Hard-decision Forward Error Correction Threshold Research Articles

Optical Amplification-Free High Baudrate Links for Intra-Data Center Communications

The enormous traffic growth sets a stringent requirement to upgrade short-reach optical links to 1.6 TbE capacity in an economically viable way. The power consumption and latency in these links should be as low as possible, especially for high-speed computing. This is possible to achieve using high baudrate on-off keying links thanks to a better noise tolerance and a relaxed requirement on linearity for electronics and photonics. In this regard, we demonstrate a 200 Gbaud on-off keying link without any optical amplification using an externally modulated laser with 3.3 dBm of modulated output power operating at 1541.25 nm wavelength. We achieve transmission over 200 meters of single-mode fiber with performance below 6.25% overhead hard-decision forward error correction threshold for each baudrate and all selection of modulation formats. We also show 108 Gbaud on-off keying link with superior performance without decision feedback equalizer up to 400 meters of single-mode fiber. In addition, we benchmark the short-reach optical link with 112 Gbaud four-level pulse amplitude modulation and 100 Gbaud six-level pulse amplitude modulation. For 108 Gbaud on-off keying and 112 Gbaud four-level pulse amplitude modulation, we can achieve an even lower bit error rate.

High bitrate data transmission in the 8-14 µm atmospheric window using an external Stark-effect modulator with digital equalization.

High bitrate mid-infrared links using simple (NRZ) and multi-level (PAM-4) data coding schemes have been realized in the 8 µm to 14 µm atmospheric transparency window. The free space optics system is composed of unipolar quantum optoelectronic devices, namely a continuous wave quantum cascade laser, an external Stark-effect modulator and a quantum cascade detector, all operating at room-temperature. Pre- and post-processing are implemented to get enhanced bitrates, especially for PAM-4 where inter-symbol interference and noise are particularly detrimental to symbol demodulation. By exploiting these equalization procedures, our system, with a full frequency cutoff of 2 GHz, has reached transmission bitrates of 12 Gbit/s NRZ and 11 Gbit/s PAM-4 fulfilling the 6.25 % overhead hard-decision forward error correction threshold, limited only by the low signal-to-noise ratio of our detector.

Deep Learning-Based Phase Retrieval Scheme for Minimum-Phase Signal Recovery

We propose a deep learning-based phase retrieval method to accurately reconstruct the optical field of a single-sideband minimum-phase signal from the directly detected intensity waveform. Our method relies on a fully convolutional Neural Network (NN) model to realize non-iterative and robust phase retrieval. The NN is trained so that it performs full-field reconstruction and jointly compensates for transmission impairments. Compared to the recently proposed Kramers-Kronig (KK) receiver, our method avoids the distortions introduced by the nonlinear operations involved in the KK phase-retrieval algorithm and hence does not require digital upsampling. We validate the proposed phase-retrieval method by means of extensive numerical simulations in relevant system settings, and we compare the performance of the proposed scheme with the conventional KK receiver operated with a 4-fold digital upsampling. The results show that the 7% hard-decision forward error correction (HD-FEC) threshold at BER 3.8e-3 can be achieved with up to 2.8 dB lower carrier-to-signal power ratio (CSPR) value and 1.8 dB better receiver sensitivity compared to the conventional 4-fold upsampled KK receiver. We also present a comparative analysis of the complexity of the proposed scheme with that of the KK receiver, showing that the proposed scheme can achieve the 7% HD-FEC threshold with 1.6 dB lower CSPR, 0.4 dB better receiver sensitivity, and 36% lower complexity.

Security enhanced underwater visible light communication system based on chaotic phase scrambling and conjugate frequency hopping

We propose an encryption technique for underwater visible light communication (UVLC) based on chaotic phase scrambling (PS) and conjugate frequency hopping (CFH). The technique is experimentally tested using an 8-level pulse amplitude modulation (PAM-8) and a 1.2 m underwater link. The security key of the phase scrambling code is generated according to a logistic map, and the frequency hopping is achieved by adding the same zero frequency points to the signal spectrum. The maximum transmission rate of 2.1 Gbit/s is measured with bit-error-rate (BER) below 7% the hard-decision forward error correction (HD-FEC) threshold of 3.8×10-3.

245Gb/s P2MP Mobile Fronthaul Downstream Transmission Using Code-Division Multiplexing and Self-Homodyne Coherent Technologies

We have proposed and experimentally demonstrated a high-speed and point-to-multipoint (P2MP) mobile fronthaul (MFH) downstream system based on the code-division multiplexing (CDM) and self-homodyne coherent (SHC) technologies. We find that compared with the traditional 16-ary quadrature amplitude modulation (16-QAM) signal transmission, the change of phase noise between two demultiplexed symbols is much larger in the CDM-16QAM signal transmission because it is the accumulation of phase noise change of n multiplexed symbols. Therefore, a low-complexity pilot sequence-assisted phase noise estimation algorithm is proposed and designed to compensate for the phase noise caused by fiber mismatch length, which makes it possible to use a low-cost distributed feedback (DFB) laser. Besides, the spread signal's distribution in the frequency domain of each code sequence is different, leading to different transmission performances between different remote radio units (RRUs). A power optimization scheme is proposed to balance the transmission performances of different RRUs by multiplying each channel's signal by a normalized weight factor at the transmitter. The experimental results show that the proposed system could successfully support the transmission of 245 Gb/s 16QAM signal from baseband unit (BBU) to 7 RRUs (each RRU could have 2 antennas to transmit signals at 2 polarizations) over 10 km standard single-mode fiber (SSMF). The measured worst bit error rate (BER) value of 14 channels is 1.77e-3 which is below the hard-decision forward error correction (HD-FEC) threshold (3.8e-3).

Silicon photonic modulators for net 300 Gbps/λ IM/DD and Net 1 Tbps/λ coherent transmission using All-Electronic equalization

In this manuscript we describe the design and transmission system performance of two traveling wave Silicon Photonic (SiP) modulators: i) an O-band, single phase shifter based Mach-Zehnder Modulator (MZM); and ii) a C-band, two phase shifter based Inphase/Quadrature Modulator (IQM). For the O-band device, we demonstrate the transmission of 134 Gbaud PAM-4 (net 250 Gbps) at a BER below the 6.7 % overhead (OH) hard-decision forward error correction (HD-FEC) threshold of 3.8 × 10−3 over 2 km of standard single-mode fiber (SSMF), and we transmit 115 Gbaud PAM-8 (net 288 Gbps) and net 305 Gbps probabilistically shaped (PS)-PAM-8 assuming the 19.02 % overhead soft-decision (SD) FEC. For the C-band device and employing dual-polarization (DP) emulation, we transmit 105 Gbaud DP-64QAM over 80 km below the 25 % overhead SD- FEC BER threshold of 5 × 10−2; featuring the first demonstration of net 1 Tbps transmission using an all-silicon IQM.

Advanced nonlinearity equalizer with TC-NL-MLSE for transmitting beyond 200-Gb/s PAM-8 in IM/DD systems.

The severe band-limited effect resulted from the low-cost optical transceiver increases the channel memory length and the number of taps of the equalizers. Besides, the interaction of fiber dispersion and square-law detection introduce nonlinear distortions in intensity modulation and direct-detection (IM/DD) transmission systems. The serious band-limited effect and nonlinear distortions degrade the transmission performance and bring challenges to current equalizers for low-complexity implementation. In this paper, we propose a trellis-compression nonlinear maximum likelihood sequence estimation (TC-NL-MLSE) algorithm to compensate the linear and nonlinear distortions with lower complexity. In the TC-NL-MLSE, we introduce a polynomial nonlinear filter (PNLF) to partly compensate both the linear distortions and nonlinear distortions. Then, we establish a look-up-table (LUT) to calculate the nonlinear branch metric (BM). To simplify the calculation, two or three levels with the highest probabilities are selected according to decision thresholds for each symbol to compress the state-trellis graph (STG). This significantly reduces computational complexity on BM calculations especially for high-order modulations. We conduct experiments to transmit beyond the 200-Gb/s PAM-8 signal over 2-km standard single mode fiber (SSMF) at C-band. The TC-NL-MLSE outperforms the reduced-state MLSE with PNLF, and can reach the 7%-overhead hard-decision forward error correction threshold. Moreover, the TC-NL-MLSE reduces the complexity by 97% compared with standard LUT-MLSE, limiting the multipliers around 100 at the expense of only 0.2-dB receiver sensitivity penalty.

Multi-band DFT-S 100 Gb/s 32 QAM-DMT transmission in intra-DCI using 10 G-class EML and low-resolution DAC.

In this paper, 100 Gb/s/λ 32 quadrature amplitude modulation discrete multi-tone (QAM-DMT) transmission using 10 G-class electro-absorption modulated laser (EML) and 4/5-bit digital-to-analog converters (DACs) are experimentally demonstrated to meet the requirement of intra-datacenter interconnection (intra-DCI). Unequal length multi-band (ULM) discrete Fourier transform spread (DFT-S) precoding is investigated to alleviate the distortion induced by the high peak-to-average power ratio (PAPR) of DMT. The results show that the required computational complexity of ULM DFT-S precoding with 2-bands (k1=256, k2=64) decreases sharply compared to the traditional DFT-S technique with only about 0.5 dB receiver sensitivity penalty. In addition, compared to the equal length multi-band (ELM) DFT-S precoding, the ULM DFT-S precoding can bring about 2.5 dB receiver sensitivity improvement with slight added computational complexity. With the assistance of ULM DFT-S precoding and noise shaping (NS) technique, the bit-error ratio (BER) of 100 Gb/s 32 QAM-DMT signal generated by 5-bit DAC over 2-km single-mode fiber (SMF) transmission can reach the hard-decision forward error correction (HD-FEC) threshold with received optical power (ROP) of -6.5 dBm, with only additional 39.9% multiplier and 33.7% adder.

Utilizing deep neural networks to extract non-linearity as entities in PAM visible light communication with noise.

Herein, we propose a novel entity extraction neural network (EXNN) with a newly designed sampling convolution kernel approach and a deep learning-based structure to differentiate noise in visible light communication (VLC) systems. In particular, EXNN is used to extract linear and nonlinear distortion in a received signal as an entity and compensate for the signal by removing it. First, we designed a deep learning structure tailored for VLC systems, used experimentation to validate our algorithm's usability, and determined an appropriate range for the hyper-parameters that govern the PAM-8 system. Second, we compared our approach with existing finite impulse response (FIR) linear and Volterra nonlinear compensation algorithms via experiments. Below the hard-decision forward error correction (HD-FEC) threshold limit of 3.8×10-3, experimental results show that the use of the EXNN increased the operating range of the direct current (DC) bias and the voltage by ∼33.3% and by ∼50% under optimal conditions, respectively. Furthermore, under corresponding optimal power conditions, the proposed approach improved the Q factor of the VLC system by 0.36 and 1.57 dB compared with the aforementioned linear and nonlinear equalizers, respectively. To the best of our knowledge, this is the first time that a deep learning operator has been custom-designed for the VLC system and we have named the completely redesigned network with this sampling convolution kernel operator as EXNN.

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).

Independent dual-single-sideband QPSK signal detection based on a single photodetector.

The two sidebands of the independent dual-single-sideband (dual-SSB) signal can carry different information to achieve higher spectral efficiency. However, the two sidebands of the independent dual-SSB vector signal are received independently. Generally, the receiver divides the signal into two channels. For each channel, we use an optical bandpass filter (OBPF) to select the left sideband (LSB) or right sideband (RSB), respectively. Then a photodetector (PD) is used for photoelectric conversion, followed by subsequent digital signal processing (DSP). To reduce the complexity and cost of the receiver, we propose a new independent dual-SSB vector signal detection scheme based on a single PD combined with conventional DSP. An electric bandpass filter (EBPF) filters out high-frequency components after photoelectric conversion, and then the signal is quadrature demodulated and processed by the DSP algorithm. The LSB and RSB are quadrature phase-shift keying (QPSK) modulated with an initial phase difference of π/4. Simulation results show that the proposed scheme performs better bit error rate (BER). For back-to-back (BTB) transmission, the BER of 2-Gbaud independent dual-SSB vector signal (1-Gbuad RSB and 1-Gbaud LSB) can reach the hard-decision forward error correction (HD-FEC) threshold of 3.8 × 10-3 when the input optical power into PD is -20 dBm. For 1-km and 2-km weak turbulence free-space optical (FSO) channel transmission, the BER of 2-Gbaud independent dual-SSB vector signal can reach the HD-FEC threshold when the input optical power into PD is -18.8 and -17 dBm, respectively. For 1-km weak turbulence FSO channel transmission, the BER of 4-, 8-, and 16-Gbuad independent dual-SSB vector signal can reach the HD-FEC threshold when the input optical power into PD is -17.8, -16, and -15 dBm, respectively.

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.

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.

Photonics aided vector millimeter-wave signal generation without DAC at W-band

In this paper, a novel scheme to generate a high-order QAM W-band mm-wave signal is proposed, which avoids the usage of expensive and power hungry digital-to-analog converter (DAC). We numerically simulate m2-QAM mm-wave signal generation and investigate the influences of phase shift and SNR on the performance of the generated W-band signals. The numerical result shows that both SNR and the modulation order m are important factors which decide the quality of generated vector mm-wave signals. Besides, we experimentally demonstrate 10 Gb/s @80 GHz QPSK signal generation based on photonic-aided frequency quadrupled generation principle, which handles the phase noise issue effectively. Moreover, 10 Gb/s @80 GHz QPSK signal transmission over 1-km DSF and 1-m wireless link is also achieved. The experiment results indicate that BER can achieve 7% hard-decision forward error correction (HD-FEC) threshold of 3.8 × 10−3 when the optical power is above −5 dBm. Due to avoiding a bandwidth limited DAC, our proposed W-band QAM vector mm-wave signal generation with a simple structure is promising for the future high-speed 5G ROF-based communication application and beyond.

A novel sampling frequency offset mitigation scheme based on rotated K-means clustering for OFDM-VLC system

Sampling frequency offset (SFO) between digital-to-analog converter (DAC) and analog-to-digital converter (ADC) will severely degrade the transmission performance of orthogonal frequency division multiplexing (OFDM) based visible light communication (VLC) system. In this paper, a novel SFO mitigation scheme based on rotated K-means clustering is proposed, which differs from traditional SFO compensation based on phase estimation and feedback. When SFO causes the constellation points to deviate from their original positions, this scheme can adaptively update the clustering centroids to achieve the correct symbol demapping without phase estimation and compensation. Experimental results indicate that after 3.5 m free-space transmission, the SFO tolerance of quadrature phase shift keying (QPSK) and 16-ary quadrature amplitude modulation (16-QAM) can reach ±130 and ±65 ppm with a bit error rate (BER) less than the hard-decision forward error correction (HD-FEC) threshold of 3.8e−3, respectively.

Spectrally sliced heterodyne coherent receiver with halved electrical bandwidth

A spectrally sliced heterodyne coherent receiver (SHCR) employing four balanced photodetectors and analog-to-digital converters with half of the signal bandwidth is proposed to complete the signal reception and field recovery. We first numerically characterize the performance of SHCR compared with an intradyne coherent receiver and then validate the principle of the SHCR in a proof-of-concept single-polarization experiment. A 60 GBaud 16-quadrature amplitude modulation transmission is experimentally demonstrated over 80 km standard single-mode fiber with a bit-error-rate of 8.5×10-4 below the 7% hard-decision forward error correction threshold of 3.8×10-3. The SHCR offers a low-cost, hybrid-free, and channel-skew-tolerant candidate for data center interconnects.

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.