PAM-4 Signal Research Articles

Analytical method for joint optimization of FFE and DFE equalizations for multi-level signals

Abstract Channel equalization is the efficient method for recovering distorted signal and correspondingly reducing bit error rate (BER). Different type of equalizations, like feed forward equalization (FFE) and decision feedback equalization (DFE) are canceling channel effect and recovering channel response. Separate optimization of tap coefficients for FFE and DFE does not give optimal result. In this case FFE and DFE tap coefficients are found separately and they are not collaborating. Therefore, the final equalization result is not global optimal. In the present paper new analytical method for finding best tap coefficients for FFE and DFE joint equalization is introduced. The proposed method can be used for both NRZ and PAM4 signals. The idea of the methodology is to combine FFE and DFE tap coefficients into one optimization problem and allow them to collaborate and lead to the global optimal solution. The proposed joint optimization method is fast, easy to implement and efficient. The method has been tested for several measured channels and the analysis of the results are discussed.

A DFB Laser With Integrated Passive Region Suitable for PAM-4 Modulation Signal

Numerous studies have shown that the use of PAM-4 modulation format for DFB lasers with integrated passive regions (DFB IPE lasers) can greatly improve information transmission capabilities. In this paper, it is found by theoretical analysis that a passive waveguide can reduce the photon concentration and injection current in the cavity under the same output optical power. The DFB IPE laser has large saturated optical power and slope efficiency, which reduces the distortion of the electro-optical conversion of the PAM-4 signal. A DFB IPE laser was fabricated with a total cavity length and passive waveguide length of 130 um and 40 um, respectively. The saturation output power, slope efficiency, and modulation bandwidth of this laser are 23.5 mW (61 mA), 0.41 W/A, 22 GHz, respectively. The relative intensity noise is also below −145 dB/Hz. Besides, we have verified the high temperature working capability of this laser in a 40 Gbps PAM-4 signal back-to-back (BTB) transmission system. When the signal peak-to-peak voltage is 750 mV, a clear eye diagram with an eye height of 196 mV is obtained at 343 K.

Design and Realization of Multi-Channel and High-Bandwidth 2.5D Transmitter Integrated With Silicon Photonic MZM

Recently, the interconnection bandwidth of the data center is rapidly increasing. To satisfy the requirement for the high-performance data center, a 4-channel 2.5D silicon photonic transmitter is proposed and the packaging structure could increase the high-density scalability of the architecture for 1.6T/3.2T co-packaging optics (CPO) module. The electrical driver and silicon photonic Mach-Zehnder modulator (MZM) are mounted to the silicon interposer by the micro-bumps. Meanwhile, the silicon interposer is mounted to the low temperature co-fired ceramic by the solder balls. The 2.5D transmitter is assembled to the motherboard by the high-speed ball grid array (BGA) connector to make it convenient to be replaced. The electrical optimization is implemented to make the insertion loss of the whole passive link within −1.55 dB under 40 GHz, which ensures the transmitter with the socket transmit the clear simulated eye diagram at 64 Gbps PAM4 rate per channel. Moreover, the thermal evaluation is performed, which includes the heat- dissipation evaluation and the thermal-induced impact on the edge light coupling. Finally, the substrates in the 2.5D transmitter are fabricated and the transmitter is realized by the improved assembly method. By the verification of the measurement, the 2.5D transmitter we proposed could work at 64 Gbps PAM4 signal transmission rate per channel with the 6pJ/bit power consumption. Regardless of the bandwidth of the electronic integrated circuit (EIC)/MZM and the BGA connector, based on the simulation electrical bandwidth, it is potential for realizing 100 Gbps PAM4 signal transmission.

The O-band 20-channel 800 GHz Arrayed Waveguide Grating based on silica platform for 1 Tb/s or higher-speed communication system

A 20-channel 800 GHz spacing silica based arrayed waveguide grating (AWG) is designed and fabricated. We extend the wavelength allocation in IEEE 802.3bs from 8 channels to 20 channels in the O-band, which improves the transmission capacity of the chip to meet the increasing demand of network traffic. The insertion loss is less than 1.59 dB by adopting a spot-size converter (SSC). The polarization-dependent loss (PDL) is less than 0.3 dB at the center wavelength of each channel. With a flat-top of spectrum, 1 dB bandwidth is more than 2.8 nm, and the adjacent crosstalk is less than −20 dB. The transmission of 28.9 Gb/s NRZ and 57.8 Gb/s PAM4 signals in a single channel are successfully realized.

300-Gb/s Transmission Using OTDM System Implemented With Sinusoidally Modulated Input Light Source

The recently proposed 2-channel optical-time-division-multiplexing (OTDM) technique utilizing a sinusoidally modulated input light source provides an attractive solution to double the per-wavelength data rate of the short-reach intensity-modulation/ direct-detection system. However, to maximize the transmission speed of such an OTDM system, it is necessary to generate the sinusoidal input light operating at the frequency much faster than the modulator’s bandwidth. As a result, the extinction ratio (ER) of the generated sinusoidal input light can be significantly reduced, which, in turn, causes a large crosstalk in this OTDM system. To solve this problem, we propose to enhance the ER of the sinusoidal input light simply by decreasing the bias voltage applied to the Mach-Zehnder modulator (MZM) used for its generation (from the quadrature point toward the null point). We estimate that, by using this technique, it is possible to increase the ER from 3.1 dB to 14.9 dB when the required sinusoidal frequency is three times faster than the MZM’s bandwidth. To verify the effectiveness of this ER enhancement technique, we realize the 2-channel OTDM system with a sinusoidally modulated input light source by using the MZMs having a 3-dB bandwidth of 17.2 GHz and demonstrate the transmission of the 300-Gb/s PAM8 signal. Thus, the ratio between the achieved data rate and the 3-dB bandwidth of the MZM is as high as ~17.4.

4-bit DAC based 6.9Gb/s PAM-8 UOWC system using single-pixel mini-LED and digital pre-compensation.

Low-cost underwater wireless optical communication (UOWC) systems are attractive for high-speed connections among unmanned vehicles or devices in various underwater applications. Here we demonstrate a high-speed and low-cost UOWC system using a low-resolution digital to analog converter (DAC), a single-pixel mini-sized light-emitting diode (mini-LED), and digital pre-compensation (DPC). The enabled DPC scheme comprises digital pre-distortion (DPD), digital pre-emphasis (DPE), and digital resolution enhancer (DRE), which pre-compensate for mini-LED nonlinearity, the bandwidth limitation of the mini-LED and avalanche photodiode detector, and DAC resolution limitation, respectively. The simulation results show that the in-band signal-to-quantization noise ratio can be increased by 6.8 dB using DRE based on a 4-bit DAC. To further improve the system capacity, we tune the level of DPE in order to optimize the trade-off between the residual inter-symbol interference and signal-to-noise ratio. With the combination of optimized DPE and DRE, we obtain a 21.1% higher data rate compared with full DPE only and demonstrate the transmission of 6.9 Gb/s PAM-8 signal over a 2-m distance underwater based on a single-pixel mini-LED and 4-bit DAC. This paper reports a cost-effective UOWC system first using a low-resolution DAC and DPC, which offers a promising path toward low-cost underwater optical wireless networks.

Performance and Complexity Analysis of Conventional and Deep Learning Equalizers for the High-Speed IMDD PON

To accommodate the exponential growth of network services in the five-generation (5G) and beyond wireless system, 50 Gb/s/λ passive optical network (PON) is developed for mobile xhaul applications. Intensity modulation and direct detection (IMDD) technology together with digital signal procession (DSP) is being considered as the promising solution for 50 Gb/s/λ PON due to its low cost, low power consumption, and compact footprint. Different DSP algorithms with varied structures are proposed for linear and nonlinear impairments compensation in the high-speed PON, while the performance and complexity analysis of these algorithms is still missing. To find the most efficient equalizers, in this paper, four conventional equalizers, including feed-forward equalizer, decision feedback equalizer (DFE), Volterra equalizer (Vol) and Volterra DFE equalizer (Vol-DFE), together with two deep learning equalizers namely fully-connected neural network, and long short-term memory equalizer are experimentally compared in a 10G optics based 50G-PON system in terms of the equalization performance, computation complexity, optimization difficulty, and generalization ability. After the evaluation of our proposed fair comparison algorithm, we consider Vol-DFE is the most efficient one considering both performance and complexity. Attributes to the strong and efficient equalization capability of Vol-DFE, C-band 50 Gb/s PAM-4 signal transmission can be supported in a 10G optics based IMDD system with a 3 dB bandwidth of 6.11 GHz, and a power budget up to 38 dB can be achieved.

Accelerating LMS-Based Equalization With Correlated Training Sequence in Bandlimited IM/DD Systems

As higher symbol rates are utilized in the intensity modulation and direct detection (IM/DD) scheme to meet the unrelenting growth of data traffic, overcoming the inter-symbol interference (ISI) induced by the limited bandwidth has become increasingly crucial. Channel equalization based on digital signal processing (DSP) is an effective solution, where least-mean squares (LMS) algorithm is adopted to adjust tap coefficients. However, the LMS algorithm usually has slow rate of convergence and requires lots of training symbols. This work proposes a novel training sequence to accelerate the LMS-based equalization. A first-order Markov chain (MC) is employed for sequence generation, which introduces correlation between samples and shapes signal spectrum. Compared with the conventional training sequence that consists of independent and identically distributed (i.i.d.) samples and has a white spectrum, the MC sequence enables faster convergence of tap coefficients and mean-squared error (MSE). Moreover, an experimental demonstration of a 43 Gbaud PAM-4 signal shows that the proposed sequence can achieve a lower pre-forward-error-correction (pre-FEC) bit error rate (BER) than that of the i.i.d. sequence with the same length. When the PAM-4 signal is transmitted over a 5-km standard single mode fiber (SSMF) with 6-dB system bandwidth of 10 GHz, more than 70% training sequence length reduction can be attained. When the fiber length is increased to 10 km and the signal suffers from severe power fading, more than 48% reduction can be achieved.

Ultrahigh extinction ratio silicon micro-ring modulator by MDM resonance for high speed PAM-4 and PAM-8 signaling.

Due to the difficulty of controlling the waveguide loss in the doping region, high-speed silicon micro-ring modulators usually have limited extinction ratio. In this work, we present a mode-division-multiplexing (MDM) resonance-enhanced silicon micro-ring modulator with an ultrahigh extinction ratio. We used a two-mode micro-ring resonator and a mode conversion circular structure to trap the light twice within a single micro-ring resonator. Proof-of-concept high extinction ratio up to 55 dB was obtained. 30 Gb/s PAM-8 and 50 Gb/s PAM-4 signaling with a bit error rate below the hard-decision forward error correction (HD-FEC) threshold were demonstrated with the fabricated modulator, indicating great potential for high-order pulse amplitude modulation (PAM).

Least Angle Regression-Based Modified Volterra Nonlinear Equalizer for Optical Interconnection System

Advanced digital signal processing (DSP) is viewed as an inevitable technology to deal with nonlinear distortions in cost-sensitive optical interconnection systems. Classic methods such as equalization based on Volterra series turn out to be quite effective solutions to compensate signal impairments. In practical imple-mentations, a great deal of efforts focus on reducing the com-putational complexity. Several model selection and dimensionality reduction approaches have been proposed to simplify the struc-ture, which employ backward strategies. However, the threshold settings for these pruning approaches are environment-sensitive. In this paper, we propose a least angle regression-based nonlinear equalization method (LaNLE). We extend the non-intrusive least angle regression technique to generalized linear models. Through an incremental process by stagewise feature selection and weight fitting, we obtain the low-complexity nonlinear structure with significant feature basis. Experimental verification is performed based on 120 Gbps PAM8-modulated 850 nm VCSEL plus MMF optical link. The results show that, compared to fully-connected Volterra nonlinear equalizer structure (VNLE), up to 60.4% and 70.1% reduction in complexity can be achieved with similar BER performance in back-to-back and 100 m transmission scenarios, respectively. In addition, we experimentally demonstrate 225 Gbps per lane PAM-8 signal transmission over 100 m MMF in a simple and cost-effective implementation manner based on mass-production 850 nm VCSEL and proposed LaNLE method.

The high‐efficiency co‐design and the measurement verification of high‐bandwidth silicon photonic microring modulator

The microring modulator (MRM) is a small-size and low-power component, which is the potential for the next-generation optical interconnection. By the theoretical analysis, increasing the electrical bandwidth, which is relevant to the cross section and the doping concentration of the doping region, is a better way to increase electro-optical (EO) bandwidth. Therefore, a new doping profile of the PN depletion region with 4 doping concentration levels is introduced considering the electrical bandwidth. Based on the new doping profile, the MRM with the 160 μm length and the 0.33 and 0.2 μm coupling space are determined considering the trade-off between the EO bandwidth, quality factor (Q), extinction ratio, area of MRM, and power consumption. Moreover, the MRM is characterised and is applied in a wavelength division multiplexing transmitter. By the measurement, the transmitter with the designed MRM could transmit PAM4 signal at 52 Gbps rate, which indicates the MRM could be potential for the 50 Gbps/ch optical interconnection.

3.8 Gb/s PAM-4 UOWC System Over a 2-m Underwater Channel Enabled by a Single-Pixel 175-μm GaN-Based Mini-LED

Blue/green light-emitting diodes (LEDs) have been studied extensively in medium/short-distance underwater optical wireless communication (UOWC), while available commercial bandwidth-limited LEDs cannot support the increased capacity. In this work, a 175-µm blue mini-LED with a high 3 dB modulation bandwidth of 580 MHz was designed and employed to implement a high-speed UOWC system to improve the bandwidth while maintaining high emitting optical power. As a result, we achieve the data rate of 3.8 Gb/s and the rate-distance product of 7.6 Gb/s·m of the PAM-4 signal with the 3.7e-3 bit error rate (BER) over the 2-m underwater channel by using a single-pixel 175-μm GaN-based mini-LED and an avalanche photodiode (APD). To the best of our knowledge, it is the highest rate-distance product among the UOWC systems based on a single-pixel LED and a single APD. In addition, we design multiple sets of comparison experiments to provide a comprehensive investigation regarding channel loss, transmission capacity, and computation complexity between the UOWC system with and without water.

C-band 67 GHz silicon photonic microring modulator for dispersion-uncompensated 100 Gbaud PAM-4.

A very-high-bandwidth integrated silicon microring modulator (MRM) designed on a commercial silicon photonics (SiP) platform for C-band operation is presented. The MRM has a 3 dB electro-optic (EO) bandwidth of over 67 GHz and features a small footprint of 24 µm × 70 µm. Using the MRM, we demonstrate intensity modulation-direct detection (IM-DD) transmission with 4-level pulse amplitude modulation (PAM-4) signaling of over 100 Gbaud. By utilizing the optical peaking effect and negative chirp in the MRM, we extend the transmission distance, which is limited by the fiber-dispersion-induced frequency fading. Using a standard single-mode fiber (SSMF) for transmission across distances of up to 2 km, we measured the data transmission of 100 Gbaud PAM-4 signals with a bit error rate (BER) under the general 7% hard-decision forward-error correction (HD-FEC) threshold. The MRM enables an extended transmission distance for 100 Gbaud signaling in the C-band without dispersion compensation.

Receiver Analog Front-End Cascading Transimpedance Amplifier and Continuous-Time Linear Equalizer for Signals of 5 to 30 Gb/s

A 5–30 Gb/s receiver analog front-end (AFE) cascading transimpedance amplifier (TIA) and continuous-time linear equalizer (CTLE) were implemented using a Taiwan Semiconductor 180 nm process. The system comprises a two-stage differential input pair CTLE, TIA, and a differential termination resistor Rm. A source-degenerated transconductance stage was adopted in the CTLE, and source follower and shunt feedback resistor stages were adopted in the TIA. The proposed CTLE could achieve high frequencies by altering the tail current with fixed degenerate capacitance CS and resistance RS. The proposed AFE achieved high bandwidth, and the use of a feedback resistor Rf and inductor Lf improved its high-frequency performance. Simulation results revealed that the CTLE can compensate for 16 dB of channel loss at a 3 GHz Nyquist frequency and can open closed eyes in a 6 Gb/s non-return-to-zero signal with a bit error rate of 0.16 × 10−12 for a 231 − 1 pseudorandom binary sequence input. The AFE could compensate for 12 dB of channel loss at a 15 GHz Nyquist frequency and can open closed eyes in a 30 Gb/s PAM4 signal from a pseudorandom binary sequence input; it consumed 27 mW of power at 1.8 V.

An SNR-improved Transmitter of Delta-sigma Modulation Supported Ultra-High-Order QAM Signal for Fronthaul/WiFi Applications

In this paper, we proposed an improved mobile fronthaul architecture employing the SNR-improved delta-sigma digitization scheme and 4-level pulse amplitude modulation (PAM-4) format. Different from traditional 2-bit quantization, this scheme deploys two-fold delta-sigma quantization, which uses 1-bit delta-sigma modulator to quantize the signal, and another 1-bit delta-sigma modulator to quantize the in-band noise. A significant reduction of the in-band noise can be achieved only applying a differentiator, bringing about a much better noise shaping performance. Meanwhile, the two 1-bit streams can be combined and transmitted in a PAM-4 manner through an intensity modulation direct detection (IM-DD) channel. We have successfully experimentally demonstrated the digitization and transmission of 65536 quadrature amplitude modulation (QAM) baseband orthogonal frequency division multiplexing (OFDM) signal with sampling rate of 1.25 GSa/s over 20-km fiber with standard 10-Gbaud PAM-4 signal, with a signal to noise ratio (SNR) of 57.7 dB. Compared to the conventional 2-bit quantized OFDM scheme, experimental results show that a significant SNR improvement of 17.7 dB has been achieved by the proposed scheme. In addition, we also realized a transmission of 16384-QAM intermediate frequency (IF) signal at the center frequency of 3.5 GHz (with an SNR of 49.6 dB). An improvement of 15.9 dB can also be maintained.

Modified Gerchberg-Saxton Algorithm Based Electrical Dispersion Pre-Compensation for Intensity-modulation and Direct-detection Systems

In intensity-modulation and direct-detection (IM-DD) communication systems, electrical chromatic dispersion (CD) compensation cannot be directly applied in the transceivers due to the absence of phase information. Gerchberg-Saxton (GS) algorithm has been utilized to iteratively solve for real-valued CD pre-compensated signal in an IM-DD system. In this scheme, the amplitude information at the transmitter and phase information before the direct detection receiver are treated as the degree of freedoms (DoFs) and jointly optimized. In this paper, a modified GS algorithm is proposed and experimentally demonstrated for CD pre-compensation in a 28-GBaud PAM-4 system over 80-km single mode fiber (SMF) transmission. Compared with the basic GS electrical dispersion pre-compensation (pre-EDC) scheme, the amplitude information of received samples at the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T/2</i> position is regarded as DoFs as well, in order to reduce the error. Besides, to accelerate the convergence speed, two error reversing factors associated with the phase error at the transmitter and amplitude error at the receiver are introduced. The experimental results show that the bit error rate (BERs) of 56-Gbps PAM-4 signal over 80-km SMF transmission without CD compensation and with 10 iterations of basic GS pre-EDC scheme are 2.35×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−1</sup> and 5.13×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−2</sup> , respectively, when a 21-taps feedforward equalizer (FFE) is equipped at the receiver side. While the BER can be reduced to below the hard-decision forward error correction (HD-FEC) threshold of 3.8×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup> by the proposed scheme with the iterative number of 10. The results reveal that the proposed scheme is a promising solution for 50-Gbps class 80-km metro optical communication links based on the IM-DD structure.

Performance enhanced probabilistically shaped PAM4 signal based on nonlinear differential coding for IM/DD system

In this paper, the probabilistically shaped pulse amplitude modulation (PS-PAM) signal is proposed in intensity modulation and direct detection (IM/DD) system. For the traditional shaping scheme with constant composition distribution matcher (CCDM), there are several problems that high-precision algorithm for long block coding, the loss of information rate for short block coding. In addition, it can increase nonlinear interference. In order to reduce computational complexity and alleviate the influence of nonlinear interference on the system, the nonlinear differential coding (NLDC) scheme is used to realize PS, which can be better integrated with the cost-effective optical access network. This paper evaluates seven shaping spectrums obtained by different NLDC coding coefficients. As the coding coefficient increases, the performance of the system gradually improves. Moreover, this paper proposed the machine learning includes neural network (NN) and improved K-means clustering algorithm at the receiver. The results show that the PS-PAM4 signal is significantly better than the ordinary PAM4 signal in improving the channel bandwidth tolerance and signal transmission rate. Under the same data rate, using NLDC can save 5.8 GHz bandwidth for the system. For the bandwidth-limited system, the PS-PAM4 signal can obtain 19Gbit/s bit rate gain compared with the ordinary PAM4 signal. Compared with the typical shaping scheme using CCDM, this scheme can achieve 2.2 GHz band tolerance gain and 5Gbit/s rate gain in nonlinear fiber channel.

C-band 200 Gbit/s/λ PAM-4 transmission over 2-km SSMF using look-up-table pre-distortion combined with nonlinear Tomlinson-Harashima pre-coding.

The performance of high baud-rate intensity modulation direct detection (IM-DD) transmissions is severely degraded by both the linear and nonlinear inter-symbol interference (ISI). Here, we propose and experimentally demonstrate a transmitter-side look-up-table pre-distortion combined with nonlinear Tomlinson-Harashima pre-coding (LUT_PD-NTHP) scheme with the capability of mitigating the linear and nonlinear ISI simultaneously, enabling a C-band 200 Gbit/s/λ PAM-4 transmission over 2-km standard single mode fiber (SSMF), under an end-to-end 10-dB bandwidth of about 20 GHz. The proposed LUT_PD-NTHP scheme is experimentally verified to be superior to the LUT pre-distortion combined with linear THP (LUT_PD-LTHP) scheme, in terms of both the receiver sensitivity and the LUT storage requirement, when only the feed-forward equalization (FFE) is used at the receiver-side. In particular, after the 200 Gbit/s PAM-4 signal transmission over the 2-km SSMF without the chromatic dispersion (CD) compensation, the proposed LUT_PD-NTHP scheme with a LUT pattern length of 3 possesses not only 0.25 dB improvement of the receiver sensitivity but also about 99% LUT pattern reduction, in comparison with the LUT_PD-LTHP scheme with a LUT pattern length of 5.

Low-latency and efficient retiming and equalizing scheme for a 112-Gbps bandwidth-limited optical PAM-4 system.

The bandwidth limitation of optoelectronic devices is a key constraint for realizing higher capacity short-reach optical communication systems. In this work, we show that the performance of the timing recovery algorithm will significantly impact the performance of bandwidth-limited optical PAM-4 signals. To address this problem, we introduce a moving average filter (MAF) into the Gardner retiming loop to realize ultra-stable retiming without any pilot symbols. It enables a significantly reduced timing jitter, especially for bandwidth-limited conditions. Based on simulations, we show that the proposed retiming scheme will give a stable sampling phase, which is beneficial to the performance of the decision feedback equalizer. Compared to the system based on the traditional Gardner timing synchronization algorithm, the 2-dB power budget gain is realized. The proposed method improves the equalization performance of short-reach optical communication systems where complexity and processing latency are important concerns.

A Compact 112-Gbaud PAM-4 Silicon Photonics Transceiver for Short-Reach Interconnects

For next generation highly integrated transceivers, silicon photonics (SiP) has attracted widespread interest in using mature CMOS production processes to manufacture high-yield, low-cost photonic integrated circuits (PIC) with the potential for integration with CMOS electronics. SiP now routinely integrate GeSi electroabsorption modulators (EAM) and GeSi waveguide photodiodes which have high responsivity and possess 3-dB electro-optic bandwidth of over 65 GHz. Their ultra-compact dimensions make it possible for multi-channel transceivers to be realized on a small chip area. In this paper, we demonstrate the high-speed capability of these devices incorporated with optimized digital signal processing (DSP) for 100 Gbaud+ PAM-4 signaling. Using integrated GeSi-EAM and GeSi-photodiode fabricated at a commercial foundry, we carried out intensity modulation and direct detection (IM-DD) transmission experiments in C-band using PAM-4, for both back-to-back and SSMF transmission at 1 km and 1.5 km. Under a 6-dB system bandwidth of ∼43GHz we attained, with the help of DSP equalization, a record 112 Gbaud (224 Gb/s), 108 Gbaud (216 Gb/s) and 100 Gbaud (200 Gb/s) are achieved over back-to-back, 1 km and 1.5 km SSMF transmission respectively, with a bit-error-rate (BER) below the hard-decision forward-error-correction (HD-FEC) threshold of 3.8E-3.