Search

The problem of Raman amplifier optimization is studied. A differentiable interpolation function is obtained for the Raman gain coefficient using machine learning (ML), which allows for the gradient descent optimization of forward-propagating Raman pumps. Both the frequency and power of an arbitrary number of pumps in a forward pumping configuration are then optimized for an arbitrary data channel load and span length. The forward propagation model is combined with an experimentally-trained ML model of a backward-pumping Raman amplifier to jointly optimize the frequency and power of the forward amplifier's pumps and the powers of the backward amplifier's pumps. The joint forward and backward amplifier optimization is demonstrated for an unrepeatered transmission of 250 km. A gain flatness of $<$ 1 dB over 4 THz is achieved. The optimized amplifiers are validated using a numerical simulator.

Vendor interoperability is one of the desired future characteristics of optical networks. This means that the transmission system needs to support a variety of hardware with different components, leading to system uncertainties throughout the network. For example, uncertainties in signal-to-noise ratio and laser linewidth can negatively affect the quality of transmission within an optical network due to, e.g. mis-parametrization of the transceiver signal processing algorithms. In this paper, we propose to geometrically optimize a constellation shape that is robust to uncertainties in the channel conditions by utilizing end-to-end learning. In the optimization step, the channel model includes additive noise and residual phase noise. In the testing step, the channel model consists of laser phase noise, additive noise and blind phase search as the carrier phase recovery algorithm. Two noise models are considered for the additive noise: white Gaussian noise and nonlinear interference noise model for fiber nonlinearities. The latter models the behavior of an optical fiber channel more accurately because it considers the nonlinear effects of the optical fiber. For this model, the uncertainty in the signal-to-noise ratio can be divided between amplifier noise figures and launch power variations. For both noise models, our results indicate that the learned constellations are more robust to uncertainties in channel conditions compared to a standard constellation scheme such as quadrature amplitude modulation and standard geometric constellation shaping techniques.

Compensation of Kerr nonlinearity-induced distortions has been shown to allow for increasing transmission rate and reach, with optical compensation techniques particularly attractive for broadband wavelength-division multiplexed (WDM) scenarios. However, they normally require additional devices within the link, which is particularly challenging for already deployed systems, and even more so for unrepeatered transmission. In this work, we focus on providing lumped optical nonlinearity suppression, either at the transmitter or at the receiver side, based on optical phase conjugation (OPC). The theory to design scaled-down OPC compensation modules is derived, and it allows to move beyond the standard mid-link OPC approach and to explore compensation modules with fibers types not directly linked to the dispersion properties of the transmission link. This design method is then validated both through numerical investigations and experimental demonstrations for a number of systems with a varying degree of complexity. Ultimately, significant performance improvement is shown by employing short OPC-based compensation structures which are carefully designed to match much longer transmission links.

This paper studies a learning approach to geometric shaping (GS) for concatenated two-level multi-level codes (MLC). Unlike standard bit-interleaved coded modulation (BICM), the proposed MLC protects only the least reliable bits (LRBs) by an inner code, and thereby efficiently reduces complexity associated with inner soft-decision (SD) decoding compared to the BICM without performance degradation. We propose a new loss function for training a geometric constellation shape in the proposed MLC, leading to maximization of the achievable rate. More specifically, considering the different coding structures for the most reliable bits (MRBs) and the LRBs, the proposed loss function combines two different functions: the union bound on a bit error rate (BER) for the MRBs and the generalized mutual information (GMI) for the LRBs. We demonstrate by simulations of wavelength division multiplexing (WDM) optical fiber systems that the proposed loss function offers a performance gain over the conventional cross entropy-based loss function. Furthermore, it is demonstrated that the proposed MLC with GS outperforms the conventional BICM with GS in terms of a transmission distance, even with significantly lower SD decoding complexity.

This paper proposes a new probabilistic amplitude shaping (PAS) approach for concatenated two-level multi-level coding (MLC). The proposed system is based on a concatenated forward error correction (FEC) scheme where outer codes are serially concatenated with inner two-level MLC. This concatenated two-level MLC scheme has recently been shown to have a potential for achieving better performance-complexity trade-offs than the conventional bit-interleaved coded modulation (BICM). Meanwhile, PAS has recently been demonstrated to offer remarkable performance gains as well as rate adaptivity. However, the majority of existing works on PAS assume the use of the binary reflected Gray code as a bit-labeling, and its application to coded modulation schemes with other bit-labelings, such as two-level MLC, may not be straightforward. In this paper, we devise a bit-labeling scheme and propose a new PAS structure for an efficient integration of PAS with two-level MLC systems. More specifically, we propose to generate signed amplitude symbols with the distribution matcher (DM) for maximizing both coding and shaping gains achieved by two-level MLC and PAS, respectively, while the conventional PAS generates unsigned amplitude symbols. It is demonstrated by simulation results that, with 256QAM and inner polar codes, the proposed two-level MLC with PAS simultaneously offers 75% reduction in the number of required inner encoding and soft-decision (SD) decoding operations for given outer and inner FEC code lengths, and up to 0.3 dB performance gain over the conventional PAS scheme.

We numerically demonstrate an all-optical nonlinearity pre-compensation module for state-ofthe-art long-reach Raman-amplified unrepeatered links. The compensator design is optimized in terms of propagation symmetry to maximize the performance gains under WDM transmission, achieving 4.0dB and 2.6dB of SNR improvement for 250-km and 350-km links.

Probabilistic constellation shaping is studied and developed for optical phase conjugation (OPC)-based nonlinearity compensation of Kerr nonlinearities in optical fiber links. The mid-link OPC scenario is considered for dispersion compensated systems. It is demonstrated in simulations and experimentally that transmission strategies optimal for classical additive white Gaussian noise (AWGN) channels can be sub-optimal for these systems without nonlinearity compensation. On the contrary, when nonlinearity compensation is applied with mid-link OPC, the channel noise is demonstrated to be Gaussian and AWGNlike transmission strategies thus remain effective. A channelagnostic probability mass function (PMF) optimization algorithm is proposed for the input constellation in order to further improve the shaping gains in both scenarios. Operating arbitrary PMFs on arbitrary channels is enabled by a channel-agnostic digital signal processing (DSP) chain. After ≈2000 km of transmission, mid-link OPC is demonstrated to provide ≈1 dB of gain in effective SNR, which translates to ≈0.4 bits/QAM symbol of gain in achievable information rate. The gain is then increased by an extra ≈0.2 bits/QAM symbol by applying probabilistic shaping.

A neural network is used to predict the optimal Maxwell-Boltzmann probabilistic constellation shaping for a nonlinear channel with inline dispersion-compensation. The network uses only system parameters available at the transmitter and thus requires no feedback.

In this paper, the performance of adaptive turbo equalization for nonlinearity compensation (NLC) is investigated. A turbo equalization scheme is proposed where a recursive least squares (RLS) algorithm is used as an adaptive channel estimator to track the time-varying intersymbol interference (ISI) coefficients associated with inter-channel nonlinear interference (NLI) model. The estimated channel coefficients are used by a MIMO 22 soft-input soft-output (SISO) linear minimum mean square error (LMMSE) equalizer to compensate for the time-varying ISI. The SISO LMMSE equalizer and the SISO forward error correction (FEC) decoder exchange extrinsic information in every turbo iteration, allowing the receiver to improve the performance of the channel estimation and the equalization, achieving lower bit-error-rate (BER) values. The proposed scheme is investigated for polarization multiplexed 64QAM and 256QAM, although it applies to any proper modulation format. Extensive numerical results are presented. It is shown that the scheme allows up to 0.7 dB extra gain in effectively received signal-to-noise ratio (SNR) and up to 0.2 bits/symbol/pol in generalized mutual information (GMI), on top of the gain provided by single-channel digital backpropagation.

In this paper, machine learning is used to create a differentiable model for the input-output power spectral profile relations of C-band erbium-doped fiber amplifiers (EDFAs). The EDFA model is demonstrated to generalize to multiple physical devices of the same make while only trained on experimental data from a single unit. The model is combined with a differentiable model for simulating stimulated Raman scattering (SRS) effects during propagation through the the optical fiber to create a differentiable model for a multi-span system with an arbitrary configuration of number of spans, length per span and launch power per span. The cascade system model is used to predict and optimize the power profile output of several such experimental configurations of up to three spans with an arbitrary target power profile. A flat target profile is exemplified experimentally, achieving $<$3 dB of power excursions for EDFAs exhibiting $>$10 dB of excursion per device in the cascade. The experimental data used to create the EDFA model is made public and available online.

In this work, we present a novel strategy to satisfying the nonlinearity compensation criteria by optical phase-conjugation (OPC). Contrary to the most common approach, which relies on tailoring power profiles using distributed Raman-amplification, we achieve the required OPC propagation symmetry through optimized dispersion management across the link. The method is applied to transmission systems with periodic lumped amplification, and the symmetry enhancement is directly translated into a substantial increase in the OPC compensation gains. This study is based on a numerical analysis combined with experimental validation of the findings. The numerical part provides a comprehensive overview of different dispersion management techniques, and compares them against the symmetric schemes we propose. It is consistently shown that the symmetry-optimized systems provide the best performance when OPC is included, with the signal-to-noise ratio (SNR) gains reaching up to 6.6 dB and 5.2 dB for transmission of a single and seven wavelength channels, respectively. These results are verified in an experimental investigation, where we implemented and compared a standard dispersion mapping scheme to the optimized design. For all distances considered, the optimized link is demonstrated superior once OPC is included, leading up to 1.9 dB improvement in SNR for seven-channel transmission.

Training of autoencoders using the back-propagation algorithm is challenging for non-differential channel models or in an experimental environment where gradients cannot be computed. In this paper, we study a gradient-free training method based on the cubature Kalman filter. To numerically validate the method, the autoencoder is employed to perform geometric constellation shaping on differentiable communication channels, showing the same performance as the back-propagation algorithm. Further investigation is done on a non-differentiable communication channel that includes: laser phase noise, additive white Gaussian noise and blind phase search-based phase noise compensation. Our results indicate that the autoencoder can be successfully optimized using the proposed training method to achieve better robustness to residual phase noise with respect to standard constellation schemes such as Quadrature Amplitude Modulation and Iterative Polar Modulation for the considered conditions.

In this work, a multilevel coding (MLC) based coded modulation scheme with two degrees of freedom in rate flexibility is proposed and compared with a bit-interleaved coded modulation (BICM) scheme from a performance versus complexity perspective. The proposed MLC scheme is based on a rate flexible inner soft-decision polar code and utilizes an outer hard-decision staircase code structure as in the 400ZR concatenated forward error-correcting code. The performance of the MLC scheme is investigated for a range of inner code lengths, inner decoder list sizes, and signaling with 16 and 64 quadrature amplitude modulation, respectively. The MLC is designed such that a portion of the staircase encoded bits can bypass the inner code. The number of required inner soft-decision decoders can thus be reduced, thereby saving computational complexity. The proposed MLC scheme simultaneously offers up to a 53.7% reduction in the number of inner decoders and up to 0.55 dB of performance improvement when compared with the similar BICM approach.

The perturbation-based nonlinearity compensation (NLC) method is considered in conjunction with a forward error correction (FEC) code that is capable of detecting block errors. The FEC decoding is performed prior to the NLC, and NLC is then performed only for blocks, that could not be decoded correctly. The total NLC complexity is thus dramatically reduced to down to 1% in some cases w.r.t. the standard, hard decision-directed NLC performed prior to the FEC decoding. Negligible FEC decoding complexity increase is required for the subsequent decoding of the nonlinearty-compensated blocks. The proposed method achieves and sometimes outperforms the standard perturbation based NLC at a fraction of the overall complexity. Polar codes are used to exemplify the method.

In this paper, we consider fast decoding of soft-decision (SD) Hamming codes as inner codes in concatenated forward error-correction (FEC) schemes for high-speed optical communication. The goal is single FPGA implementations at speeds of 400 Gb/s and beyond. A low complexity maximum a posteriori (MAP) probability decoding is applied to a (128,120) Hamming code. Chase decoding of a (128,119) Hamming code is also implemented. The VHDL designs for both decoding schemes are presented. The FEC performance and FPGA resource utilization are investigated and compared. Synthesis results indicate that, both the Chase and the MAP decoder leave sufficient resources available to also accommodate a powerful outer hard decision code, on a single FPGA. Furthermore, MAP decoding of (128,120) Hamming code features lower hardware complexity and provides a higher data throughput.

Probabilistic constellation shaping is investigated in the context of nonlinear fiber optic communication channels. Based on a general framework, different link types are considered—1. dispersion-managed channels, 2. unrepeatered transmission channels and 3. ideal distributed Raman amplified channels. These channels exhibit nonlinear effects to a degree that conventional probabilistic constellation shaping strategies for the additive white Gaussian (AWGN) noise channel are suboptimal. A channel-agnostic optimization strategy is used to optimize the constellation probability mass functions (PMFs) for the channels in use. Optimized PMFs are obtained, which balance the effects of additive amplified spontaneous emission noise and nonlinear interference. The obtained PMFs cannot be modeled by the conventional Maxwell-Boltzmann PMFs and outperform optimal choices of these in all the investigated channels. Suboptimal choices of constellation shapes are associated with increased nonlinear effects in the form of non-Gaussian noise. For dispersion-managed channels, a reach gain in 2 spans is seen and across the three channel types, gains of >0.1 bits/symbol over unshaped quadrature-amplitude modulation (QAM) are seen using channel-optimized probablistic shaping.

In this paper, a rate-adaptive coded modulation (CM) system combining polar codes and many-to-one probabilistic shaping is constructed and experimentally demonstrated. We propose to control the polar codes using a fraction of bits referred to as pre-set bits. This not only allows to offset the puncturing loss of rate-adaptive polar codes but also provides shaping gains compared to the non-punctured polar codes. Pre-set bits and many-to-one shaping are combined to form a rate-adaptive bit-interleaved CM system. We experimentally evaluate the system performance for 10x8-GBd dual polarization 256 quadrature amplitude modulation (QAM) wavelength division multiplexed (WDM) system with various input data rates ranging from 61 Gbps to 91 Gbps per carrier. The experimental results demonstrate a 200 km reach increase over a wide range of distances compared to the non-punctured polar codes and punctured polar codes.

A family of texture-based generative models for fingerprint images is proposed. The generative models are used to estimate upper bounds on the image entropy for systems with small sensor acquisition. The identification capacity of such systems is then estimated using the mutual information between different samples from the same finger. Similar to the generative model for entropy estimation, pixel-level model families are proposed for estimating similarity between fingerprint images with a given global affine transformation. These models are used for mutual information estimation, and are also adopted to compensate for local deformations between samples. Finally, it is shown that sensor sizes as small as 52x52 pixels are potentially sufficient to discriminate populations as large as the entire world population that ever lived, given that a complexity-unconstrained recognition algorithm is available which operates on the lowest possible pixel level.

Autoencoder-based geometric shaping is proposed that includes optimizing bit mappings. Up to 0.2 bits/QAM symbol gain in GMI is achieved for a variety of data rates and in the presence of transceiver impairments. The gains can be harvested with standard binary FEC at no cost w.r.t. conventional BICM.

In this work, we present a comprehensive experimental and numerical investigation of the impact of system parameters on wavelength converters based on four-wave-mixing, with focus on practical system implementations in addition to the interaction within the nonlinear medium. The input signal power optimization is emphasized according to the trade-off between the linear and the nonlinear impairments, and the origin of the limitations at the optimum is studied. The impact of the input signal quality on the converted idler is discussed, and depending on the dominant noise contribution a varying conversion penalty is demonstrated. The penalty is also shown to scale with increasing number of WDM channels due to additional nonlinear cross-talk between them. Finally, by means of numerical simulations we extend the experimental characterization to high pump powers, showing the impact of parametric noise amplification, and different pump laser linewidths, which lead to increased phase-noise transfer. The experimental characterization employs an integrated AlGaAs-on-insulator waveguide, and the numerical simulations accompany the results to make the analysis general for $\chi^{(3)}$ materials that satisfy the assumptions of the split-step Fourier method.

In this paper, we propose a polar-coded transmission system with adjustable data rate for coherent optical transmission employing quadrature amplitude modulation (QAM). The proposed system is based on a many-to-one constellation shaping method for achieving a range of data rates with arbitrarily small rate steps. An implicitly punctured polar-coded modulation system is then designed by combining polar coded bit-interleaved coded modulation system (BICM) with many-to-one labellings. The scheme is experimentally evaluated in a wavelength division multiplexed (WDM) system with five carriers modulated at 16 GBaud with polarization multiplexed (PM) 256QAM. Data rates ranging from 121 Gbps to 182 Gbps per carrier are experimentally demonstrated and the system can be directly extended to achieve higher data rates. Synchronization and equalization of PM-256QAM received symbols is performed with a pilot rate of 5%. The experimental results show 1.2 dB of shaping gain over the conventionally punctured polar codes in the optical back-to-back scenario. The maximum transmission system reach is increased by 200 km to 400 km w.r.t the conventionally punctured polar codes. It is shown that the rate adaptation does not require a change of modulation format and/or underlying forward error-correction (FEC) code. Finally, the performance of all 5 WDM channels is validated for the optimal input power.

Optical phase conjugation is a well-known technique to provide dispersion and nonlinearity compensation directly in the optical domain. The link properties play an important role in the achievable improvements in transmission reach/rate. Here, we review our recent investigations on the impact of sub-optimum transmission links as well as our effort on the implementation of the optical phase conjugator itself looking beyond using highly nonlinear fibers as nonlinear medium and focusing on integrated silicon waveguides. Preliminary results on combining optical phase conjugation with digital techniques such as probabilistic shaping will also be discussed.

Gains offered by mid-link OPC and probabilistic shaping are compared in a dispersion-managed link with 64QAM input. Probabilistic shaping is optimized online and tailored to the specific channel and transceiver conditions, including the OPC stage.

The nonlinear Fourier transform is a new approach of addressing the capacity limiting Kerr nonlinearities in optical communication systems. It exploits the property of integrability of the lossless nonlinear Schrödinger equation and thus incorporates nonlinearities as an element of the transmission. However, practical links employing erbium-doped fiber amplifiers include losses/gains and introduce noise which breaks the integrability of the nonlinear Schrödinger equation. Although the lossless path average approximation proposes an integrable model, its imprecision still leads to unintended distortions and thus performance degradation. We propose an alternative receiver for nonlinear frequency division multiplexing optical communication systems using techniques from machine learning. It is highly adaptive as it learns from previously transmitted pulses and thus holds no assumptions on the system and noise distribution. The detection method presented is fully applied in time-domain and omits the nonlinear Fourier transform. The numerical results provide a benchmark for nonlinear Fourier transform based detection of high order solitons for fiber links with losses and noise present.