Forward Error Correction Research Articles

Digital backpropagation based on binary logarithmic step size distribution for fibre non‐linearity compensation

AbstractCapacity crunch has become critical in recent years as commercial communication systems approach their theoretical data rate limits. This work presents a low‐complexity digital backpropagation (DBP) implementation approach based on step size distribution that uses a binary logarithmic step size method to achieve high data rate optical transmission. The proposed scheme shows performance improvements (∆Q) of 2.36, 1.19, and 0.71 dB over linear compensation, constant step size (CSS) DBP, and logarithmic step size DBP techniques in a 2400 km 112 Gbit/s DP‐16 quadrature amplitude modulation (QAM) system, respectively. At 13 dBm, a high performance (Q) of 10.9 dB (BER = 2.25 × 10−4) is achieved, above the 3.80 × 10−3 hard‐decision forward error correction (HD‐FEC) limit, using the proposed scheme. Also, the allowable transmission distance is extended by 960 km at the HD‐FEC limit over the linear compensation technique. The optimization achieves a 38% saving in the number of DBP calculation steps compared to the CSS DBP, which considerably reduces the computational cost since a few steps are required for effective non‐linearity compensation.

Simultaneously enhancing capacity and security in free-space optical chaotic communication utilizing orbital angular momentum

Optical chaotic signals emitted from an external-cavity feedback or injected laser diode enable small-signal information concealment in a noise-like carrier for secure optical communications. Due to the chaotic bandwidth limitation resulting from intrinsic relaxation oscillation frequency of lasers, multiplexing of optical chaotic signal, such as wavelength division multiplexing in fiber, is a typical candidate for high-capacity secure applications. However, to our best knowledge, the utilization of the spatial dimension of optical chaos for free-space secure communication has not yet been reported. Here, we experimentally demonstrate a free-space all-optical chaotic communication system that simultaneously enhances transmission capacity and security by orbital angular momentum (OAM) multiplexing. Optical chaotic signals with two different OAM modes totally carrying 20 Gbps on–off keying signals are secretly transmitted over a 2 m free-space link, where the channel crosstalk of OAM modes is less than −20 dB, with the mode spacing no less than 3. The receiver can extract valid information only when capturing approximately 92.5% of the OAM beam and correctly demodulating the corresponding mode. Bit error rate below the 7% hard-decision forward error correction threshold of 3.8×10−3 can be achieved for the intended recipient. Moreover, a simulated weak turbulence is introduced to comprehensively analyze the influence on the system performance, including channel crosstalk, chaotic synchronization, and transmission performance. Our work may inspire structured light application in optical chaos and pave a new way for developing future high-capacity free-space chaotic secure communication systems.

A Hybrid Millimeter-Wave and Free-Space-Optics Communication Architecture with Adaptive Diversity Combining and HARQ Techniques

We propose and demonstrate a hybrid communication architecture that combines millimeter-wave (MMW) in the radio frequency (RF) domain and free-space-optics (FSO) technologies using adaptive combining and hybrid automatic repeat request (HARQ) techniques. At the receiving end, we employed joint signal processing with an adaptive diversity combining technique (ADCT) based on a maximum ratio combining (MRC) algorithm. We derived closed-form expressions for the outage probability and throughput of the hybrid RF and FSO (RF/FSO) system, considering various characteristics of atmospheric turbulence in the FSO link. Experimental testing with 10-Gbaud quadrature phase shift keying (QPSK) data was conducted under different simulated atmospheric turbulence intensities, FSO and MMW speed-ratios, and forward error correction (FEC) overheads. Additionally, we validated improvements in terms of bit error ratio (BER), outage probability, and throughput performance.

Demonstration of 120 Gbit/s turbulence-resilient coherent optical communication employing cylindrical vector beam multiplexing

Free space optical (FSO) communication has gained widespread attention due to its advantages, including high confidentiality, high communication capacity, and no limitation of spectrum. One of the great challenges in FSO communication is the transmission performance degradation in atmospheric turbulence channel due to wavefront distortion and scintillation. Here, we proposed and experimentally demonstrated a 120 Gbit/s vector beam multiplexed coherent optical communication system with turbulence-resilient capacity. Four multiplexed vector beams, each carrying a 30 Gbit/s quadrature phase-shift keying signal, propagate through different turbulence conditions. The influence of turbulence channel on the vector beam impairments is experimentally investigated. Under the weaker turbulence conditions, the system bit error rates are below the forward error correction threshold of 3.8 × 10−3. In comparison with the Gaussian mode, the communication interruption probability of the vector beams system decreases from 36% to 12%-18% under stronger turbulence conditions.

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.

Performance Evaluation of LoRa Communications in Harsh Industrial Environments

LoRa technology is being integrated into industrial applications as part of Industry 4.0 owing to its longer range and low power consumption. However, noise, interference, and the fading effect all have a negative impact on LoRa performance in an industrial environment, necessitating solutions to ensure reliable communication. This paper evaluates and compares LoRa’s performance in terms of packet error rate (PER) with and without forward error correction (FEC) in an industrial environment. The impact of integrating an infinite impulse response (IIR) or finite impulse response (FIR) filter into the LoRa architecture is also evaluated. Simulations are carried out in MATLAB at 868 MHz with a bandwidth of 125 kHz and two spreading factors of 7 and 12. Many-to-one and one-to-many communication modes are considered, as are line of sight (LOS) and non-line of Sight (NLOS) conditions. Simulation results show that, compared to an environment with additive white Gaussian noise (AWGN), LoRa technology suffers a significant degradation of its PER performance in industrial environments. Nevertheless, the use of forward error correction (FEC) contributes positively to offsetting this decline. Depending on the configuration and architecture examined, the gain in signal-to-noise ratio (SNR) using a 4/8 coding ratio ranges from 7 dB to 11 dB. Integrating IIR or FIR filters also boosts performance, with additional SNR gains ranging from 2 dB to 6 dB, depending on the simulation parameters.

Integrated physical-layer secure visible light communication and positioning system based on polar codes

Visible light communication (VLC) with physical-layer security can provide information-theoretic security for the optical wireless channel based on the characteristics of the channel instead of encryption algorithms and secret keys at application layer. Since precise location information of communication parties is crucial for estimating channel states and designing secure communication schemes, this paper proposes an integrated visible light communication and positioning system which provides triple functionalities of high-accuracy indoor positioning, physical-layer secure visible light communication, and flicker mitigation illumination. A heterogeneous signal hybrid line coding scheme is proposed for the transmitter to converge the high-speed communication data signals and the low-speed positioning data signals, and a hybrid heterogeneous signal extraction scheme is proposed for the receiver to separate the hybrid heterogeneous signals with a high-bandwidth photodetector and a low-pass complementary metal-oxide-semiconductor (CMOS) image sensor. Based on the positioning information and the communication scheme, a polar codes-based forward error correction coding scheme is designed to achieve physical-layer security and transmission reliability simultaneously. Numerical results show that the proposed system can reach a secrecy code rate of 0.76 for a single-input single-output indoor VLC channel and a transmission efficiency of 0.38 without perceivable flicker. Experimental results show that the proposed system can achieve an average positioning accuracy of 3.35 cm and decrease the bit error rate of a legitimate receiver to a near error-free level (lower than 10−7) while keeping the bit error rate of an eavesdropper at 0.4887 (nearly 0.5) with a transmission data rate of 1 Mbps, resulting in near-zero suppression of the eavesdropped information and a high secrecy capacity of 0.9994.

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.

Side-emitting fiber-based distributed receiver for visible light communication uplink.

We present a distributed receiver for visible light communication based on a side-emitting optical fiber. We show that 500 kbps data rate can be captured with a bit-error rate below the forward-error correction limit of 3.8·10-3 with a light-emitting diode (LED) transmitter 25 cm away from the fiber, whereas by increasing the photodetector gain and reducing the data rate down to 50 kbps, we improve the LED-fiber distance significantly up to 4 m. Our results lead to a low-cost distributed visible-light receiver with a 360° field of view for indoor low-data rate, Internet of Things, and sensory networks.

Efficient learning-driven data transmission algorithm for cloud-to-thing continuum

In the cloud-to-thing continuum paradigm, the efficient transmission of learning-driven data is critical for facilitating real-time decision-making and continuous learning processes. Fountain codes have gained popularity as Forward Error Correction (FEC) schemes in application layer networking due to their ability to recover lost data packets. Gaussian Elimination (GE) algorithms, which form the core of Fountain codes, can be optimized to improve transmission efficiency. We introduces techniques that leverage GE algorithms to enhance the transmission of learning-driven data within the cloud-to-thing continuum. A fast matrix element architecture is developed to improve computational speed. Additionally, a pipelined normalization component based on binary trees is introduced to enable parallel processing. A pipelined elimination component utilizing binary trees is also presented to further boost transmission speeds and efficiency. These techniques are implemented using Field Programmable Gate Array (FPGA) technology. Their performance is evaluated against existing methods, demonstrating significant gains in transmission efficiency. By effectively managing increasing Internet traffic loads and optimizing the flow of learning-driven data, these approaches facilitate more efficient communication between cloud-based AI systems and edge devices. Ultimately, this research supports enhanced real-time decision-making and continuous learning processes across the full cloud-to-thing continuum.

Design and performance investigation of a coherent optical system based multi-band OFDM with various indexes

Abstract In this work, a comprehensive study of a multi-band optical orthogonal frequency division multiplexing (MB-OOFDM) system is investigated. Different OFDM indexes (128,256,512, and 1024) are utilized with the coherent detection CD technique. High-order modulation 16-quadrature amplitude modulation (16-QAM) is used to obtain high spectral efficiency. Transmission studies indicated that 128 subcarriers with 2-bands exhibit a higher optical signal-to-noise ratio (OSNR) of 23 dB with lower bit error rate (BER) of 1 × 10−4, while 1024 subcarriers with 8-bands shows a lower OSNR of 22 dB with a higher BER of 3 × 10−3. Even though the higher subcarrier type has the lowest BER, it provides a superior solution when combined with wavelength-division multiplexing (WDM) in the presence of forward error correction (FEC). The performance of the system with 40 Gbps along 800 km of uncompensated fiber has designed and simulated using Optisystem software.

MIMO Systems with Neural Networks in OFDM-Based WDM Visible Light Communications

In this paper, we describe a wavelength-division multiplexing visible-light communication (VLC) system using two colored light-emitting diodes (LEDs) with similar emission wavelengths. A multi-input multi-output signal-separation method using a neural network is proposed to cancel the optical cross chatter caused by the spectral overlap of LEDs. The experimental results demonstrate that signal separation using neural networks can be achieved in wavelength-multiplexed VLC systems with a bit error rate of less than 3.8 × 10-3 (forward error correction limit). Furthermore, the simulation results reveal that the carrier-to-noise ratio (CNR) is improved by 2 dB for the successive interference canceller (SIC) compared to the zero-forcing method.

S-Band WDM Transmission Using PPLN-Based Wavelength Converters and 400-Gb/s C-Band Real-Time Transceivers

Multi-band WDM transmission beyond the C+L-band is a promising technology for achieving larger capacity transmission by a limited number of installed fibers. In addition to the C- and L-band, we can expect use the S-band as the next band. Although the development of optical components for new bands, particularly transceivers, entails resource dispersion, which is one of the barriers to the realization of multi-band systems, wavelength conversion by transparent all-optical signal processing enables new wavelength band transmission using existing components. Therefore, we proposed a transmission system including a new wavelength band such as the S-band and made it possible to use a transceiver for the existing band by performing the whole-band wavelength conversion without using a transceiver for the new band. As a preliminary verification to demonstrate multi-band WDM transmission including S-band, we investigated the application of a novel wavelength converter between C-band and S-band, which consists of periodically poled lithium niobate waveguide, to the proposed system. We first characterized the conversion efficiency and noise figure of the wavelength converter and estimated the transmission performance of the system through the wavelength converter. Using the evaluated wavelength converters and test signals of 64 channels arranged in the C-band at 75-GHz intervals, we constructed an experimental setup for S-band transmission through an 80-km standard single-mode fiber. We then demonstrated error-free transmission of real-time 400-Gb/s DP-16QAM signals after forward error correction decoding. From the experimental results, it was clarified that thewavelength converter which realizes the uniformlossless conversion covering the whole C-band effectively achieves the S-band WDM transmission, and it was verified that the capacity improvement of the multi-band WDM system including the S-band can be expected by applying it in combination with the C+L-band WDM system.

High-security three-dimensional optical transmission mechanism utilizing time-frequency-space interleaving disruption.

In this paper, we propose a high-security three-dimensional optical transmission system utilizing time-frequency-space interleaving chaos, which simultaneously enhances the reliability and security of the system. The four-wing 3D chaos model encrypts the time-frequency space interleaved modulation domain of a orthogonal time-frequency space (OTFS) modulation signal and the modulated phase information simultaneously, improving the system's security. We also experimentally validate the proposed high-security 3D-OTFS method, utilizing the hexadecimal modulation technique. The modulated OTFS signal achieves a transmission rate of 34.1 Gb/s over a 2-km seven-core fiber link, with the OTFS signal exhibiting a maximum of 1.31 dB receiver sensitivity gain compared to orthogonal frequency division multiplexing (OFDM) signals under the forward error correction threshold of the bit error rate. The achieved keyspace is equal to 5 × 1048. The findings demonstrate that the proposed high-security three-dimensional optical transmission mechanism, based on time-frequency-space interleaved disruption, exhibits excellent anti-interference ability and confidentiality performance. Consequently, it holds promising prospects for future applications in optical communications.

XPM estimation and compensation in the WDM system based on a low-complexity inner FEC.

In this work, we focus on compensation of inter-channel nonlinearity in optical wavelength division multiplexed (WDM) systems. We consider pre-coding with a high-rate forward error correction (FEC) code and a low-complexity and low-latency decoding and equalization scheme at the receiver. The 2 × 2 multiple-input multiple-output (MIMO) recursive least square (RLS) equalizer is applied to reduce the inter-symbol interference (ISI) caused by the inter-channel nonlinearity, while the decoder improves the quality of the data feedback. Decisions based on feedback reliability have been implemented to prevent error propagation. We demonstrate that our system can readily utilize the inner FEC part of a mainstream concatenated optical FEC designs such as the 400ZR standard FEC. We evaluate the proposed algorithm for the dual-polarization 16QAM and 256QAM optical links. Based on our simulation results, the Q-factor has been increased by 0.36 and 0.67 dB for the 16QAM and 256QAM, respectively. The optimum launch power has been increased by 0.4 dB for both cases.

Multimode Fabry-Perot laser as a reservoir computing and extreme learning machine photonic accelerator

In this work, we introduce Fabry–Perot lasers as neuromoprhic nodes in the context of time-delayed reservoir computing and extreme learning machine (ELM) for the processing of temporal signals and the high-speed classification of images. By exploiting the multi-wavelength emission capabilities of the Fabry–Perot lasers, additional processing nodes can be introduced, thus raising the computational power without sacrificing processing speed. An experimental validation of this concept using a Fabry–Perot ELM is presented targeting a time depedent task such as channel equalization for a 50 km 28 Gbaud ‘PAM-4’ transmission, offering hard-decision forward error correction compatible performance. Additionally, the Fabry–Perot neuromorphic concept has been further strengthened by modifying the data entry technique by parallelelly assigning different samples of the input signal to different modes so as to significantly reduce speed penalty. Numerical simulations revealed that this alternative data insertion technique can offer a reduction of the processing delay and physical footprint by 75% compared to the conventional approach assigning the same symbols to all Fairy–Perot modes. Moreover, by using a similar data processing scheme in ‘MNIST’ image classification task we were able to numerically achieve a processing speed of 255.1 Mimages s−1 and a classification accuracy up to 95.95%.

High-speed spatial light modulation enabling 25-Gbit/s twisted light encoding/decoding and 260-m security free-space data transmission.

Spatial domain of light beam is an important degree of freedom to be extensively explored. As a set of spatial domains, twisted lights have some natural properties such as orthogonality and security, providing great potentials in optical communications especially for data encoding/decoding. However, the speed of traditional spatial light modulators has always been criticized. Here we present a hundred-meter security free-space data transmission based on high-speed spatial light modulation by exploiting temporal-to-spatial domain mapping. We demonstrate 25-Gbit/s twisted light encoding/decoding and 260-m security free-space data transmission in the experiment. The encoding/decoding link will lead to 3-dB improvement in bit error rate (BER) performance compared with a single channel in theory and ∼1-dB optical signal-to-noise ratio (OSNR) penalty at the forward error correction (FEC) threshold of 3.8e-3 in practice. The experiment results also show favorable security performance of the proposed encoding/decoding link system.

Unidirectional Ring-Based WDM Fiber Network for Both Downlink and Uplink Signal Access

In the paper, a dual-bidirectional ring-type wavelength-division-multiplexing (WDM) access network with downlink and uplink signal access simultaneously using a single fiber backbone in clockwise and counterclockwise directions, respectively. The proposed network architecture is simple and easy to implement via the designed remote node (RN) and optical line termination (OLT) modules, but it also can double the downlink traffic using the original WDM downlink wavelengths. The presented ring-type WDM network can also avoid the Rayleigh backscattering (RB) beat noise when the same wavelengths are applied as downlink and uplink channels concurrently. In the measurement, 50 km long-reach and 15 km short-reach fiber transmission lengths are achieved for the symmetrical 10 and 28 Gbit/s on-off keying (OOK) data access, respectively. In addition, based on the obtained power budgets of eight downlink WDM signals and network design at the forward error correction (FEC) threshold, 16 optical network units (ONUs) can be supported simultaneously.

Research on Adaptive Transmit Diversity Strategy for Reducing Interference in Underwater Optical Multi-Beam Non-Orthogonal Multiple Access Systems

With the rapid development of the underwater Internet of Things (IoT), the number of underwater communication nodes is rapidly increasing. The access capacity of a traditional multi-antenna communication system is limited by the number of transmitting antennas, and multi-beam communication systems using non-orthogonal multiple access (NOMA) technology can enhance the access capacity of the system. However, this can lead to serious inter-beam and intra-beam interference. To address the severe issues of inter-beam and intra-beam interference in underwater multi-beam NOMA systems, we propose an adaptive transmit diversity strategy. We design an algorithm for adaptive selection and merging beams based on the degree of interference between beams in space, which merges LED beams with high interference. Diversity technology is used to reduce interference between beams, and spatial multiplexing is still performed between LED groups with low interference. Within the same beam, we use an OFDM-NOMA scheme to match and group the users. Signals from different user groups are sent through different subcarriers to improve resource utilization. This enhances access capacity while reducing NOMA inter-user interference. Simulation results show that the bit error rate (BER) of users with the adaptive transmit diversity strategy satisfies the forward error correction (FEC) limits in the presence of high inter-beam interference and has a better reachable rate and BER performance compared to the multi-beam access system without interference management. We also analyze the system BER performance of the proposed strategy in the multi-user case, and the BER of all 32 access nodes are lower than the FEC threshold at a communication distance of 5 m. This demonstrates that the strategy can effectively reduce the interference of the multi-beam NOMA system.

Simultaneous dual-channel data transmission through a multimode fiber via wavefront shaping

The increasing demand for transmission capacity in fiber-optic communications makes multimode fibers (MMFs) attractive by enabling simultaneous multi-channel data transmission. However, inherent mode crosstalk among transmission channels limits its applicability. In this Letter, we propose to overcome this problem via wavefront shaping. By actively modulating the incident light with a special wavefront, not only the transmitted power for a specific channel can be enhanced but also crosstalk among different transmission channels can be mitigated. As a proof of concept, we experimentally demonstrated wavefront shaping assisted dual-channel optical communications through a single MMF. 10 Gbaud four-level pulse amplitude modulation signals were sent through both channels simultaneously, enabling a total bit rate of 40 Gbps. Both channels were analyzed with bit error rates below the hard-decision forward error correction limit, confirming the validity of the proposed scheme.