Error Correction Threshold Research Articles

Net 30-Tb/s bidirectional IM/DD optical interconnect over 19-core fiber enabled by WDM uplink/downlink twin-SSB PAM-4 transmission.

High-capacity optical interconnects with short reach are hugely demanded driven by the exponential growth of data traffic. In this work, four-channel wavelength division multiplexing (WDM) uplink/downlink twin single-sideband (twin-SSB) signals are implemented by a wavelength selective switch (WSS) at once, which simplifies the structure of multi-channel SSB transmitters and reduces the cost of high-capacity optical interconnect. Compared to a double sideband scheme, it has been experimentally proven that the performance of SSB transmission over standard single-mode fiber (SSMF) at C-band with an ultra-high baud rate has been greatly improved, which has the ability to effectively overcome the power fading induced by chromatic dispersion in an intensity modulation and direct detection (IM/DD) system. Besides, Rayleigh backscattering cross talk introduced by the same wavelengths in single-fiber bidirectional transmission is avoided by the proposed uplink/downlink twin-SSB scheme, which achieves 0.5-dB receiver sensitivity improvement compared to the conventional scheme. Finally, whtat is believed to be a record C-band 36.48-Tb/s PAM-4 4λ WDM IM/DD bidirectional optical interconnect is successfully demonstrated over 1-km 19-core fiber under a 20% soft-decision forward error correction (SD-FEC) threshold of 2.4×10-2 for beyond net 30-Tb/s large-capacity optical interconnection application.

Probabilistic shaping probability distribution scrambling based on a chaotic system for integrating secure transmission and adaptive key updating

A probabilistic shaping probability distribution scramble (PSPDS) scheme based on chaotic systems is proposed to fulfill both secure transmission and adaptive key updating. The chaotic Chen and logistic systems are adopted to generate a chaotic random sequence. The probabilistic shaping is achieved by constant composition distribution matching (CCDM) and probabilistic amplitude shaping architecture. The chaotic, random sequences are used to scramble the probability distribution of CCDM, improving security. The session key is embedded into a probability distribution. The legal receiver extracts the error-free session key when OSNR is higher than the requirement of the forward error correction threshold. We employ a coherent OFDM 16QAM transmission experiment on 120 km fiber, confirming our proposed scheme with a net rate of 9.95 Gbit/s. The results show that the PSPDS scheme has no encryption penalty compared with the baseline without encryption. The key updating rate has the ability to vary adaptively and reaches 224.2 Mbit/s by adjusting the block length of CCDM in our experiment. The key space reaches 10136. Even if an illegal party obtains a ciphertext signal, the plaintext and session key can hardly be inferred due to a probability distribution scramble.

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.

Accurate optimal quantum error correction thresholds from coherent information

Quantum error correcting (QEC) codes protect quantum information from decoherence as long as error rates fall below critical error thresholds. In general, obtaining thresholds implies simulating the QEC procedure using, in general, suboptimal decoding strategies. In a few cases and for sufficiently simple noise models, optimal decoding of QEC codes can be framed as a phase transition in disordered classical spin models. In both situations, accurate estimation of thresholds demands intensive computational resources. Here we use the coherent information of the mixed state of noisy QEC codes to accurately estimate the associated optimal QEC thresholds already from small-distance codes at moderate computational cost. We show the effectiveness and versatility of our method by applying it first to the topological surface and color code under bit-flip and depolarizing noise. We then extend the coherent information based methodology to phenomenological and quantum circuit level noise settings. For all examples considered, we obtain highly accurate estimates of optimal error thresholds from small, low-distance instances of the codes, in close agreement with threshold values reported in the literature. Our findings establish the coherent information as a reliable competitive tool for the calculation of optimal thresholds of state-of-the-art QEC codes under realistic noise models. Published by the American Physical Society 2024

Bias-aided DD-LMS equalizer for optical multipath-interference-impaired high-speed PAM4 transmission systems

Multipath interference (MPI) noise induces drastic fluctuations in high-speed 4-level pulse amplitude modulation (PAM4) intensity modulation direct detection (IMDD) systems, severely degrading the transmission performance. Here, we propose a bias-aided decision-directed least mean square (DD-LMS) equalizer to eliminate the MPI noise. In the simulation, the proposed bias-aided DD-LMS equalizer could adeptly track and compensate the MPI-impaired PAM4 signal, markedly improving the bit error rate (BER) performance under different MPI levels and laser linewidths. Within a 112 Gbps PAM4 transmission system, the proposed equalizer achieves a MPI tolerance over 4 dB at the KP4-forward error correction (FEC) threshold (2.4 × 10−4), outperforming existing MPI suppression techniques.

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.

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.

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.

Low complexity deep neural network equalizer based on the multi-source domain transfer learning in IMDD system.

In this paper, we demonstrate a newly designed multi-source domain transfer learning (MST) scheme to reduce the training cost of deep neural network (DNN) based equalizer in intensity-modulation and direct-detection (IMDD) systems. Different from a common transfer learning algorithm, in this scheme, data with different channel parameters is selected and proportionally used to construct a multi-source domain dataset. This allows training the source domain in a single task while ensuring the model's generalization ability and stability. In an 80Gb/s PAM-4 IMDD short reach system, our proposed MST equalizer was proven effective. The corresponding results demonstrate that, compared to a conventional DNN equalizer, the proposed MST equalizer can achieve a bit error rate that meets the hard decision-forward error correction threshold while saving 87% of the iteration epochs and 65% of the training data.

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.

An unsupervised coherent receiver digital signal processing algorithm based on spectral clustering with no data preamble

AbstractA coherent optical receiver digital signal processing (DSP) scheme is proposed based on spectral clustering, which utilises spectral clustering to cluster the signals outputted by the DSP. Compared to existing blind DSP algorithms for coherent optical receivers operating at over 100Gbps with PM‐mQAM, the proposed scheme effectively suppresses various physical impairments, achieving lower bit error rates (BERs) at the same transmission distance, thus enabling longer transmission distances under the same forward error correction threshold. Furthermore, simulations of the proposed scheme on a 14GBaud PM‐16QAM coherent optical transmission system show that, at a BER of 1.9E‐2, the maximum transmission distance increases from 1700 to 2000 km, and at a BER of 3.8E‐3, it increases from 700 to 900 km.

Neural network-based electrical dispersion pre-compensation for a 56 Gb/s PAM-4 over an 80 km fiber in intensity-modulation and direct-detection systems.

A neural network (NN)-based electrical dispersion pre-compensation (pre-EDC) scheme in intensity-modulation and direct-detection (IM/DD) systems is proposed and experimentally demonstrated in this Letter. The scheme enables 56 Gbit/s four-level pulse amplitude modulation (PAM-4) generation at a transmitter over an 80 km single-mode fiber (SMF) transmission in the C-band. The NN is utilized to better fit nonlinear phase-amplitude transformation due to the chromatic dispersion (CD) in IM/DD systems, in place of the existing Gerchberg-Saxton (GS) iterative algorithm and linear GS-based finite impulse response (GS-FIR) non-iterative compensation schemes. The experimental results show that the measured bit error ratio (BER) can be reduced to below the 7% hard-decision forward error correction (HD-FEC) threshold of 3.8 × 10-3 with 0 dBm receiver optical power (ROP) by the NN-based non-iterative pre-EDC scheme, which also saves up to 81% of computational complexity compared to the GS-based scheme. The results indicate that our proposed scheme is promising for the CD pre-compensation at the transmitter.

PAM4-modulated 2-micron band for enhanced indoor optical communications: experimental evaluation.

This research explores the application of PAM4 modulation to optical signals in the 2-μm wavelength band for indoor optical communication. Experiments conducted in a simulated atmospheric turbulence environment demonstrated a BER of 10-5 for the 2-μm laser carrier with PAM4, surpassing the forward error correction threshold. Power loss comparisons to a back-to-back setup showed minimal degradation under various turbulence levels, with losses of 1.80 dB, 1.91 dB, 2.09 dB, and 2.55 dB for non-turbulent, weak-turbulent, moderate-turbulent, and strong-turbulent conditions, respectively. The system's sensitivity was measured at -7.69dBm, emphasizing its effectiveness in detecting low-power signals. OptiSystem simulations indicated that PAM4 necessitates a higher optical OSNR than NRZ, suggesting the necessity for sophisticated signal processing techniques for systems operating in the 2-μm band. The study's results contribute to the body of knowledge on high-bandwidth optical communication and suggest future research avenues aimed at enhancing system performance while maintaining cost-effectiveness.

Physical layer security--enhanced optical communication based on chaos masking and chaotic hardware encryption.

The security and confidentiality of information are crucial in contemporary communication systems. In this work, we propose a physical layer security-enhanced optical communication scheme based on dual-level protection with chaos masking (CMS) and chaotic hardware encryption. The integration of CMS and chaotic hardware encryption contributes to enhancing the security of the system. Different uncorrelated chaos generated from a single Fabry-Perot (FP) laser are employed to independently mask and encrypt the confidential signals for multiple channels in a wavelength division multiplexing (WDM) system. Thanks to the CMS and temporal intensity scrambling, the signals are encrypted into a noise-like signal to against direct demasking or decryption attacks. Compared to individual CMS or encrypting the signals using stand-alone dispersion components, numerical results demonstrate that the proposed scheme significantly enhances communication security. The decrypted bit error rate (BER) for 10 Gb/s data in each channel at the legitimate receiver is lower than the hard decision forward error correction threshold (HD-FEC) of 3.8 × 10-3 for a proof-of-principle demonstration. This approach enables multi-path parallel and independent security-enhanced chaotic optical communication, offering a promising solution for high-capacity secure optical communication.

Performance evaluation of an 80 Gbps dual-polarization orbital-angular-momentum-based underwater optical wireless communication system

In this paper, a new underwater optical wireless communication (UOWC) system is proposed. It integrates dual-polarization (DP) states with orbital angular momentum (OAM) beams. By leveraging the inherent orthogonality of different OAM modes, the system achieves enhanced signal quality and increased transmission capacity. Each polarization state carries data of four OAM beams, with each capable of carrying 10 Gbps of information. Additionally, a single laser diode (LD) source operating at 532 nm is employed. To evaluate the performance of the proposed system, the effects of attenuation across various water types are considered. Propagation range, bit error rate (BER), and eye diagrams are utilized as comprehensive performance metrics. The obtained results indicate that, below the error correction threshold (3.8×10−3), our proposed UOWC system achieves impressive underwater transmission ranges. Specifically, we observe a longer range of 44 m for pure sea (PS) water that exhibits the lower attenuation, which is decreased to 26.5 m for clear ocean (CL) and 15.5 m for coastal ocean (CS). Furthermore, it decreased reaching shorter ranges of 8 m for harbor I (HI) and 4.45 m for harbor II (HII), which have the highest attenuation.

Orbital angular momentum mode multiplexing communication in multimode fibers

Vortex beams with orbital angular momentum (OAM) have infinite mode orthogonality, which can greatly boost communication capacity through mode-division multiplexing. However, current exploration of OAM beam transmission primarily focuses on free-space or specialty fibers limited by the OAM spiral phase wavefront characteristics. Due to the mode field phase sensitivity, these methods are constrained by turbulence interference and fabrication error tolerance, restricting transmission distance of OAM beam at practical application. Herein, we propose an OAM transmission scheme using commercial multimode fiber (MMF) exploiting the eigenmodes superposition theory. Leveraging linear superposition of HE and EH vector modes with ± (π/2) phase shift over MMF, OAM excitation and transmission can be supported with low interference. Simultaneously, due to the decreased demand for fabrication precision in the gradient core structure, the tolerance for machining errors is enhanced. As a proof-of-concept, we have demonstrated a multidimensional OAM multiplexing communication with 640-channel (4 OAM modes, 80 wavelengths and 2 polarization states) over a 5 km MMF, successfully transmitting QPSK-OFDM signals at a total rate of 15 Tbit/s. The system demonstrated OAM mode purity exceeding 65% and bit error rate (BER) below the forward error correction (FEC) threshold (3.8 × 10−3). Multiplexed OAM signals can be effectively transmitted in MMF over short to medium distances with acceptable mode crosstalk, while remaining compatible with wavelength and polarization dimensions, enabling the construction of multi-dimensional multiplexing local area networks.