HD-FEC Threshold Research Articles

Non-orthogonal multiple access scheme based on color-coded four-dimensional constellation pairing mapping

This paper proposes a short-range optical access method based on four-dimensional non-orthogonal multiple access (4D-NOMA), utilizing 4D constellation pairing mapping and two-dimensional inverse discrete Fresnel transform (2D-IDFnT) technology, achieving high compatibility with OFDM systems. An innovative color-coded 4D constellation pair mapping scheme was designed, introducing two types of four-dimensional spatial structures with 32 constellation points. By extending the three-dimensional constellation to four dimensions through color coding, the constellation figure of merit (CFM) increased by 22.2%. A 43.29 Gb/s 4D-NOMA transmission over a seven-core optical fiber was successfully demonstrated, verifying the feasibility and superiority of the proposed solution. Compared to conventional low-dimensional constellations, 4D-NOMA exhibits significant improvements in bit error rate and signal transmission sensitivity. Under the HD-FEC threshold, it provides approximately 0.9 dB and 1.3 dB sensitivity gains over traditional three-dimensional and two-dimensional constellations, respectively. This study indicates that the four-dimensional constellation structure and the 4D-NOMA scheme hold great potential for future short-range optical access systems.

LUT enabled low-complexity electrical dispersion pre-compensation scheme for IM-DD systems.

Frequency selective fading caused by chromatic dispersion (CD) and direct detection is the primary impediment for IM-DD systems in achieving a large capacity-distance product. Gerchberg-Saxton (GS) based electrical dispersion pre-compensation (pre-EDC) schemes enhance IM-DD systems' robustness against chromatic dispersion (CD), but their high computational complexity limits practical implementation. In this Letter, a novel, to the best of our knowledge, low-complexity pre-EDC scheme enabled by the cluster-assisting look-up table (CLUT) technique is proposed to further reduce the computation complexity of the non-iterative FIR-based pre-EDC scheme, in which convolution operation is replaced by tables look-up and accumulation processing. And a key strategy is proposed to balance the number and the total size of the LUTs by establishing LUTs for each cluster center after clustering the tap weights. To validate the effectiveness of the proposed scheme, we experimentally demonstrate the transmission of 80 Gbit/s PAM-4 signals and 100 Gbit/s PAM-6 signals over 20 km standard single-mode fiber (SSMF). The experimental results show that the proposed scheme can eliminate the multiplication in convolution operations and reduce the addition times of 58.54% for PAM-4 and 51.22% for PAM-6 signals at the BER of 7% HD-FEC threshold without any penalty.

Mobile fronthaul solution based on visible light fiber communication and zero-padding 8-D CAP modulation.

With the deployment of the fifth-generation (5 G) emerging technologies, such as massive multiple-input multiple-output (mMIMO), conventional mobile fronthaul (FH) schemes based on Common Public Radio Interface (CPRI) are limited in their abilities to support ultra-high data rate, large bandwidth and massive connectivity. This has led to a growing demand for alternative solutions that can better fulfill these requirements. Visible light communication (VLC) has recently gained increasing research interest as a potential complementary technology for beyond-5 G communication, offering advantages such as unlicensed and abundant spectrum, high bandwidth and cost-efficiency. In this paper, we propose a novel mobile fronthaul solution based on visible light fiber communication (VLFC), incorporating innovative zero-padding N-D (N>2) carrierless amplitude and phase (CAP) modulation. To avoid strong low-frequency noise (LFN) in the practical VLFC system, we innovatively propose zero-padding N-D CAP based on the actual distribution of LFN for the first time. In contrast to frequency division multiplexing (FDM), N-D CAP eliminates guard bands and ensures similar performance among multiple channels. To prove the concept, we demonstrate the transmission of PAM8 symbols at three typical visible light wavelengths (R/G/B) over 100 m multi-mode fiber (MMF) using zero-padding 8-D CAP modulation. The experiment verifies that zero-padding significantly enhances communication performance, with all 8 channels achieving similar BER. Communication performance improves as wavelengths are longer due to attenuation and dispersion caused by MMF. Finally, we have achieved a total data rate of 10.8Gbps at 635 nm (red), 9.0Gbps at 520 nm (green), and 7.5Gbps at 488 nm (blue) under the 7% HD-FEC threshold.

Minimalist Deployment of Neural Network Equalizers in a Bandwidth-Limited Optical Wireless Communication System with Knowledge Distillation.

An equalizer based on a recurrent neural network (RNN), especially with a bidirectional gated recurrent unit (biGRU) structure, is a good choice to deal with nonlinear damage and inter-symbol interference (ISI) in optical communication systems because of its excellent performance in processing time series information. However, its recursive structure prevents the parallelization of the computation, resulting in a low equalization rate. In order to improve the speed without compromising the equalization performance, we propose a minimalist 1D convolutional neural network (CNN) equalizer, which is reconverted from a biGRU with knowledge distillation (KD). In this work, we applied KD to regression problems and explain how KD helps students learn from teachers in solving regression problems. In addition, we compared the biGRU, 1D-CNN after KD and 1D-CNN without KD in terms of Q-factor and equalization velocity. The experimental data showed that the Q-factor of the 1D-CNN increased by 1 dB after KD learning from the biGRU, and KD increased the RoP sensitivity of the 1D-CNN by 0.89 dB with the HD-FEC threshold of 1 × 10-3. At the same time, compared with the biGRU, the proposed 1D-CNN equalizer reduced the computational time consumption by 97% and the number of trainable parameters by 99.3%, with only a 0.5 dB Q-factor penalty. The results demonstrate that the proposed minimalist 1D-CNN equalizer holds significant promise for future practical deployments in optical wireless communication systems.

Deep Learning Equalizer Connected with Viterbi-Viterbi Algorithm for PAM D-Band Radio over Fiber Link.

D-band (110-170 GHz) has been regarded as a potential candidate for the future 6G wireless network because of its large available bandwidth. At present, the lack of electrical amplifiers operating in the high frequency band and the strong nonlinear effect, i.e., the D-band, are still important problems. Therefore, effective methods to mitigate the nonlinear issue resulting from the ROF link are indispensable, among of which machine learning is considered the most effective paradigm to model the nonlinear behavior due to its nonlinear active function and structure. In order to reduce the computation amount and burden, a novel deep learning neural network equalizer connected with typical mathematical frequency offset estimation (FOE) and carrier phase recovery (CPR) algorithms is proposed. We implement D-band 45 Gbaud PAM-4 and 20 Gbaud PAM-8 ROF transmission simulations, and the simulation results show that the real value neural network (RVNN) equalizer connected with the Viterbi-Viterbi algorithm exhibits better compensation ability for nonlinear impairment, especially when dealing with serious inter-symbol interference and nonlinear effects. In our experiment, we employ coherent detection to further improve the receiver sensitivity, so a complex baseband signal after down conversion at the receiver is inherently produced. In this scenario, the complex value neural network (CVNN) and RVNN equalizer connected with the Viterbi-Viterbi algorithm have better BER performance with an error rate lower than the HD-FEC threshold of 3.8 × 10-3.

Deep learning based end-to-end visible light communication with an in-band channel modeling strategy.

Aside from ambient light noise, shot noise, and linear/nonlinear effects, strong low-frequency noise (LFN) severely affects the signal quality in LED-based visible light communication (VLC) systems, which hinders the implementation of data-driven end-to-end (E2E) deep learning approaches in real LED-VLC systems. We present a deep learning-based autoencoder to deal with this challenge. A novel modeling strategy is proposed to bypass the influence of the LFN and other low signal-to-noise ratio data when training the channel model of our E2E framework. The deep learning-based autoencoder then embeds the differentiable channel model and learns to combat the majority of channel impairments. In the E2E LED-VLC experiment, 1.875 Gbps transmission is achieved under the 7% HD-FEC threshold, 0.325 Gbps faster than the baseline. The E2E framework is robust to signal bias and amplitude variations, implying dimming support in the indoor environment.

Complex-Valued 2D-CNN Equalization for OFDM Signals in a Photonics-Aided MMW Communication System at the D-Band

Orthogonal frequency division multiplexing (OFDM) is a promising solution in photonics-aided millimeter-wave (MMW) communication systems, which combine the features of fiber and wireless links. In such a fiber-wireless system, the broadband OFDM signals could be affected by the multipath effect, chromatic dispersion, frequency synchronization error, and other complex impairments. Therefore, both inter-symbol interference (ISI) and inter-carrier interference (ICI) will cause performance degradation. In this experiment, a D-band photonics-aided MMW communication system is demonstrated. To compensate for the linear and nonlinear distortions during the fiber and wireless transmission, we proposed a novel time-frequency domain equalizer based on a two-dimensional convolutional neural network (2D-CNN) with a complex-valued structure. Moreover, a residual branch is adopted. We investigate the bit error rate (BER) performance of the OFDM signals transmission with different modulation formats. With the aid of complex-valued 2D-CNN based equalization, 40 Gbit/s 16QAM and 55 Gbit/s PS-64QAM signals can be successfully transmitted over 200 m wireless distance at the D-band while satisfying the HD-FEC (3.8 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup> ) and SD-FEC (2.0 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−2</sup> ) threshold, respectively. Moreover, the complex-valued structure can bring significant sensitivity improvements compared to the real-valued 2D-CNN equalization.

Neural-Network-Based Nonlinear Tomlinson-Harashima Precoding for Bandwidth-Limited Underwater Visible Light Communication

Underwater visible light communication (UVLC) based on light-emitting diodes (LEDs) is considered a potential candidate for underwater wireless data transmission. However, the implementation of high-speed UVLC remains a challenge due to bandwidth limitation and nonlinear effects. In this paper, we investigate the performance of Tomlinson-Harashima precoding (THP) in the bandwidth-limited UVLC system for the first time. Apart from research on linear and Volterra series-based nonlinear THP, neural network (NN)-based THP is first proposed and conducted. At the transmitter, the intersymbol interference (ISI) and nonlinearity can be partially mitigated through a feedback neural network (FBN) without error propagation. A modulo operator is employed to eliminate instability. In addition, for the precoded signals, the power spectral density (PSD) is near-white. Therefore, it is possible to avoid the spectrum-shaping-induced signal-to-noise ratio (SNR) loss problem that is common in pre-emphasis methods. At the receiver, another modulo operator is used for decoding. An adaptive feedforward neural network (FFN) is applied to compensate for the channel state information (CSI) mismatch of the FBN and mitigate the remaining ISI and nonlinear impairments. In the demonstrated UVLC system, the experimental results prove the feasibility of the proposed method. The Q factor is increased by 3.39 dB at a data rate of 2.2 Gbps. 630 MBd CAP-16 transmission under a 7&#x0025; HD-FEC threshold is realized, which is 90 MBd higher than that when employing linear postequalization only.

A modified Volterra equalizer for compensation distortion in C-band DML-based short reach limited-bandwidth system with 80-Gb/s PAM-4 signals

In this paper, we investigate the system model of intensity modulation with direct detection (IM/DD)-based high-speed short-reach link with directly modulation laser (DML) and bandwidth-limitation optics devices. And, based on this model, we propose a modified Volterra equalizer to compensate distortion by constructing second-order feature vectors for support vector machine (SVM) trainer in this high-capacity and limited-bandwidth system. Owing to high-dimensional mapping characteristics of SVM, for our scheme, only a single classification hyperplane is needed to be trained to achieve satisfactory equalization performance for the multi-classification tasks of PAM-M, which would reduce the calculation complexity. Moreover, the 80-Gb/s PAM-4 per wavelength transmission experiment with 10-G optics in 20-km standard single mode fiber (SSMF) DML system is conducted and utilized to manifest the feasibility and effectiveness of our scheme. The results show that our scheme can reach the HD-FEC threshold and achieve outstanding performance than commonly used equalizers.

K-means Cluster Algorithm Applied for Geometric Shaping Based on Iterative Polar Modulation in Inter-Data Centers Optical Interconnection

The demand of delivering various services is driving inter-data centers optical interconnection towards 400 G/800 G, which calls for increasing capacity and spectrum efficiency. The aim of this study is to effectively increase capacity while also improving nonlinear noise anti-interference. Hence, this paper presents a state-of-the-art scheme that applies the K-means cluster algorithm in geometric shaping based on iterative polar modulation (IPM). A coherent optical communication simulation system was established to demonstrate the performance of our proposal. The investigation reveals that the gap between IPM and Shannon limit has significantly narrowed in terms of mutual information. Moreover, when compared with IPM and QAM using the blind phase searching under the same order at HD-FEC threshold, the IPM-16 using the K-means algorithm achieves 0.9 dB and 1.7 dB gain; the IPM-64 achieves 0.3 dB and 1.1 dB gain, and the IPM-256 achieves 0.4 dB and 0.8 dB gain. The robustness of nonlinear noise and high capacity enable this state-of-the-art scheme to be used as an optional modulation format not only for inter-data centers optical interconnection but also for any high speed, long distance optical fiber communication system.

Digital back propagation based on the feedback-convergence for fiber nonlinearity compensation with low computational complexity and high performance

In this paper, an improved digital back propagation (DBP) method is proposed for the compensation of fiber non-linearity, which is based on the feedback-convergence assisted split-step Fourier method. The algorithm has been experimentally verified in a 1000 km 80 Gbit/s PDM-16QAM system. By optimizing the structure of nonlinear convergence within the DBP method, the accuracy of nonlinear compensation is improved comparing with the traditional algorithms while complexity reduced. The results show that the OSNR penalty for BER of HD-FEC threshold has reduced by 1.1 dB, and the transmission distance can be increased by ∼155 km for the threshold value of BER=1×10−4 compared to the traditional DBP method. When OSNR = 26 dB, the complexity of FC-DBP decreases 36.91% comparing with the traditional DBP method.

Piecewise Linear Equalizer for DML Based PAM-4 Signal Transmission Over a Dispersion Uncompensated Link

Directly modulated laser (DML) and direct detection (DD) based pulse-amplitude modulation (PAM) for short reach optical communications has attracted lots of research interests due to its low cost and simple configuration. However, the directly modulated PAM signal usually suffers from distortions after the transmission over a dispersion uncompensated link. Due to the adiabatic chirp of the DML working in a high output power region, different intensity levels of the PAM signal correspond to different frequency offsets, thus resulting in amplitude-dependent skew after the transmission over a dispersion uncompensated link. It will degrade signal quality and limit transmission distance. In this article, we, for the first time, propose a computational efficient piecewise linear (PWL) equalizer to correct the amplitude-dependent skew due to the interaction between the DML chirp and chromatic dispersion in the fiber. By using the PWL equalizer, the amplitude-dependent skew is corrected, and we successfully transmit 56 Gb/s PAM-4 signal over 40 km and 84 Gb/s PAM-4 signal over 20 km dispersion uncompensated link in the C band, with a bit error ratio (BER) below the HD-FEC threshold (3.8 × 10− 3). To demonstrate the low computational complexity of the PWL, we compare its complexity with 2nd order Volterra equalizer for a similar BER performance. The results show that the computational complexity can be reduced by 61.4% and 40.4% for the 56 Gb/s and 84 Gb/s PAM-4 signal transmission, respectively.

Demonstration of C-Band Amplifier-Free 100 Gb/s/ Direct-Detection Links Beyond 40-km SMF Using a High-Power SSB Transmitter

100 G/λ amplifier-free direct detection (DD) systems beyond 40-km reach are desirable to enable the next generation cost- and power-efficient 800 G-ER optical modules. Though such systems in the O-band have been demonstrated, an interest remains to leverage the investment in long haul C-band transceivers. To our knowledge, this article reports the first C-band amplifier-free DD system at beyond 100 G throughput over reaches of 40 and 60-km using a high-power single-sideband transmitter (HPSSBT). This transmitter configuration allows for a cost-efficient 100 G transceiver for the datacenter interconnect requiring only a single digital-to-analog converter (DAC), a Mach–Zehnder modulator, a single-ended photodiode with integrated trans-impedance amplifier (PD+TIA), and an analog-to-digital converter (ADC). In this article, we studied the performance impact of key system parameters including the digitally regenerated DC component of the photocurrent, the driving voltage, and the launch power. We also characterized the sensitivity impact of the system nonlinearity and demonstrated the transmission of 155.14 Gb/s and 104.67 Gb/s net rate single sideband (SSB) PAM-4 signals over 40-km and 60-km of single-mode fiber (SMF) below the HD-FEC threshold of 3.8 × 10−3, respectively. Due to the colored SNR, we further approached the system capacity by transmitting a probabilistically-shaped multi-subcarrier (PS-MSC) signal, allowing a throughput of 176 Gb/s over a 40-km SMF assuming an SD-FEC with a normalized general mutual information (NGMI) threshold of 0.88.

Spectral-Shaping Technique Based on Nonlinear-Coded-Modulation for Short-Reach Optical Transmission

The amount of data center traffic is rapidly increasing, and it is necessary for short-reach optical transmission such as Ethernet to realize a higher capacity data link. Therefore, the next-generation Ethernet links will require the higher data rate. In such a situation, transmission distance is limited by the bandwidth limitation due to optical and electrical devices in the Ethernet transceiver. In this article, we propose a nonlinear-coded-modulation which shapes the signal spectrum in order to realize the higher tolerance to bandwidth limitation. We apply this technique to a 92-Gbaud PAM4 signal and confirm that the proposed technique achieves the 7% HD-FEC threshold in 184-Gb/s transmission with the bandwidth limitation of 20 GHz through an O-band 10-km transmission experiment. We also investigate the applicability of MLSE to the proposed technique and show that the KP4-FEC threshold can be achievable with 2-memory MLSE and 5-tap channel-shortening filter. In addition, we study the applicability of the proposed technique to a QAM signal which is conventionally utilized in coherent systems. We compare the proposed nonlinear-coded QAM to the conventional duobinary QAM and show that the performance of the proposed QAM signal is greater than that of the duobinary QAM signal with MLSE where the signal degradation is induced by additive white Gaussian noise.

A SiGe HBT BiCMOS 1-to-4 ADC Frontend Enabling Low Bandwidth Digitization of 100 GBaud PAM4 Data

Market forecasts for intra and inter data center interconnects predict high growth rates in the upcoming years. This is associated with increasing requirements in terms of costs, power consumption, and bit rate per wavelength. Today, PAM4 systems are frequently used at up to 100 Gb/s per wavelength. The next logical step is to double the symbol rate to allow bit rates of 200 Gb/s at the same modulation format and at the same direct detection scheme. Such systems require three-digit gigasample analog-to-digital converters with bandwidths larger than 50 GHz, which are not available today as CMOS components. To extend the bandwidth of CMOS converters, we suggest the use of ADC frontends, which sample and demultiplex the analog input signals simultaneously. At the outputs of such ADC frontends, the signals can then be digitized by parallel converters with lower bandwidth and at a lower conversion rate. In this article, we present the circuit implementation of a 1-to-4 ADC frontend in IHP 130 nm SiGe HBT BiCMOS and demonstrate its integration into a 100 GBaud PAM4 transmission system with only 14 GHz of digitizer bandwidth. For optimum performance, the mitigation of intersymbol and interchannel interferences is mandatory in the transmission system. We describe and compare two different receiver DSP architectures for reduction of these interferences and evaluate their performances in electrical and optical back-to-back experiments. Furthermore, we report on transmission experiments over 500 m, 10 km, and 40 km SMF at 1550 nm wavelength. With linear equalization, we obtained a BER below the HD-FEC threshold of 3.8 × 10−3 and with 3 rd order Volterra equalization, we even achieved a BER below the KP4 threshold of 2.3 × 10 −4 .

Experimental study of single channel 100 Gbit/s PAM4 transmission over 40 km using 17 GHz EML and APD at O band

Abstract Single channel 100 Gbit/s PAM4 transmission at O band is experimentally studied based on low cost intensity modulation and direct detection (IM-DD). By the use of advanced digital signal processing algorithms, we successfully achieve a receiver sensitivity of −17.3 dBm at 7% HD-FEC threshold of 3.8E-3 over 40 km un-amplified SSMF transmission with 17 GHz (3 dB bandwidth) commercial electric absorption modulated laser (EML) and avalanche photodiode (APD). To the best of author’s knowledge, we hereby report the best receiver sensitivity for 100 Gbit/s/λ IM-DD system. Due to the low cost and high sensitivity merits, the proposed scheme will be a promising way for high speed short-haul optical transmissions in the future.

Transmitter and receiver DSP for 112 Gbit/s PAM-4 amplifier-less transmissions using 25G-class EML and APD.

The transmission performance of 112 Gbit/s PAM-4 signal with commercial 25 G-class EML and APD is experimentally studied by using advanced digital signal processing (DSP) algorithms, i.e. pre-equalization (Pre-EQ), error-table based pre-correction (ETC), least-mean square (LMS) based equalization, direct detection faster than Nyquist (DD-FTN) algorithm. Among them, Pre-EQ and ETC are implemented at the transmitter, and ETC is a symbol-pattern-dependent pre-compensation algorithm based on the look-up-table approach. In order to obtain these pre-compensated parameters readily, a joint equalization and error table generation (JEEG) module is proposed. Employing the combination of ETC, LMS, and DD-FTN, a single line 112 Gbit/s PAM-4 40 km amplifier-less transmission with a record receiver sensitivity of -16.6 dBm (at 7% HD-FEC threshold) is experimentally demonstrated. In addition, the computational complexities of different DSP schemes are analyzed and discussed in detail. The receiver computational complexity can be effectively reduced by employing appropriate ETC and Pre-EQ in the transmitter.

Experimental study of performance enhanced IM/DD transmissions based on constellation switching.

In this work, we experimentally investigate the performance improvement in IM/DD systems using constellation switching (CS), which is simple to implement with a reasonably low complexity. By encoding extra bits on the selection of a PAM constellation pattern from a set of constellations, a lower symbol rate can be used to achieve the same system bit rate compared with standard PAM systems based on a single constellation pattern. In our experiments with bandwidth limited components, including a 14 GHz bandwidth digital-to-analog converter (DAC), we demonstrate that the CS signals can improve the receiver sensitivity. In particular, in the 112 Gbit/s PAM4 case, the required receiver power was reduced by 0.8 dB and 1.1 dB using the CS at the HD FEC threshold of BER = 4 × 10-3 in the back-to-back (B2B) and 3 km fiber transmission, respectively. Similarly, in the 84 Gbit/s two-dimension (2D) PAM4 case, the required receiver power was reduced by 1.05 dB and 3.5 dB at the HD FEC threshold of BER = 4 × 10-3 in the back-to-back (B2B) and 5 km fiber transmission, respectively. Moreover, we show by simulations that the improved performance of using the CS signals is also observed over a wide range of transmitter bandwidth, further indicating the merits of using the CS in IM/DD PAM transmissions.

Amplifier-free 200-Gb/s tandem SSB doubly differential QPSK signal transmission over 80-km SSMF with simplified receiver-side DSP.

We numerically demonstrate 80-km standard single-mode fiber transmission without optical amplification, dispersion compensation or carrier recovery using 200-Gb/s tandem single sideband modulated doubly differential QPSK. Simulation results show that doubly differential encoding enables practically constant system performance for frequency offsets within ± 2.3 GHz and allows a linewidth tolerance of 2.5 × 10-3 at 1-dB receiver sensitivity penalty. Employing 2.9-MHz linewidth lasers, the receiver sensitivity penalty at 7% HD-FEC threshold for 80-km transmission is less than 0.2 dB. By adding a 12-symbol decision feedback in the 2nd differential operation of doubly differential decoding, the receiver sensitivity is improved by 3.7 dB.

Experimental investigation of extended Kalman Filter combined with carrier phase recovery for 16-QAM system

Performance of Extended Kalman Filter combined with the Viterbi–Viterbi phase estimation (VVPE-EKF) for joint phase noise mitigation and amplitude noise equalization is experimental demonstrated. Experimental results show that, for 11.2 Gbaud SP-16-QAM, the proposed VVPE-EKF achieves 0.9 dB required OSNR reduction at bit error ratio (BER) of 3.8e-3 compared to the VVPE. The result of maximum likelihood combined with VVPE (VVPE-ML) is only 0.3 dB. For 28 GBaud SP-16-QAM signal, VVPE-EKF achieves 3 dB required OSNR reduction at BER=3.8e-3 (7% HD-FEC threshold) compared to VVPE. And VVPE-ML can reduce the required OSNR for 1.7 dB compared to the VVPE. VVPE-EKF outperforms DD-EKF 3.7 dB and 0.7 dB for 11.2 GBaud and 28 GBaud system, respectively.