Hard-decision Forward Error Correction Threshold Research Articles

An Improved End-to-End Autoencoder Based on Reinforcement Learning by Using Decision Tree for Optical Transceivers.

In this paper, an improved end-to-end autoencoder based on reinforcement learning by using Decision Tree for optical transceivers is proposed and experimentally demonstrated. Transmitters and receivers are considered as an asymmetrical autoencoder combining a deep neural network and the Adaboost algorithm. Experimental results show that 48 Gb/s with 7% hard-decision forward error correction (HD-FEC) threshold under 65 km standard single mode fiber (SSMF) is achieved with proposed scheme. Moreover, we further experimentally study the Tree depth and the number of Decision Tree, which are the two main factors affecting the bit error rate performance. Experimental research afterwards showed that the effect from the number of Decision Tree as 30 on bit error rate (BER) flattens out under 48 Gb/s for the fiber range from 25 km and 75 km SSMF, and the influence of Tree depth on BER appears to be a gentle point when Tree Depth is 5, which is defined as the optimal depth point for aforementioned fiber range. Compared to the autoencoder based on a Fully-Connected Neural Network, our algorithm uses addition operations instead of multiplication operations, which can reduce computational complexity from 108 to 107 in multiplication and 106 to 108 in addition on the training phase.

Simplified twin-single-sideband direct detection system separating left and right sideband signals using a digital signal processing algorithm instead of optical bandpass filters.

Twin-single-sideband (twin-SSB) signals can be generated based on an in-phase- quadrature (I/Q) modulator, and two independent left sideband (LSB) and right sideband (RSB) signals carry individual data to effectively harvest the advantage of twin-SSB modulation, which achieves higher spectral efficiency. However, the conventional twin-SSB scheme employs two optical bandpass filters (OBPFs) and two photodetectors (PDs) for complete separation and detection at the receiver side. To mitigate the crosstalk between RSB and LSB signals and reduce the complexity and cost of the twin-SSB system, we propose a new scheme to realize twin-SSB without OBPFs separating LSB and RSB signals by a single-ended PD to improve system performance. According to the beating characteristics of the LSB and RSB, we can separate two independent sideband signals using a digital signal processing (DSP) algorithm added to the receiver end. Our simulation results demonstrate that our proposed scheme can obtain good bit error ratio (BER) performance of LSB and RSB signals. We designed a twin-SSB system with different modulation formats in the two sidebands, adopting geometric shaping 3PSK (GS-3PSK) modulation for the LSB and quadrature phase shift keying (QPSK) modulation for the RSB. The BER of the LSB GS-3PSK and RSB QPSK signal can reach hard-decision forward error correction (HD-FEC) when the received optical power (ROP) was > -17.5 and > -16 dBm, respectively, at different baud rates of 1-, 2-, and 4-Gbaud with a carrier frequency of 12-GHz over 10-km standard single-mode fiber (SSMF) transmission. For an 8-Gbaud baud rate with a carrier frequency of 12-GHz over 5-km SSMF transmission, the BER of the two sideband signals can still be below the HD-FEC threshold of 3.8 × 10-3 when the ROP was > -17 and > -16 dBm, respectively.

Sub-sampling generation of ultra-high baud rate PAM/QAM signals via high-order partial response narrowing

Ultra-high baud rate signal generation and detection is of great importance for future intra-data-center interconnect (intra-DCI). In this work, based on a single digital-to-analog convertor (DAC) with 120GSa/s sampling rate, we experimentally demonstrate sub-sampling generation of pulse amplitude modulation (PAM) signals by using high-order partial response narrowing (HPRN) scheme. High-order partial response is utilized to concentrate most of the signal energy into the Nyquist region of DAC sampling rate. A digital brick-wall filter is then employed to avoid spectral overlap by removing the out-of-band components in the frequency domain. The manually induced inter-symbol interference (ISI) can be eliminated by maximum likelihood sequence detection (MLSD) at the receiver. In the experiment, 210Gbaud on-off keying (OOK) signal can be successfully generated and transmitted over 500m standard single-mode fiber (SSMF) with bit-error rate (BER) below the 20% hard-decision forward error correction (HD-FEC) threshold of 1.5×10−2, achieving sub-sampling rate of 0.571. For high-order modulation formats, 217.5Gb/s (145Gbaud) PAM-3 BTB generation and 256Gb/s (128Gbaud) PAM-4 500m transmission are also realized, respectively. Furthermore, for coherent detection systems, 160Gbaud quadrature phase shift keying (QPSK) signal generation is demonstrated by applying HPRN on the in-phase and quadrature components separately, and using carrier phase recovery including pilot symbol group-based coarse estimation and shaped constellation-based blind phase search (BPS) algorithm. The results reveal that the HPRN scheme can extend the usage of DAC at the expense of higher optical signal-to-noise ratio (OSNR) for 200G high-speed optical links and beyond.

Noise Shaping Enhanced DMT Signal Transmission Utilizing Low-Resolution DAC

In order to reduce the quantization noise of low-resolution DAC, we study a noise shaping technique that can reshape the white quantization noise to an irregular spectrum, in which the noise in the data subcarrier band is almost transformed into the null subcarrier band. Both in simulation and experiment, we verify the effectiveness of the investigated scheme in 25 GHz 16-QAM/32-QAM/64-QAM DMT transmission systems. The experimental results show that the noise shaping technique can enhance the receiver sensitivity of 4-bit quantized 16-QAM DMT and 5-bit quantized 32-QAM DMT by 4.3 dB and 2.5 dB respectively, at BER of hard decision forward error correction (HD-FEC) threshold (3.8 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup> ). In addition, with the aid of noise shaping, the performance of 4-bit quantization 16-QAM DMT system is the same as the 8-bit quantization 16-QAM DMT system at the HD-FEC threshold. The experimental results reveal that the proposed noise shaping scheme is a good solution for high-speed, low-cost short reach intra-DCI with low-resolution DAC in future 6G networks evolved from 5G mobile networks.

Optical fiber nonlinearity equalizer with support vector regression based on perturbation theory

With the development of high-speed and large-capacity optical fiber communication technology, nonlinear damage has been one great obstacle to the development of optical fiber communication. Transmission distance and signal energy are two main factors that affect the nonlinear damage. The nonlinear compensation algorithm based on perturbation theory can compensate nonlinear damage. However, the coefficients of perturbation matrix cannot be calculated easily. In this paper, we make use of machine learning as a tool, propose an equalizer with support vector regression based on perturbation theory. For a 120 Gb/s, 375 km transmission distance, dual-polarization 64 quadrature amplitude modulation communication system, bit error ratio (BER) is lower than hard-decision forward error correction threshold 3.8×10−3 in the launched optical power (LOP) from -4 dBm to 3 dBm and when LOP is 1 dBm, BER is lower than forward error correction threshold 1.0×10−3 . Moreover, it is shown that the optimum LOP is increased by 2 dB.

Transmission of a 56 Gbit/s PAM4 signal with low-resolution DAC and pre-equalization only over 80 km fiber in C-band IM/DD systems for optical interconnects.

A low-cost intensity modulation and direct detection scheme using a 4-bit digital-to-analog converter for 56 Gbit/s pre-equalized PAM-4 generation at the transmitter and without receiver side post-equalization over 80 km single-mode fiber transmission in a C-band is experimentally demonstrated in this Letter. Pre-equalization includes pre-emphasis for channel response, a modified Gerchberg-Saxton algorithm with five iterations for chromatic dispersion compensation, and a noise shaping technique implemented by a five-tap finite impulse response filter for quantization noise suppression. Enabled by the pre-equalization techniques, the bit error rate of the received signal without post-equalization can reach the hard-decision forward error correction threshold with -2dBm receiver optical power. The experimental results indicate that our proposed scheme is a promising candidate for the standardization of 400 GbE wavelength division multiplexing-based long-haul distance data center interconnects.

190Gbaud OOK signal generation with a sub-sampling rate of 0.63 using silicon photonic dual-drive Mach–Zehnder modulator

Intensity modulation with direct detection (IM/DD) has been served as a low-cost technology of data center optical interconnects. To achieve higher data rate, high-order partial response (PR) signaling is utilized to narrow the signal bandwidth below the Nyquist frequency of digital-to-analog converter (DAC) sampling rate. In this work, we experimentally demonstrate ultra-high speed optical interconnects based on a conventional silicon photonic traveling-wave Mach–Zehnder modulator (MZM) with a 3-dB bandwidth of 28.5 GHz. By applying PR narrowing and digital anti-aliasing brick-wall filter that serves to avoid spectral overlap, up to 190Gbaud OOK signal is generated using a 120GSa/s DAC with a sampling ratio as low as 0.63. Furthermore, a 180Gbaud OOK signal is generated and transmitted over 500 m standard single-mode fiber (SSMF) below 20% hard-decision forward error-correction (HD-FEC) threshold of 1.5 × 10−2.

Experimental demonstration of a chaotic communication system with a switchable chaotic carrier wavelength based on two weak-resonant-cavity Fabry–Perot laser diodes

Based on two weak-resonant-cavity Fabry–Perot laser diodes (WRC-FPLDs) with almost identical mode intervals, we propose and demonstrate experimentally, a chaotic communication system with switchable chaotic carrier wavelength. In such a scheme, a WRC-FPLD (called T-WRC-FPLD) subject to filtered feedback provided by a tunable optical filter (TOF) is taken as the transmitter, and the other WRC-FPLD (called R-WRC-FPLD) under optical injection from the T-WRC-FPLD is taken as the receiver. Through setting the central wavelength of the TOF and selecting the matched feedback strength, a desired mode in the T-WRC-FPLD can be chosen to stimulate and output a chaotic signal, whose central wavelength is determined by the central wavelength of the TOF. Thus, the T-WRC-FPLD under filtered feedback can provide a chaotic carrier with a switchable central wavelength. The chaotic signal output from the T-WRC-FPLD is sent to the R-WRC-FPLD and drives the R-WRC-FPLD for generating a chaotic signal. Under proper injection strength, high-quality chaotic synchronization between the T-WRC-FPLD and R-WRC-FPLD can be realized, and therefore the chaotic communication with switchable carrier wavelength can be implemented in this system. We adopt three different chaotic signals provided by three different modes in the T-WRC-FPLD as the chaotic carriers, respectively, and inspect the performances of the system. The experimental results show that, for the three cases, all the correlation coefficients between the T-WRC-FPLD and R-WRC-FPLD can be larger than 0.94 under optimized operating parameters. Via the high-quality chaotic synchronization between the T-WRC-FPLD and R-WRC-FPLD, a 5 Gb/s message encrypted in each chaotic carrier can be successfully decrypted at the receiver for the three cases, and the bit error ratios are all lower than 3.8 × 1 0 − 3 , which is the hard-decision forward error correction threshold.

8 × 10 Gb/s Downstream PAM-4 Transmission for Cost-Effective Coherent WDM-PON Application

We experimentally demonstrate digital signal processing (DSP)-free 8 × 10 Gb/s 4-level pulse-amplitude modulation (PAM-4) transmission for cost-effective coherent wavelength division multiplexing passive optical network (WDM-PON) with 20 GHz channel spacing over the C-band. The polarization-independent coherent receiver at optical network unit (ONU) including a 3 × 3 fiber coupler and a polarization beam splitter (PBS) followed by three single-ended photodiodes (PDs), is simple and cost-effective, because neither DSP nor phase/frequency locking is necessary for the coherent detection of PAM-4 signal. We numerically compare the performance between the transmitted signal diversity and the local oscillator (LO) signal diversity schemes, and optimize the parameters of heterodyne detection, in order to enhance the power budget. Based on the LO signal diversity scheme, we can achieve an average receiver sensitivity of -26 dBm for eight wavelength channels at a bit error ratio (BER) below the hard-decision forward error correction (HD-FEC) threshold (i.e., 3.8 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> ), leading to a power budget of 29 dB after 25 km standard single-mode fiber (SSMF) transmission. Moreover, we verify an unequally spaced PAM-4 signaling, leading to contribution of 1 dB receiver sensitivity improvement for 10 Gb/s/λ PON.

Transmission of a 112-Gbit/s 16-QAM over a 1440-km SSMF with parallel Kramers-Kronig receivers enabled by an overlap approach and bandwidth compensation.

We investigate the parallelized performance of the conventional Kramers-Kronig (KK) and without the digital up-sampling KK (WDU-KK) receivers in a 112-Gbit/s 16-ary quadrature amplitude modulation (16-QAM) system over a 1440-km standard single-mode fiber (SSMF). A joint overlap approach and bandwidth compensation filter (OLA-BC) architecture is presented to mitigate the edge effect caused by the Hilbert transform and the Gibbs phenomenon induced by the FIR filter, respectively. Moreover, the computational complexity of the OLA-BC based parallelized KK/WDU-KK receiver is also discussed. Parallelized KK/WDU-KK receivers based on the presented OLA-BC architecture can effectively mitigate the edge effect and the Gibbs phenomenon together with more than two orders of magnitude improvement in terms of bit-error-ratio (BER) compared with parallelized KK/WDU-KK receivers without OLA-BC receivers in back-to-back (B2B) case. Finally, we successfully transmit the 16-QAM signals over 960-km SSMF with a BER lower than 7% hard-decision forward error correction (HD-FEC) threshold (3.8 × 10-3) and 1440-km SSMF with a BER lower than 20% soft-decision FEC (SD-FEC) threshold (2 × 10-2).

Experimental demonstration of secure 100 Gb/s IMDD transmission over a 50 km SSMF using a quantum noise stream cipher and optical coarse-to-fine modulation.

In this paper, we experimentally demonstrate a secure 100 Gb/s 214-level intensity modulation and direct detection transmission over a 50 km standard single-mode fiber (SSMF) using a quantum noise stream cipher (QNSC) technique and 8-bit digital to analog converters. Optical coarse-to-fine modulation (CTFM) has been proposed to simultaneously enhance the security and overcome the weakness of low modulation depth in the traditional CTFM scheme. The optical power instead of the radio-frequency signal power is adjusted to satisfy the required peak-to-peak relation for CTFM, and thus the coarse and fine modulation has the same modulation depth. Two optical CTFM schemes based on an optical coupler and a polarizing beam combiner (PBC) are proposed and their pros and cons are analyzed and compared. Considering the trade-off of transmission performance and security performance, the optical CTFM scheme based on PBC is preferred in our experiment. 214-level pulse amplitude modulation (PAM) is achieved using two dual-drive Mach-Zehnder modulators (DD-MZM). Simultaneously, each DD-MZM is also used to achieve single-sideband (SSB) modulation to eliminate the power fading induced by fiber dispersion. By these means, 100 Gb/s 214-level PAM-QNSC signal transmission over 50 km SSMF with the bit error rate below the 7% overhead hard-decision forward error correction threshold of 3.8×10-3 is achieved. The results validate that the proposed scheme is effective to realize low-cost, high-speed, and highly secure optical transmission in the data center.

IM/DD mode division multiplexing transmission enabled by machine learning-based linear and nonlinear MIMO equalization

We demonstrate two mode division multiplexing transmission systems through few-mode fiber by using two degenerate LP11 modes in high speed and low cost optical interconnection scenarios. Two novel MIMO equalizers based on machine learning are proposed and utilized to eliminate the impairments. In the ultra-low cost optical interconnection, the linear equalizer based on the elastic net can effectively reduce the bit error rate to the hard-decision forward error correction threshold with an extremely fast convergence speed. With the help of the nonlinear equalizer based on the neural network, high speed short-reach transmission has been achieved. By multiplexing two degenerate modes with the bit rate of 100 Gb/s/λ, 2 × 100 Gb/s transmission of 30 G-class 1550 nm optical devices has been realized. Without the optical amplifier, the receiver sensitivity could be around -11 dBm in 2 × 50 Gb/s transmission. This provides potential solutions for the future evolution of short-reach optical links.

Low-Complexity Geometric Shaping

Approaching Shannon's capacity via geometric shaping has usually been regarded as challenging due to modulation and demodulation complexity, requiring look-up tables to store the constellation points and constellation bit labeling. To overcome these challenges, in this paper, we study lattice-based geometrically shaped modulation formats in multidimensional Euclidean space. We describe and evaluate fast and low complexity modulation and demodulation algorithms that make these modulation formats practical, even with extremely high constellation sizes with more than $10^{28}$ points. The uncoded bit error rate performance of these constellations is compared with the conventional QAM formats in the additive white Gaussian noise and nonlinear fiber channels. At a spectral efficiency of 2 bits/sym/polarization, compared with 4-QAM format, transmission reach improvement of more than 38% is shown at the hard-decision forward error correction threshold of $2.26\times 10^{-4}$.

Optical Single Sideband Signal Reconstruction Based on Time-Domain Iteration

Due to its low cost, simple architecture and robustness to fiber dispersion, single sideband (SSB) transmission with direct detection (DD) system is an attractive solution for 80-km inter data center interconnects (DCIs). However, it will suffer performance penalty caused by the signal-to-signal beating interference (SSBI). Kramers-Kronig (KK) receiver has been extensively investigated for SSBI elimination by reconstructing the SSB signal. The nonlinear operations in KK algorithm require up-sampling to cope with spectral broadening, which results in high complexity for practical application. Optical signal phase retrieval method based on the minimum phase signal has also been investigated for SSB signal recovery, in which the SSB and DC-Value properties are iteratively imposed on the amplitude signal in frequency domain. In this paper, we propose a low complexity iterative algorithm for minimum phase signal recovery without up-sampling in time domain. Finite impulse response (FIR) filter is applied to iteratively generate the SSB signal and update the phase component. Based on the proposed scheme, the transmission of 30 GHz SSB 16-QAM discrete multitone (DMT) signal over 80 km single mode fiber (SMF) is successfully demonstrated with the bit error rate (BER) below the hard-decision forward error correction (HD-FEC) threshold of 3.8 × 10−3. The experimental results show that, the BER performance of KK scheme with up-sampling factor of 2, frequency-domain iterative scheme and our proposed scheme is almost the same. However, compared with the KK scheme, the proposed method can save the numbers of adders and multipliers by the factors of 29 and 7, while the factors are 5.5 and 4 comparing to the frequency-domain iteration scheme.

Performance assessment of a silicon traveling-wave Mach–Zehnder modulator employing quasi-TM mode propagation

A silicon Mach–Zehnder modulator (MZM) with quasi-TM mode propagation is investigated for non-return-to-zero on–off keying modulation. The quasi-TM PN phase shifter phase-loss characteristics have been determined and shown to exhibit better performance compared to quasi-TE phase shifter with the same waveguide cross-sectional area and device parameters. The phase shifter modulation efficiency is 1.02 V.cm. The MZM transfer characteristics are determined for the dual-arm push–pull driving scheme, and a traveling-wave electrode structure is employed to enhance the device bandwidth. A 3-dB bandwidth of 74 GHz is obtained at 2.5-V reverse bias. The modulator high-speed characteristics are studied for different data rates over single-mode fiber transmission. A 30-km fiber transmission with an open eye at 160 Gbps with 2-V peak-to-peak drive is obtained with an extinction ratio of 2.3 dB and bit-error-rate (BER) of ∼2.77 × 10 − 06. The effect of fiber dispersion on the BER shows dispersion tolerance from 0 to −1.73 ps . nm − 1 . km − 1 for 30-km fiber transmission below the hard-decision forward error correction threshold at 100-Gbps operation.

800 Gbit/s transmission over 1 km single-mode fiber using a four-channel silicon photonic transmitter

We demonstrate the optical transmission of an 800 Gbit/s ( 4 × 200 Gbit / s ) pulse amplitude modulation-4 (PAM-4) signal and a 480 Gbit/s ( 4 × 120 Gbit / s ) on–off-keying (OOK) signal by using a high-bandwidth (BW) silicon photonic (SiP) transmitter with the aid of digital signal processing (DSP). In this transmitter, a four-channel SiP modulator chip is co-packaged with a four-channel driver chip, with a measured 3 dB BW of 40 GHz. DSP is applied in both the transmitter and receiver sides for pre-/post-compensation and bit error rate (BER) calculation. Back-to-back (B2B) BERs of the PAM-4 signal and OOK signal are first measured for each channel of the transmitter with respect to a variety of data rates. Similar BER performance of four channels shows good uniformity of the transmitter between different channels. The BER penalty of the PAM-4 and OOK signals for 500 m and 1 km standard single-mode fiber (SSMF) transmission is then experimentally tested by using one channel of the transmitter. For a 200 Gbit/s PAM-4 signal, the BER is below the hard-decision forward error correction (HD-FEC) threshold for B2B and below the soft-decision FEC (SD-FEC) threshold after 1 km transmission. For a 120 Gbit/s OOK signal, the BER is below SD-FEC threshold for B2B. After 500 m and 1 km transmission, the data rate of the OOK signal shrinks to 119 Gbit/s and 118 Gbit/s with the SD-FEC threshold, respectively. Finally, the 800 Gbit/s PAM-4 signal with 1 km transmission is achieved with the BER of all four channels below the SD-FEC threshold.

200-Gbit/s PAM4 Generation by a Dual-Polarization Mach-Zehnder Modulator Without DAC

In this experiment, we generate PAM4 signals based on a dual-polarization Mach-Zehnder modulator (DP-MZM) without DAC. Two high-speed binary OOK signals with different driving voltages are used to modulate a DP-MZM. After modulation, the intensity of the optical OOK signal in a polarization state is 0.7 times of the other. In this way, up to 200-Gbit/s PAM4 signals can be successfully generated. We also measure the BER performance of the generated PAM4 signals after 1-km dispersion shifting fiber (DSF) transmission. Based on the experimental results, the generated 160-Gbit/s PAM4 signal can be successfully transmitted over 1-km DSF, satisfying the hard-decision forward error correction (HD-FEC) threshold of $3.8\times 10 ^{\mathbf {-3}}$ . Moreover, the system can support up to 200-Gbit/s PAM4 signal transmission over 1-km DSF when satisfying the soft-decision forward error correction (SD-FEC) threshold of $2\times 10 ^{\mathbf {-2}}$ .

Enhanced performance of MIMO multi-branch hybrid neural network in single receiver MIMO visible light communication system.

For the single receiver multiple-input-multiple-output (SR-MIMO) visible light communication (VLC) system, the superposing of two transmitters will introduce severe distortion in the time-domain and frequency-domain. In this paper, we first proposed a MIMO multi-branch hybrid neural network (MIMO-MBNN) as the post-equalizer in the SR-MIMO pulse amplitude magnitude eight levels (PAM8) VLC system. Compared with the traditional single-input-single-output least mean square equalizer with Volterra series (SISO-LMS) and SISO deep neural network (SISO-DNN), MIMO-MBNN can achieve at most 3.35 dB Q factor improvement. Furthermore, the operation range of MIMO-MBNN is at least 2.33 times of SISO-DNN and SISO-LMS among the measured signal peak to peak voltage. At last, 2.1 Gbps data rate is achieved by MIMO-MBNN below the 7% hard-decision forward error correction (HD-FEC) threshold. As far as we know, this is the highest data rate in the SR-MIMO VLC system.

Low-chirp push-pull dual-ring modulator with 144 Gb/s PAM-4 data transmission.

We experimentally demonstrate a low-chirp high-speed push-pull dual-ring modulator. The device is formed by two parallel cascaded add-drop ring modulators which has a Fabry-Perot resonance spectrally similar as electromagnetically induced transparency (EIT) effect. Differential drive signals are applied to the two rings to shift the individual resonances towards opposite directions, creating intensity modulation with suppressed frequency chirp. We present static and dynamic characterization of the device, including chirp parameter. We also demonstrate 144 Gb/s PAM-4 data transmission with 1-km standard single-mode fiber (SSMF) with BER below hard-decision forward error correction (HD-FEC) threshold with 7% overhead.

Cascade recurrent neural network-assisted nonlinear equalization for a 100 Gb/s PAM4 short-reach direct detection system.

We propose a novel, to the best of our knowledge, cascade recurrent neural network (RNN)-based nonlinear equalizer for a pulse amplitude modulation (PAM)4 short-reach direct detection system. A 100 Gb/s PAM4 link is experimentally demonstrated over 15 km standard single-mode fiber (SSMF), using a 16 GHz directly modulated laser (DML) in C-band. The link suffers from strong nonlinear impairments which is mainly induced by the mixture of linear channel effects with square-law detection, the DML frequency chirp, and the device nonlinearity. Experimental results show that the proposed cascade RNN-based equalizer outperforms other feedforward or non-cascade neural network (NN)-based equalizers owing to both its cascade and recurrent structure, showing the great potential to effectively tackle the nonlinear signal distortion. With the aid of a cascade RNN-based equalizer, a bit-error rate (BER) lower than the 7% hard-decision forward error correction (FEC) threshold can be achieved when the receiver power is larger than 5 dBm. Compared with traditional non-cascade NN-based equalizers, the training time could also be reduced by half with the help of the cascade structure.