Soft-decision Forward Error Correction Research Articles

Joint signal-to-signal beat interference mitigation for the field recovery of symmetric carrier-assisted differential detection with low carrier-to-signal power ratio

As a combination of direct detection and coherent detection technologies, self-coherent detection has the advantages of low cost and optical field recovery ability. However, most of the self-coherent detection techniques are limited to single sideband (SSB) signals. Recently, carrier-assisted differential detection (CADD) has been proposed to realize complex-valued double sideband (DSB) signals, but it requires a high carrier-to-signal power ratio (CSPR) to mitigate the signal-to-signal beat interference (SSBI). Later, a more cost-effective symmetric CADD (S-CADD) has been proposed while the required CSPR is still high. In order to alleviate the high requirements of CSPR, we propose a scheme based on the joint of digital pre-distortion (DPD) at transmitter and clipping at receiver to further improve the S-CADD system performance. This joint processing can not only solve the problem of non-uniform distribution of subcarrier signal-to-noise ratio (SNR) caused by non-ideal transfer function, but also the error propagation problem caused by enhanced SSBI under low CSPR. After the validation of the 64 Gbaud 16-ary quadrature amplitude modulation (16-QAM) orthogonal frequency division multiplexing (OFDM) signal transmitted over 80 km standard single mode fiber (SSMF), the CSPR required by the proposed scheme to reach the 20% soft decision-forward error correction (SD-FEC) and 7% hard decision-forward error correction (HD-FEC) can be reduced by 1.3 dB and 2.8 dB, respectively, with a comparison of the conventional S-CADD. The results show the potential of the proposed scheme in the short-reach optical transmissions.

Polar-coded Channel Polarization for Reducing Complexity of Soft-decision Forward Error Correction

Polar-coded Channel Polarization for Reducing Complexity of Soft-decision Forward Error Correction

Experimental demonstration of optical waveform transmission with multiple-eigenvalue 16-APSK modulation.

The multi-eigenvalue multiplexing-based discrete spectrum-modulated nonlinear frequency-division multiplexing (DS-NFDM) system with higher-order modulation format has been demonstrated experimentally. After designing the coefficients of the eigenvalue set and the constellation point distribution of 16-amplitude phase shift keying (16-APSK), the realizations of 14-, 30-, and 46-eigenvalue multiplexed DS-NFDM signals have been implemented. The results show that 46-eigenvalue and 30-eigenvalue multiplexed DS-NFDM signals can transmit 50 km and 400 km over a nonzero dispersion-shifted fiber (NZDSF) under soft-decision forward error correction (SD-FEC) threshold of 2.4E-2, respectively. This demonstration shows for the first time, to the best of our knowledge, the record for multiplexed eigenvalue number and data rate of the multiple-eigenvalue-based DS-NFDM system.

High-order QAM NANF transmission utilizing MIMO equalizer integrated with low-complexity decision-directed carrier phase estimation.

We experimentally realized a high-speed nested anti-resonant nodeless fiber (NANF) transmission with the assistance of the polarization division multiplexing (PDM) and probabilistic shaping (PS) technology. In this system, a low-complexity multiple-input multiple-output (MIMO) real-valued equalizer (RVE) is integrated with decision-directed carrier phase estimation (DDCPE), which is robust against the IQ cross talk and a tiny phase disturbance between PS symbols. By using the proposed MIMO-RVEDDCPE, the 60-Gbaud PDM-PS-256QAM signal has been delivered through 2-km NANF satisfying the soft-decision forward error correction (SD-FEC) threshold.

Delta-sigma modulation supporting the 4194304QAM dual polarization signal at the W-band transmission over a 4.6 km wireless distance.

In this Letter, we propose a dual-polarized coherent millimeter-wave system based on differential delta-sigma modulation (D-DSM) intended for long-distance wireless transmission in the W-band. The proposed system can transmit polarization-division-multiplexed (PDM) D-DSM signals with modulation orders up to 4194304QAM over a wireless channel for 4.6 km at a signal baud rate of 20 G. After 4.6 km of wireless transmission, we successfully achieve a bit error rate (BER) lower than the hard-decision forward error correction (HD-FEC) of 3.8 × 10-3 for 34.51 Gbit/s PDM-524288QAM and a BER lower than the soft-decision forward error correction (SD-FEC) of 4.2 × 10-2 for 32.23 Gbit/s PDM-4194304QAM.

Geometrically Shaped Odd-Bit QAM Constellations Suitable for Principal Component-Based Phase Estimation

For high-speed optical communication systems, laser phase noise (LPN) stands as a pivotal factor influencing the quality of the received signal. Therefore, the employment of a highly accurate carrier phase recovery (CPR) algorithm at the receiving end is indispensable to ensure the reliability of transmission. While a CPR algorithm called principal component-based phase estimation (PCPE) has been proven to be capable of achieving low-complexity and high-performance phase recovery for even-bit quadrature amplitude modulation (QAM) (i.e., square QAM) signals, it is not compatible with traditional cross-shaped odd-bit QAM signals. To circumvent this problem, a signal constellation design scheme based on geometric shaping (GS) is proposed. The pair-wise optimization (PO) algorithm is used to optimize the constellation structure of 32QAM and 128QAM signals in order to obtain results that are compatible with the PCPE algorithm. Monte Carlo simulation results reveal that for odd-bit QAM signals utilizing PCPE for phase recovery, the proposed GS constellations enhance the mutual information (MI) performance across the entire measured signal-to-noise (SNR) range. Moreover, compared with regular 32QAM and 128QAM constellations using the well-known blind phase search (BPS) algorithm, the proposed GS and PCPE scheme can achieve SNR gains of 1.10 dB and 2.59 dB, respectively, when considering the 20% soft-decision forward error correction (SD-FEC) overhead. Verification through commercial simulation software corroborates these findings, demonstrating that the proposed GS constellations are particularly suitable for the PCPE algorithm, especially under conditions of high optical signal-to-noise ratio (OSNR). To the best of our knowledge, this is the first time that the incompatibility between the PCPE algorithm and odd-bit QAM signals has been investigated, and the proposed GS scheme has broadened the application scope of the low-complexity CPR algorithm.

Collaborative FFE-assisted simplified soft-output MLSE with LDPC for high-speed IM-DD transmissions.

In this paper, we propose a feed-forward equalizer (FFE)-assisted simplified soft-output MLSE (sMLSE) by collaborating the maximum likelihood sequence estimation (MLSE) with soft-decision low-density-parity-check (LDPC) decoding. The simplified sMLSE results in undetermined log-likelihood ratio (LLR) magnitudes when the reserved level is less than or equal to the half of modulation order. This severely degrades the performance of soft-decision forward error correction (SD-FEC) decoding. In the FFE-assisted simplified sMLSE, we use the LLRs calculated from pre-set FFE to replace these undetermined LLRs of simplified sMLSE. Thus, the proposed method eliminates the SD-FEC decoding performance degradation resulted from simplification. We conduct experiments to transmit 184-Gb/s PAM-4 or 255-Gb/s PAM-8 signal in IM-DD system at C-band to evaluate the performance of the proposed sMLSE. The results show that the proposed sMLSE can effectively compensate for the degradation of LLR quality. For 255-Gb/s PAM-8 signal transmissions, the FFE-assisted simplified sMLSE achieves almost the same SD-FEC decoding performance as the conventional sMLSE but with 85% complexity reduction.

SNR-enhanced signal delivery scheme with delta-sigma modulation in a four-mode fiber system.

This Letter proposes a scheme for optimizing the signal-to-noise ratio (SNR) of signal to improve the system performance by a 1 bit delta-sigma modulation (DSM) in a four-mode MDM system for mobile fronthaul. A 1 bit digitalized signal with an SNR of 60 dB from transmitter digital signal processing (Tx DSP) can be achieved. Based on this system, an experimental demonstration of the ultrahigh-order 1048576-QAM signal transmission over a 50 km strong-coupling few-mode fiber (FMF) is successfully realized. With DSP, the bit error rate (BER) of the received 1048576-QAM signals over four modes transmission is below the 20% soft-decision forward error correction (20% SD-FEC) threshold of 2.4 × 10-2. To the best of our knowledge, this is the first time that the combination of DSM technology and strong-coupling MDM system is achieved and that the highest-modulation order with DSM reported in MDM system is reached. This experimental demonstration of the proposed novel scheme in MDM system can provide an effective solution for ultra-large-capacity mobile fronthaul in the future.

300-Gbit/s/λ 8-Level Pulse-Amplitude-Modulation (PAM8) with a silicon microring modulator utilizing long short term memory regression and deep neural network classification

We present the first experimental demonstration up the authors' knowledge a high-capacity short-reach optical communication link which employs a long-short-term-memory (LSTM) and deep-neural-network (DNN) for enabling 300-Gbit/s (100 Gbaud) 8-level pulse amplitude modulation (PAM8) generated by a single 55-GHz bandwidth silicon microring modulator (SiMRM) with a driving voltage of 1.8-Vpp. As PAM8 modulation has a lower average level-to-level transition energy when compared with that in PAM4, it could be possible to achieve higher energy efficiency when utilizing PAM8 at the same driving voltage. To recover the PAM8 modulation, LSTM and DNN are utilized for regression and classification respectively. The LSTM contains memory cells for dealing with signal time domain dependencies, and has the ability to store, read, and reject data passing through the neural network. The subsequent DNN performs the classification of the 8 levels. Experimental results show that 300 Gbit/s PAM8 modulation is achieved at back-to-back (B2B) and 270 Gbit/s PAM8 is achieved after 1 km standard single-mode-fiber (SSMF) transmission satisfying the soft-decision forward error correction (SD-FEC) bit-error-rate requirement (BER) of 2.4 × 10-2.

Low-Complexity Conditional Generative Adversarial Network (c-GAN) Based Nonlinear Equalizer for Coherent Data-Center Interconnections

Nonlinear impairments emerging from both fiber optical links and optoelectrical devices are the major bottleneck for enhancing the throughput of photonic data-center interconnection (DCI). Here, we propose a data-driven nonlinear equalizer based on a conditional generative adversarial network (c-GAN) for high-speed and large-capacity photonic DCI. Its performance is experimentally evaluated by transmitting C-band 40-channel 60-GBaud dual polarization-16 quadrature amplitude modulation (DP-16QAM) dense wavelength division multiplexing (DWDM) signals over 20-km standard single-mode fiber (SSMF). Our experimental results verify that, the proposed c-GAN equalizer outperforms both traditional nonlinear equalizers and other data-driven counterparts, in terms of both the bit-error ratio (BER) and computational complexity. Only the proposed c-GAN equalizer can guarantee the BER performance of all 40 channels to reach the threshold of 20% soft decision forward error correction (SD-FEC) at BER=0.027, leading to a net transmission capacity of 16 Tb/s. Meanwhile, the computational complexity of the proposed c-GAN equalizer can be significantly reduced by 31.8%, 80.7%, and 98.8%, respectively, in comparison with Volterra filter equalizer (VFE), multilayer perceptron (MLP), and long short-term memory neural network (LSTM-NN) schemes.

Hybrid Constellation Shaping 64QAM Based on Hexagonal Lattice of Constellation Subset

Increasing demand for higher-speed and large-capacity data communications has driven the development of constellation shaping technology. This paper proposes a hybrid constellation shaping scheme for 64-quadrature amplitude modulation (64QAM) based on hexagonal lattice of a constellation subset. The proposed scheme aims to enhance the nonlinear tolerance of higher-order modulated signals and further improve the constellation shaping gain. The initial quantitative characterization of the constellation is firstly performed based on the hexagonal lattice structure. Then, the objective function of maximizing constellation figure of merits (CFM) is utilized to determine the position distribution of constellation points, resulting in the generation of the geometric shaping-64QAM (GS-64QAM) signal. Finally, according to concentric hexagonal layers, all constellation points are divided into multiple subsets where points within the same subset are assigned the same probability, and the hybrid shaping-64QAM (HS-64QAM) signal is generated. To validate the effectiveness of the proposed scheme, the experimental verification was demonstrated in a 120 Gbit/s multi-span coherent optical communication system. Experimental results indicate that, at the soft-decision forward error correction threshold, HS-64QAM achieves an optical signal-to-noise ratio (OSNR) gain of 1.9 dB and 4.1 dB over uniform GS-64QAM in back-to-back and 375 km transmission scenarios, respectively. Furthermore, HS-64QAM achieves an OSNR gain of 2.7 dB and 7.6 dB over uniform Square-64QAM in back-to-back and 375 km transmission scenarios, respectively.

Attention-assisted autoencoder neural network for end-to-end optimization of multi-access fiber-terahertz communication systems

We propose an end-to-end (E2E) fiber-terahertz (THz) integrated communication system based on an attention-assisted multi-access autoencoder (AMAE) neural network. The AMAE neural network comprises artificial neural networks (ANNs) that function as transmitters (T-ANNs), channel models, and receivers (R-ANNs) for multiple users. By connecting the computational graph of multiple T-ANNs and R-ANNs, we jointly optimize the AMAE to facilitate E2E multi-access communication. Attention mechanisms guide the optimization process to achieve fair and efficient power allocation and orthogonality among different users. We experimentally evaluated the performance of our proposed E2E framework in a 60 Gbit/s multi-channel (1, 5, and 10 km) fiber-THz hybrid system. The results indicate that our AMAE approach outperforms the conventional single-carrier quadrature amplitude modulation scheme by over 3 dB in receiver sensitivity and 11 Gbit/s in capacity under the 20% soft-decision forward error correction threshold in the same-channel back-to-back condition. Additionally, under the performance balance constraint, our approach achieves a transmission speed of 60 Gbit/s within a 10 GHz bandwidth in the multi-channel setting.

FPGA implementation for 44.2368-Gbit/s PAM8 signal transmission with pruned pre-equalization.

In this experiment, we demonstrated an intensity modulation and direct-detection (IM/DD) system based on a field-programmable gate array (FPGA). The PAM8 signals are successfully delivered at 44.2368 Gbit/s over a 45-km standard single-mode fiber (SSMF), satisfying the soft-decision forward error correction (SD-FEC) criterion of 2.4 × 10-2, and the net bit rate may reach 36.864 Gbit/s without the need of optical amplifiers. At the transmitter, we used a pruned pre-equalization algorithm to process the PAM8 signals, and the high-speed parallel PAM8 signals were processed at the receiver using 64 parallel constant modulus algorithm (CMA) and decision-directed least mean square (DD-LMS) equalizers. Additionally, we analyzed the bit error rate (BER) performance of the DD-LMS equalizer in FPGA simulation with various data lengths, both before and after equalization.

PDM-OFDM 1-bit DSM 1024QAM/4096QAM signals at W-band transmission over 4.6-km wireless distance.

In this Letter, we propose the application of delta-sigma modulation (DSM) higher-order quadrature amplitude modulation (QAM) technology in long-distance transmission of W-band wireless communication, and demonstrate, for the first time to the best of our knowledge, the wireless transmission of millimeter wave signals in the W-band based on 1-bit DSM quantization using polarization-division-multiplexed orthogonal frequency division multiplexing (PDM-OFDM) 1024QAM/4096QAM for 4.6 km. We successfully achieved a bit error rate (BER) of 40-Gbit/s PDM-OFDM 1024QAM and 48-Gbit/s PDM-OFDM 4096QAM after 4.6-km wireless transmission, both lower than the soft decision forward error correction (SD-FEC) of 4.2 × 10-2. To the best of our knowledge, this is the first time that up to 4096QAM signals have been quantized and transmitted based on 1-bit DSM in a 4.6-km-long distance W-band millimeter wave system.

Experimental Comparison of Carrier Phase Recovery Algorithms for Uniform and Probabilistically Shaped QAM in a 324.1 Gb/S Fiber-mm-Wave Integration System at W-Band

We have experimentally implemented a photonics-aided large-capacity fiber-mm-wave wireless communication system employing a simple dual-polarized single-input single-output (SISO) wireless based on polarization multiplexing at the W-band. To compare the performance of different algorithms, 18G-baud, and 35G-baud 16-level quadrature-amplitude-modulation (16QAM), probabilistically shaped 16QAM (PS-16QAM), 64QAM and PS-64QAM signal using different carrier phase recovery (CPR) algorithms are transmitted in the system. Moreover, we compare the Viterbi–Viterbi (VV), improved new algorithm based on VV (NVV), blind phase search (BPS), and two-stage BPS algorithms’ computational complexity to better compare different algorithms. Using the experiment result, we can demonstrate that the BPS algorithm is about half a magnitude better than the NVV algorithm for PS-QAM signals, while the NVV algorithm has the lowest computational complexity. Additionally, we also achieve error-free wireless transmission at a net data rate of 324.1 Gb/s with the bit error ratio (BER) below the forward-error correction (FEC) threshold of 1 × 10−2 assuming soft-decision forward-error correction (SD-FEC) when using the BPS algorithm.

A Novel 64 QAM-OFDM Optical Access System Based on Bit Reconstruction

This paper proposes a novel orthogonal frequency division multiplexing (OFDM) optical access scheme based on bit reconstruction. In this method, correlation is introduced into the data information of optical line terminals (OLT) through the logical coding circuits and partition mapping. Even after passing through the optical fibre channel, the strong correlation after bit reconstruction can still be used in the optical network unit (ONU) for reliable decoding. In the simulation experiments, a 60 Gbit/s bit reconstruction 64 quadrature amplitude modulation (QAM) OFDM signal was successfully transmitted over a 10/20 km single-mode fibre (SMF). The simulation results show that the proposed scheme can effectively achieve reliable transmission with gains of about 1.3 dB and 0.51 dB at a 20% soft decision-forward error correction (SD-FEC) threshold, respectively. The proposed scheme is a promising candidate for a next-generation passive optical network (NGPON) solution.

Fast-Convergence Digital Signal Processing for Coherent PON Using Digital SCM

It is foreseeable that the 100 Gb/s/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\lambda$</tex-math></inline-formula> and beyond passive optical network (PON) will be required in future optical access networks to meet the explosive growth of data traffic. The coherent optical systems could be a promising solution for the future beyond 100G PON. Coherent PON using digital subcarrier multiplexing (DSCM) can provide flexible bandwidth allocation to a large number of access subscribers by dividing subcarriers of the DSCM signal into time slots for time-and-frequency division multiple access. When the optical network unit is allocated a new subcarrier, digital signal processing (DSP) should converge fast in the allocated time slot to ensure a low handoff latency for real-time bandwidth allocation. However, the traditional coherent DSP is hard to realize fast convergence due to blind and complex algorithms. In this paper, we design a specific training sequence (TS) structure and propose data-aided DSP to achieve fast convergence for coherent PON. The feasibility of the proposed scheme is experimentally verified in an 8 Gbaud/SC×8 SCs 400 Gb/s-net-rate coherent PON using DSCM with 16 quadrature amplitude modulation. The experimental results show that fast convergence is jointly realized by the proposed TS structure and data-aided DSP using a 416-symbol TS with a 52 ns duration. The receiver sensitivity at the 20% soft-decision forward error correction limit is approximately -27 dBm and an optical power budget of about 35.5 dB is achieved with a booster amplifier.

Ultra-Wideband Multi-Octave Planar Interconnect for Multi-Band THz Communications

An ultra-wideband (UWB) interconnect technology using indium phosphide (InP)-based transitions for coupling the output signals from terahertz (THz) photodiodes featuring coplanar waveguide (CPW) outputs to low-loss dielectric rod waveguides (DRWs) is presented. The motivation is to exploit the full bandwidth offered by THz photodiodes without limitations due to standard rectangular waveguide interfaces, e.g., for future high data rate THz communications. Full electromagnetic wave simulations are carried out to optimize the electrical performance of the proposed InP transitions in terms of operational bandwidth and coupling efficiency. The transitions are fabricated on 100-µm-thin InP and integrated with silicon (Si) DRWs. Experimental frequency domain characterizations demonstrate efficient THz signal coupling with a maximum coupling efficiency better than − 2 dB. The measured 3-dB and 6-dB operational bandwidths of 185 GHz and 280 GHz, respectively, prove the multi-octave ultra-wideband features of the developed interconnect technology. The 6-dB operational bandwidth covers all waveguide bands between WR-12 to WR-3, i.e., a frequency range between 60 and 340 GHz. In addition, the multi-octave performances of the fabricated interconnects were successfully exploited in proof-of-concept THz communication experiments. Using intermediate frequency orthogonal frequency division multiplexing (OFDM), THz communications are demonstrated for several frequency bands using the same interconnect. Considering soft-decision forward error correction, error-free transmission with data rates of 24 Gbps at 80 GHz and 8 Gbps at 310 GHz is achieved.

4096-QAM OFDM THz-Over-Fiber MIMO Transmission Using Delta-Sigma Modulation

A terahertz (THz)-over-fiber multiple-input multiple-output (MIMO) transmission of 4096-ary quadrature amplitude modulation (QAM) orthogonal frequency division multiplexing (OFDM) supported by 46-GBaud quadrature phase shift keying (QPSK) signal at 320 GHz is experimentally demonstrated in this letter. By employing the polarization division multiplexing (PDM) technique and 1-bit delta-sigma modulation (DSM) quantization, we successfully implement 4.6-GHz 4096-QAM OFDM signal transmission over 20 km of standard single-mode fiber (SSMF) and a 3-m MIMO wireless link, and satisfy the soft-decision forward error correction (SD-FEC) threshold of 1.0 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> with 15% overhead, which corresponds to a net rate of 84.4 Gbps for THz-over-fiber transmission. To the best of our knowledge, fusing OFDM and PDM, this is the highest rate achievable for DSM applications in THz communication. This experimental demonstration can provide a promising solution for high-order QAM signals in a fiber-wireless seamless network in future 6G networks.

Demonstration high-order QAM transmission based on one-bit delta-sigma modulation in radio-over-fiber system

In the letter, we propose to use delta-sigma modulator (DSM) technology to transmit OFDM high-order QAM signals in a single-carrier radio-over-fiber (RoF) system, and conduct experimental verification. The experiment demonstrates the transmission of OFDM-256/1024/4096 QAM signals using one-bit DSM in the W band in a 20 km SSMF and 1 m wireless RoF system, and successfully realized that the BER of OFDM-256 and 1024 QAM after system transmission is lower than the hard decision forward error correction (HD-FEC) threshold of 3.8 × 10−3, and the BER after 4096 QAM transmission is lower than the soft decision forward error correction (SD-FEC) threshold of 4.0 × 10−2. The combination of DSM and the photonics-aided RoF solution can effectively solve the problem that the nonlinear damage caused by the bottleneck of the optoelectronic device in the RoF system limits the transmission of high-order QAM signals, and it is expected to be applied in the future 6G optical wireless network.