of standard single-mode fibre (SSMF) with erbium-doped fibre amplifiers (EDFAs). Based on the above simulation results, we further point out the drawbacks of our current system and quantify the error introduced by the transceiver algorithms and non-integrability of the channel., Comment: submitted to Journal of Lightwave Technology

We propose an autoencoding sequence-based transceiver for communication over dispersive channels with intensity modulation and direct detection (IM/DD), designed as a bidirectional deep recurrent neural network (BRNN). The receiver uses a sliding window technique to allow for efficient data stream estimation. We find that this sliding window BRNN (SBRNN), based on end-to-end deep learning of the communication system, achieves a significant bit-error-rate reduction at all examined distances in comparison to previous block-based autoencoders implemented as feed-forward neural networks (FFNNs), leading to an increase of the transmission distance. We also compare the end-to-end SBRNN with a state-of-the-art IM/DD solution based on two level pulse amplitude modulation with an FFNN receiver, simultaneously processing multiple received symbols and approximating nonlinear Volterra equalization. Our results show that the SBRNN outperforms such systems at both 42 and 84\,Gb/s, while training fewer parameters. Our novel SBRNN design aims at tailoring the end-to-end deep learning-based systems for communication over nonlinear channels with memory, such as the optical IM/DD fiber channel., Comment: accepted for publication in Optics Express

Mitigation of optical fiber nonlinearity is an active research field in the area of optical communications, due to the resulting marked improvement in transmission performance. Following the resurgence of optical coherent detection, digital nonlinearity compensation (NLC) schemes such as digital backpropagation (DBP) and Volterra equalization have received much attention. Alternatively, optical NLC, and specifically optical phase conjugation (OPC), has been proposed to relax the digital signal processing complexity. In this work, a novel hybrid optical-digital NLC scheme combining OPC and a Volterra equalizer is proposed, termed Volterra-Assisted OPC (VAO). It has a twofold advantage: it overcomes the OPC limitation in asymmetric links and substantially enhances the performance of Volterra equalizers. The proposed scheme is shown to outperform both OPC and Volterra equalization alone by up to 4.2 dB in a 1000 km EDFA-amplified fiber link. Moreover, VAO is also demonstrated to be very robust when applied to long-transmission distances, with a 2.5 dB gain over OPC-only systems at 3000 km. VAO combines the advantages of both optical and digital NLC offering a promising trade-off between performance and complexity for future high-speed optical communication systems.

An accurate, closed-form expression evaluating the nonlinear interference (NLI) power in coherent optical transmission systems in the presence of inter-channel stimulated Raman scattering (ISRS) is derived. The analytical result enables a rapid estimate of the signal-to-noise ratio (SNR) and avoids the need for integral evaluations and split-step simulations. The formula also provides new insight into the underlying parameter dependence of ISRS on the NLI. The proposed result is applicable for dispersion unmanaged, ultra-wideband transmission systems that use optical bandwidths of up to 15 THz. The accuracy of the closed-form expression is compared to numerical integration of the ISRS Gaussian Noise model and split-step simulations in a point-to-point transmission, as well as in a mesh optical network scenario., Comment: Version 2: The plots of figure 4 and 5 were placed out of order in version 1. In version 2, they have been swapped and are now in correct order

An analytical model to estimate nonlinear performance in ultra-wideband optical transmission networks is presented. The model accurately accounts for inter-channel stimulated Raman scattering, variably loaded fibre spans and is validated through C+L band simulations for uniform and probabilistically shaped 64-QAM.

We demonstrate, for the first time, a b-modulated dual-polarisation NFDM transmission in simulation, achieving a record net data rate of 400 Gbps (SE of 7.2 bit/s/Hz) over 960 km. The proposed scheme shows 1 dB Q-factor improvement over qc-modulation scheme., Comment: Accepted by ECOC 2018

A geometrically-shaped 256-QAM constellation, tailored to the nonlinear optical fibre channel, is experimentally demonstrated. The proposed constellation outperforms both uniform and AWGN-tailored 256-QAM, as it is designed to optimise the trade-off between shaping gain, nonlinearity and transceiver impairments.

Nonlinearity mitigation using digital signal processing has been shown to increase the achievable data rates of optical fiber transmission links. One especially effective technique is digital back propagation (DBP), an algorithm capable of simultaneously compensating for linear and nonlinear channel distortions. The most significant barrier to implementing this technique, however, is its high computational complexity. In recent years, there have been several proposed alternatives to DBP with reduced computational complexity, although such techniques have not demonstrated performance benefits commensurate with the complexity of implementation. In order to fully characterize the computational requirements of DBP, there is a need to model the algorithm behavior when constrained to the logic used in a digital coherent receiver. Such a model allows for the analysis of any signal recovery algorithm in terms of true hardware complexity which, crucially, includes the bit-depth of the multiplication operation. With a limited bit depth, there is quantization noise, introduced with each arithmetic operation, and it can no longer be assumed that the conventional DBP algorithm will outperform its low complexity alternatives. In this work, DBP and a single nonlinear step DBP implementation, the \textit{Enhanced Split Step Fourier} method (ESSFM), were compared with linear equalization using a generic software model of fixed point hardware. The requirements of bit depth and fast Fourier transform (FFT) size are discussed to examine the optimal operating regimes for these two schemes of digital nonlinearity compensation. For a 1000 km transmission system, it was found that (assuming an optimized FFT size), in terms of SNR, the ESSFM algorithm outperformed the conventional DBP for all hardware resolutions up to 13 bits., Comment: 8 pages, 8 figures, journal submission

In this paper, we implement an optical fiber communication system as an end-to-end deep neural network, including the complete chain of transmitter, channel model, and receiver. This approach enables the optimization of the transceiver in a single end-to-end process. We illustrate the benefits of this method by applying it to intensity modulation/direct detection (IM/DD) systems and show that we can achieve bit error rates below the 6.7\% hard-decision forward error correction (HD-FEC) threshold. We model all componentry of the transmitter and receiver, as well as the fiber channel, and apply deep learning to find transmitter and receiver configurations minimizing the symbol error rate. We propose and verify in simulations a training method that yields robust and flexible transceivers that allow---without reconfiguration---reliable transmission over a large range of link dispersions. The results from end-to-end deep learning are successfully verified for the first time in an experiment. In particular, we achieve information rates of 42\,Gb/s below the HD-FEC threshold at distances beyond 40\,km. We find that our results outperform conventional IM/DD solutions based on 2 and 4 level pulse amplitude modulation (PAM2/PAM4) with feedforward equalization (FFE) at the receiver. Our study is the first step towards end-to-end deep learning-based optimization of optical fiber communication systems., Comment: submitted to IEEE/OSA Journal of Lightwave Technology

Hybrid distributed Raman-EDFA amplifiers, with a continuous 91 nm gain bandwidth, are used to enable a record single mode fibre transmission capacity of 120.0 Tbit/s using 312x35 GBd DP-256QAM over 9x70 km spans.

A Gaussian noise (GN) model is presented that properly accounts for an arbitrary frequency dependent signal power profile along the link. This enables the evaluation of the impact of inter-channel stimulated Raman scattering (ISRS) on the optical Kerr nonlinearity. Additionally, the frequency dependent fiber attenuation can be taken into account and transmission systems that use hybrid amplification schemes can be modeled, where distributed Raman amplification is partly applied over the optical spectrum. To include the latter two cases, a set of coupled ordinary differential equations must be numerically solved in order to obtain the signal power profile yielding a semi-analytical model. However for lumped amplification and negligible variation in fiber attenuation, a less complex and fully analytical model is presented which is referred to as the ISRS GN model. The derived model is exact to first-order for Gaussian modulated signals and extensively validated by numerical split-step simulations. A maximum deviation of $0.1$~dB in nonlinear interference power between simulations and the ISRS GN model is found. The model is applied to a transmission system that occupies an optical bandwidth of $10$~THz, representing the entire C+L band. At optimum launch power, changes of up to $2$~dB in nonlinear interference power due to ISRS are reported. Furthermore, comparable models published in the literature are benchmarked against the ISRS GN model., Comment: 10 pages, 7 figures

Meeting the ever-growing information rate demands has become of utmost importance for optical communication systems. However, it has proven to be a challenging task due to the presence of Kerr effects, which have largely been regarded as a major bottleneck for enhancing the achievable information rates in modern optical communications. In this work, the optimisation and performance of digital nonlinearity compensation are discussed for maximising the achievable information rates in spectrally-efficient optical fibre communication systems. It is found that, for any given target information rate, there exists a trade-off between modulation format and compensated bandwidth to reduce the computational complexity requirement of digital nonlinearity compensation., Comment: Invited paper

It is predicted that demand in optical access networks will reach multi-Gb/s per user. However, the limited performance of the direct detection receiver technology currently used in the optical network units at the customers' premises restricts data rates/user. Therefore, the concept of coherent-enabled access networks has attracted attention in recent years, as this technology offers high receiver sensitivity, inherent frequency selectivity, and linear field detection enabling the full compensation of linear channel impairments. However, the complexity of conventional (dual-polarisation digital) coherent receivers has so far prevented their introduction into access networks. Thus, to exploit the benefits of coherent technology in the ONUs, low complexity coherent receivers, suitable for implementation in ONUs, are needed. In this paper, the recently proposed low complexity coherent (i.e., polarisation-independent Alamouti-coding heterodyne) receiver is, for the first time, compared in terms of its minimum receiver sensitivity with five previously reported receiver designs, including a detailed discussion on their advantages and limitations. It is shown that the Alamouti-coding based receiver approach allows the lowest number of photons per bit (PPB) transmitted (with a lower bound of 15.5 PPB in an ideal system simulations) whilst requiring the lowest optical receiver hardware complexity. It also exhibits comparable complexity to the currently deployed direct-detection receivers, which typically require >1000 PPB. Finally, a comparison of experimentally achieved receiver sensitivities and transmission distances using these receivers is presented. The highest spectral efficiency and longest transmission distance at the highest bit rate reported using the Alamouti-coding receiver, which is also the only one, to date, to have been demonstrated in a full system bidirectional transmission., Comment: 12 pages, 10 figures, 2 tables and 46 referecens

A new probabilistic shaping distribution that outperforms Maxwell-Boltzmann is studied for the nonlinear fiber channel. Additional gains of 0.1 bit/symbol MI or 0.2 dB SNR for both DP-256QAM and DP-1024QAM are reported after 200 km nonlinear fiber transmission.

The efficiency of digital nonlinearity compensation (NLC) is analyzed in the presence of noise arising from amplified spontaneous emission noise (ASE) as well as from a non-ideal transceiver subsystem. Its impact on signal-to-noise ratio (SNR) and reach increase is studied with particular emphasis on split NLC, where the digital back-propagation algorithm is divided between transmitter and receiver. An analytical model is presented to compute the SNR's for non-ideal transmission systems with arbitrary split NLC configurations. When signal-signal nonlinearities are compensated, the performance limitation arises from residual signal-noise interactions. These interactions consist of nonlinear beating between the signal and co-propagating ASE and transceiver noise. While transceiver noise-signal beating is usually dominant for short transmission distances, ASE noise-signal beating is dominant for larger transmission distances. It is shown that both regimes behave differently with respect to the optimal NLC split ratio and their respective reach gains. Additionally, simple formulas for the prediction of the optimal NLC split ratio and the reach increase in those two regimes are reported. It is found that split NLC offers negligible gain with respect to conventional digital back-propagation (DBP) for distances less than 1000 km using standard single-mode fibers and a transceiver (back-to-back) SNR of 26 dB, when transmitter and receiver inject the same amount of noise. However, when transmitter and receiver inject an unequal amount of noise, reach gains of 56% on top of DBP are achievable by properly tailoring the split NLC algorithm. The theoretical findings are confirmed by numerical simulations., Comment: 8 pages, 4 figures, 1 tables

Achievable information rates (AIRs) of wideband optical communication systems using ~40 nm (~5 THz) EDFA and ~100 nm (~12.5 THz) distributed Raman amplification are estimated based on a first-order perturbation analysis. The AIRs of each individual channel have been evaluated for DP-64QAM, DP-256QAM, and DP-1024QAM modulation formats. The impact of full-field nonlinear compensation (FF-NLC) and probabilistically shaped constellations using a Maxwell-Boltzmann distribution were studied and compared to electronic dispersion compensation. It is found that a probabilistically shaped DP-1024QAM constellation combined with FF-NLC yields AIRs of ~75 Tbit/s for the EDFA scheme and ~223 Tbit/s for the Raman amplification scheme over 2000 km standard single mode fibre transmission.

Achievable rates of the nonlinear frequency-division multiplexing (NFDM) and wavelength-division multiplexing (WDM) subject to the same power and bandwidth constraints are computed as a function of transmit power in the standard single-mode fiber. NFDM achieves higher rates than WDM., Comment: Invited paper to be presented at The Optical Fiber Communications Conference and Exposition (OFC), March 2017

The channel law for amplitude-modulated solitons transmitted through a nonlinear optical fibre with ideal distributed amplification and a receiver based on the nonlinear Fourier transform is a noncentral chi-distribution with $2n$ degrees of freedom, where $n=2$ and $n=3$ correspond to the single- and dual-polarisation cases, respectively. In this paper, we study capacity lower bounds of this channel under an average power constraint in bits per channel use. We develop an asymptotic semi-analytic approximation for a capacity lower bound for arbitrary $n$ and a Rayleigh input distribution. It is shown that this lower bound grows logarithmically with signal-to-noise ratio (SNR), independently of the value of $n$. Numerical results for other continuous input distributions are also provided. A half-Gaussian input distribution is shown to give larger rates than a Rayleigh input distribution for $n=1,2,3$. At an SNR of $25$ dB, the best lower bounds we developed are approximately $3.68$ bit per channel use. The practically relevant case of amplitude shift-keying (ASK) constellations is also numerically analysed. For the same SNR of $25$ dB, a $16$-ASK constellation yields a rate of approximately $3.45$ bit per channel use.