Forward Error Correction Research Articles

D-Band 4.6 km 2 × 2 MIMO Photonic-Assisted Terahertz Wireless Communication Utilizing Iterative Pruning Deep Neural Network-Based Nonlinear Equalization

In this paper, we explore the enhancement of a 4.6 km dual-polarization 2 × 2 MIMO D-band photonic-assisted terahertz communication system using iterative pruning-based deep neural network (DNN) nonlinear equalization techniques. The system employs advanced digital signal processing (DSP) methods, including down-conversion, resampling, matched filtering, and various equalization algorithms to combat signal distortions. We demonstrate the effectiveness of DNN and iterative pruning techniques in significantly reducing bit error rates (BERs) across a range of symbol rates (10 Gbaud to 30 Gbaud) and polarization states (vertical and horizontal). Before pruning, at 10 GBaud transmission, the lowest BER was 0.0362, and at 30 GBaud transmission, the lowest BER was 0.1826, both of which did not meet the 20% soft-decision forward error correction (SD-FEC) threshold. After pruning, the BER at different transmission rates was reduced to below the hard decision forward error correction (HD-FEC) threshold, indicating a substantial improvement in signal quality. Additionally, the pruning process contributed to a decrease in network complexity, with a maximum reduction of 85.9% for 10 GBaud signals and 63.0% for 30 GBaud signals. These findings indicate the potential of DNN and pruning techniques to enhance the performance and efficiency of terahertz communication systems, providing valuable insights for future high-capacity, long-distance wireless networks.

Research on Rate Adaptation of Underwater Optical Communication with Joint Control of Photoelectric Domain

As the communication distance changes, the received signal strength of an underwater optical communication system will change, and the range of its variation may not only exceed the dynamic range of the photoelectric detection device but also cause the reliability of communication to change due to the change in the received signal-to-noise ratio. In order to maintain better communication over a longer distance, this paper proposes a rate-adaptive method for underwater optical communication with joint control in the photoelectric domain. In the optical domain, the incident light’s power is adaptively adjusted by controlling the transmittance of the liquid crystal light valve to reduce saturation distortion. In the electrical domain, the constellation distribution is optimized according to the desired probability mass function, and the modulation order is adjusted in real time by estimating the received signal-to-noise ratio of the link. The simulation results show that under the forward error correction (FEC) threshold, the proposed method increases the dynamic range of the photomultiplier tube (PMT) by about 10 dB and expands the dynamic range of the system’s communication distance.

Bi-directional SMF-NDF-optical/5G NR wireless converged systems

This study presents the transmission of fifth-generation (5G) new radio (NR) signals over bi-directional single-mode fiber (SMF)-negative dispersion fiber (NDF)-optical/5G NR wireless converged systems, using two cascaded reflective semiconductor optical amplifiers (RSOAs). Downstream transmission of 5G NR 16-quadrature amplitude modulation (QAM) signals achieved an aggregate net bit rate of 228.037 Gb/s, comprising 59.813, 74.766, and 93.458 Gb/s at 150, 250, and 325 GHz, respectively. The system achieved a low bit error rate (BER) and clear constellation patterns. However, systems without NDF exceed the forward error correction 7% threshold, indicating the importance of NDF in compensating for fiber dispersion. Moreover, for upstream transmission, two cascaded RSOAs are used to transmit 5G 16-QAM-orthogonal frequency division multiplexing signals, achieving a total data rate of 40 Gb/s. The use of two cascaded RSOAs in the system significantly improved upstream performance, resulting in low BERs and clear constellation patterns. This system not only achieved high data rates but also extended transmission coverage to support the deployment of advanced 5G NR applications.

Enhancing the efficiency of wavelength-shift fiber-based detectors for optical wireless communications

A wavelength-shift fiber-based optical detector promises to revolutionize the deployment of optical wireless communication (OWC) due to its inherent advantages over traditional receivers. These advantages include a flexible structure, a wide field of view (FOV), and a large active area. Despite progress in previous studies, there remains a gap in optimizing the re-utilization of unabsorbed light within wavelength-shift fiber (WSF) and maximizing the efficiency of light focusing onto photodetectors. To address these challenges, this study explores three novel, to the best of our knowledge, approaches to enhance the light conversion and detection efficiency of WSF-based optical detectors. First, a reflective mirror is employed behind the WSF array to increase the light absorption and re-emission probability. Second, a reflective mirror is placed at one end of the WSF array to direct the light toward the opposite end. Third, a tightly bundled WSF array configuration focuses the emitted light onto the photodetector’s active area. Experimental results demonstrate that each approach significantly improves the peak-to-peak voltage. This work presents an optical detector design featuring a large active area of 0.4cm×20cm, based on a blue-to-green color-converting WSF and achieving a high 3-dB bandwidth of up to 48 MHz. This design enables real-time data transmission at rates of 275 Mbps using non-return-to-zero on-off keying (NRZ-OOK) modulation over a distance of 1 m. Additionally, the transmission link operates at over 250 Mbps, with bit error rates (BERs) below the forward error correction (FEC) limit, under a wide FOV of 60°. This work opens exciting possibilities for revolutionizing photodetection schemes in non-line-of-sight free-space optical communications.

Effects on Age of Information From Forward Error Correction in LoRa Transmissions

Effects on Age of Information From Forward Error Correction in LoRa Transmissions

1.2 km wireless transmission of 512-QAM signals at 220 GHz using delta-sigma modulation

We have experimentally demonstrated, for the first time, photonics-aided J-band 7.48-Gb/s QPSK signals and 2.5-Gb/s 512-QAM signals using delta-sigma modulation over 1.2-km wireless link. After 1.2-km wireless transmission, the bit error rate (BER) of the 512-QAM is below the 20% soft decision forward error correction (SD-FEC) threshold of 2 × 10−2. As far as we know, this is the longest distance achieved for wireless transmission in a photonics-aided J-band wireless transmission system.

End-to-end learning of joint noise shaping and probabilistic shaping for OAM mode division multiplexing transmission.

Intensity modulation direct detection (IM/DD) orbital angular momentum (OAM) mode division multiplexing (MDM) technology can greatly expand the capacity of a communication system, which is a promising solution for the next generation of high-speed passive optical networks (PONs). However, there are serious obstacles such as mode coupling, device nonlinear impairment, and quantization noise in an IM/DD OAM-MDM system with a low-resolution digital-to-analog converter (DAC). In this Letter, we propose a novel, to the best of our knowledge, end-to-end (E2E) learning scheme based on a double residual feature decoupling network (DRFDnet) emulator with joint probabilistic shaping (PS) and noise shaping (NS) for the OAM-MDM IM/DD transmission. Our DRFDnet emulator can accurately build a complex nonlinear model of an OAM-MDM system by separating the signal impairments into linear and nonlinear. Meanwhile, a DRFDnet-based E2E scheme for joint PS and NS is presented with the aim of compensating the signal impairment for the OAM-MDM IM/DD system. An experiment is carried out on a 200 Gbit/s PON system based on the OAM-MDM IM/DD transmission. The experimental results demonstrate that the proposed DRFDnet-based joint PS and NS scheme is a promising solution to effectively mitigate nonlinear distortions and outperforms the CGAN-based joint PS and NS scheme and traditional joint PS and NS scheme with receiver sensitivity improvements of 1.2 dBm and 2.5 dBm under hard-decision forward error correction (HD-FEC) thresholds, respectively. Our experimental results demonstrate that the proposed DRFDnet emulator-based E2E learning scheme is a viable candidate for future PON.

Large‐Scale High‐Density Multimode Optical Switch Matrix

AbstractOptical switching technology is emerging as a solution to the limitations of traditional electronic switching. Combining optical switching with mode‐division multiplexing effectively overcomes the limitations of expanding switching capacity solely by increasing the number of ports. This paper introduces a compact four‐mode 2 × 2 optical switch and a four‐mode reconfigurable non‐blocking 4 × 4 optical switch matrix based on the Beneš architecture. The multimode 2 × 2 switch achieves an extinction ratio larger than 15 dB for all modes in the wavelength range of 1530–1590 nm. The multimode 4 × 4 switch matrix has an extinction ratio exceeding 9 dB for all modes and states in the C‐band, with a compact size (1.46 × 0.23 mm2) and low power consumption (0–154 mW). It supports high‐integrity 50 Gbaud PAM4 signal transmission with a bit error rate below the forward error correction limit. These devices pave the way for enhanced integration density and capacity in optical switching systems.

Full-duplex dynamic TDMA scheme and clock synchronization and compensation method for the multi-user UWOC system.

In this Letter, we propose a full-duplex dynamic time division multiple access (FDD-TDMA) scheme for multi-user underwater wireless optical communication (UWOC). It supports full-duplex communication through wavelength division duplex (WDD) and enhances the system throughput using dynamic time resource allocation. Additionally, a clock synchronization and compensation method is proposed for precise clock synchronization without time-keeping. With the proposed FDD-TDMA scheme and the clock synchronization and compensation method, we establish a two-user UWOC system based on on-off keying (OOK) modulation. Experiments are conducted in a 10 m water pool environment. The experimental results show that the designed system can achieve a data rate of 25 Mbps without error codes and 40 Mbps with a bit error rate (BER) below the forward error correction (FEC) limit. The FDD-TDMA scheme notably improves the system throughput when communication demands among users are variable compared to the conventional time division multiple access (TDMA). Moreover, a reduction in phase deviations from microseconds to ten nanoseconds is achieved by the clock synchronization and compensation method.

Ultra-high-cardinality geometric shaping in the finite SNR regime.

Four-dimensional (4D) constellations with up to 131 072 points (17 bit/4D-sym) are designed for the first time using geometric shaping. The constellations are optimized in terms of mutual information (MI) and generalized MI (GMI) for the additive white Gaussian noise (AWGN) channel, targeting a forward error correction (FEC) rate of 0.8 at finite signal-to-noise ratios. The presented 15-17 bit constellations are currently the highest-performing constellations in the literature, having a gap to the AWGN capacity as low as 0.17 dB (MI) and 0.45 dB (GMI) at 17 bit/4D-sym. For lower cardinalities, our constellations match or closely approach the performance of previously published optimized constellations. We also show that (GMI-)optimized constellations with a symmetry constraint, optimized for a FEC rate of 0.8, perform nearly identical to their unconstrained counterparts for cardinalities above 8 bit/4D-sym. A symmetry constraint for MI-optimized constellations is shown to have a negative impact in general. The proposed procedure relies on a Monte-Carlo-based approach for evaluating performance and is extendable to other (nonlinear) channels. Stochastic gradient descent is used for the optimization algorithm for which the gradients are computed using automatic differentiation. This article is part of the theme issue 'Celebrating the 15th anniversary of the Royal Society Newton International Fellowship'.

Nonlinear integrated optical resonators for optical fibre data recovery

We apply in simulation a reservoir computer based on evanescently coupled GaAs microrings for real-time compensation of a nonlinear distortion of a 50 Gbaud 16-QAM signal with the launch power up to 14 dBm in a standard single-mode optical fibre. We clearly evidence the crucial role of fast nonlinear response in enabling all-optical signal recovery in real time. With our system we are able to recover from linear and nonlinear distortion caused by a 20 km fibre and 12 dBm launch power below the forward error correction limit.

Low-complexity adaptive multipath interference and channel noise mitigation scheme based on optimized detection for bandwidth-limited IM/DD systems.

In this Letter, we propose a low-complexity adaptive multipath interference (MPI) and channel noise mitigation (AMCM) scheme in the receiver digital signal processing (DSP) for bandwidth-limited intensity modulation and direct detection (IM/DD) transmission systems. Following channel equalization, MPI and channel noise are distributed in the low- and high-frequency parts, respectively, and exhibit the characteristics of bandstop filtering. The proposed AMCM is designed based on optimized detection, which incorporates an adaptive bandpass filter (BPF) and a log-maximum a posteriori estimation with a lookup table-based fixed number of surviving states (LUT-based FS-MAP) decoder. The adaptive BPF is capable of mitigating the MPI and channel noise based on spectral distribution. Moreover, the LUT-based FS-MAP decoder can eliminate intersymbol interference (ISI) introduced by the BPF. The proposed AMCM is implemented in an O-band 56-Gbaud IM/DD optical 4-level pulse amplitude modulation (PAM-4) system with a 10.7-GHz bandwidth over a 10-km standard single-mode fiber with different linewidths. The results demonstrate that the proposed AMCM scheme can enhance signal-to-interference ratio (SIR) tolerance to 11 dB with only three real-valued multiplications per symbol, achieving a 7% hard-decision forward error correction threshold. To the best of our knowledge, for the first time, this represents the inaugural instance of optimized detection being employed for MPI mitigation.

Enhanced ABLO-OFDM performance by using composite multi-mode index modulation in IM/DD systems

In intensity modulation direct detection (IM/DD) systems, an adaptively biased layered optical orthogonal frequency division multiplexing (ABLO-OFDM) scheme is proposed based on composite multi-mode index modulation (CMM-IM). The ABLO-OFDM has a simple structure, easy demodulation, low complexity, and effectively reduces the peak-to-average power ratio (PAPR). Since CMM-IM extends the index to the constellation domain, it increases the number of index bits to further improve the spectral efficiency (SE). By dynamically adjusting the number of activated subcarriers and the number of layers, various signal power can be achieved to enhance system flexibility and reliability. The system performance of four schemes is compared and analyzed in IM/DD systems. The result shows that, for the same SE, CMM-ABLO (4,3) achieves a 3 dB receiver sensitivity gain compared with CMM-ABLO (8,2). When L is 3, four schemes can transmit over about 50 km single-mode fiber under the soft decision forward error correction (SD-FEC) threshold. When L is 1 and the sample rate is less than 20 GSa/s, both CMM-ABLO (4,2) and CMM-ABLO (4,3) can achieve error-free transmission. Moreover, as the number of layers increases, PAPR decreases and it reaches a maximum reduction of 9.6 dB.

Physical Layer Security of Fiber-optic Wiretap Channel with Forward Error Correction Coding

Abstract In this paper, by using effective leakage value, we quantitatively assess the security performance of the fiber-optic wiretap channel with forward error correction coding. As the eavesdropper is far from the transmitter, effective leakage value initially decreases slowly and then will vary rapidly. As the eavesdropper is close to the transmitter, effective leakage value of (7,4) block code is larger than that of the (7,3) block code. However, when the eavesdropping distance is far, the system security performances of both are almost the same. Furthermore, effective leakage value using OTDR is analyzed and discussed.

Neural Network Equalisation for High-Speed Eye-Safe Optical Wireless Communication with 850 nm SM-VCSELs

In this paper, we experimentally illustrate the effectiveness of neural networks (NNs) as non-linear equalisers for multilevel pulse amplitude modulation (PAM-M) transmission over an optical wireless communication (OWC) link. In our study, we compare the bit-error-rate (BER) performances of two decision feedback equalisers (DFEs)—a multilayer-perceptron-based DFE (MLPDFE), which is the NN equaliser, and a transversal DFE (TRDFE)—under two degrees of non-linear distortion using an eye-safe 850 nm single-mode vertical-cavity surface-emitting laser (SM-VCSEL). Our results consistently show that the MLPDFE delivers superior performance in comparison to the TRDFE, particularly in scenarios involving high non-linear distortion and PAM constellations with eight or more levels. At a forward error correction (FEC) threshold BER of 0.0038, we achieve bit rates of ~28 Gbps, ~29 Gbps, ~22.5 Gbps, and ~5 Gbps using PAM schemes with 2, 4, 8, and 16 levels, respectively, with the MLPDFE. Comparably, the TRDFE yields bit rates of ~28 Gbps and ~29 Gbps with PAM-2 and PAM-4, respectively. Higher PAM levels with the TRDFE result in BERs greater than 0.0038 for bit rates above 2 Gbps. These results highlight the effectiveness of the MLPDFE in optimising the performance of SM-VCSEL-based OWC systems across different modulation schemes and non-linear distortion levels.

FPGA implementation of power-lite Volterra-inspired neural network equalizer in 180-Gb/s net bitrate IMDD short-reach optical system.

A white-box power-lite Volterra-inspired neural network (VINN) equalizer is proposed to solve the problem of complexity discontinuity in a Volterra nonlinear equalizer (VNLE). By adjusting the granularity of the solution space, it conserves computational resources while maintaining nonlinear compensation capability. The performance of VINN is verified on a field-programmable gate array (FPGA) in a short-reach intensity modulation and direct detection (IMDD) system, and a 240-Gb/s real-time signal processing rate is achieved. Under the 25% overhead soft-decision forward error correction (SD-FEC) bit error rate (BER) threshold, we realize a record net rate of up to 180 Gb/s based on the FPGA.

Single-carrier 220-Gbit/s sub-THz wireless transmission over 214 m using a photonics-based system.

We have demonstrated, for the first time to our knowledge, a single-carrier 220-Gbit/s wireless link over 214-m distance within hard-decision forward error correction (HD-FEC) limit using a 300-GHz-band photonics-based system incorporated with on-line digital signal processing (DSP). The approach to obtaining these results was to optimize the transmission system by using a low-noised two-tone laser system to the transmitter and receiver and to apply the unique Fresnel region of the antenna to achieve longer distances. These research results are expected to serve as a low-cost and basic communication system technology for promising backhaul wireless communications in the sixth-generation era.

Theoretical probability distribution model and reduction techniques based on an interleaved DFT spread for PAPR in a digital sub-carrier multiplexing system

This paper presents a theoretical probability distribution model for peak-to-average power ratio (PAPR) in the digital sub-carrier multiplexing (DSCM) system, which has not previously been proposed in the literature. To reduce PAPR, an interleaved discrete Fourier transform spread DSCM (I-DFT-S-DSCM) scheme is proposed, which introduces reversible correlations between subcarriers. To investigate the effectiveness of the proposed schemes, a 64-GBaud 16 quadrature amplitude modulation (16-QAM) DSCM system with 4, 8, and 16 sub-carriers was constructed. In the digital domain, the results demonstrate that the proposed theoretical PAPR probability distribution model exhibits mean squared errors (MSE) below 10−5 for the observed and model-predicted complementary cumulative distribution functions (CCDF) in both DSCM and I-DFT-S-DSCM schemes. Regarding PAPR reduction, the I-DFT-S-DSCM scheme demonstrated a reduction in PAPR of up to 1.44 dB compared to the conventional DSCM scheme. To further investigate the impact of PAPR on the bit error rate (BER) performance of the DSCM system, the I-DFT-S-DSCM scheme is implemented with 8 subcarriers transmitted over a 100-km standard single-mode fiber (SSMF). A comparative analysis with DSCM indicates that I-DFT-S-DSCM achieves a PAPR reduction of approximately 1.1 dB and improves receiver sensitivity by approximately 0.7 dB at a 7% hard-decision forward error correction (HD-FEC) threshold, in 100-km single-mode fiber SSMF transmissions.

Controlled alignment imaging optical MIMO communication system based on light spot detection of arrayed light sources

Visible light communication (VLC) technology has become one of the potential key technologies for 6 G due to its unique features, such as abundant license-free spectrum, high confidentiality, and low electromagnetic interference. In this paper, an optical multiple-input multiple-output (MIMO) communication system based on imaging reception is proposed, which can improve the data transmission rate and reduce interference between different sub-channels. To overcome the problem of optical communication link alignment, in this paper, we established an imaging optical MIMO communication system with a controlled light source array (CLSA) and proposed an optical alignment strategy to address the alignment issue. The scheme decouples the constraint that the light spot cannot be aligned with the detector in the communication system under the influence of optical parameters. Based on the light spot detection CLSA module, the communication system can ensure the stability of the link alignment when the communication distance changes. Experimental results show that when the communication distance is 20-80 m, the bit error rate (BER) of the communication system remains below 10-6. The single-channel communication rate of the system is 5 Mbps, and the total communication rate is 20 Mbps through the four-channel rate multiplexing. Moreover, if the communication distance increases to the range of 80-100 m, the BER increases, but it is always lower than the forward error correction (FEC) threshold.

Optical matrix computing for optical forward error correction encoding

Forward error correction (FEC) has been widely used in today's communication systems, implemented by electronics. For optical communications, on-the-fly optical processing is highly desired for reduced optical-electrical-optical (OEO) conversions, so as to reduce the latency and cost. In this work, we present a proof-of-concept study of an optical FEC encoding method based on optical matrix computing by wavelength-division multiplexing (WDM) with time-wavelength interleaved manipulation. The optical FEC encoder realized by optical fiber devices features nearly equivalent net encoding gain compared with the theoretical electrical encoder. The experimental results indicate effective error correction, with 2-dB net gain in on-off keying (OOK) transmission at 20 Gb/s, supporting the realization of transmission-computing-merged systems. Meanwhile, the proposed method also supports the whole realization of FEC with both encoding and decoding.