Error Rate Threshold Research Articles

Optimization of probabilistic and geometrical shaping in RoF system based on overlapping labels

We used a hybrid probabilistic geometric shaping scheme that uses a probabilistic shaping method with labels and a pairwise optimization (PO) algorithm to transmit signals in a 2 × 2 MIMO Photon-assisted millimeter wave (MMW) radio-over-fiber (RoF) system in the D-band. This scheme has low complexity and a simple recovery method. This scheme optimizes 16-ary quadrature amplitude modulation (16QAM) to probabilistically shaped 9-ary quadrature amplitude modulation (PS-9QAM) by adding labels, and optimizes it to hybrid probabilistically and geometrically shaped 9-ary quadrature amplitude modulation (PGS-9QAM) by geometric shaping using the PO algorithm. The experimental results prove the optimization effect of this scheme. Under the bit error rate threshold of 0.0038, when the net bit rate is the same, compared with 16QAM, PS-9QAM and PGS-9QAM, the optical power at the transmitter can be reduced by 0.8 dB and 1.45 dB respectively. When the transmission power is the same, compared with 16QAM, the net rates of PS-9QAM and PGS-9QAM can be increased by 7.5Gbit/s and 9Gbit/s respectively.

Purity‐Assisted Zero‐Noise Extrapolation for Quantum Error Mitigation

AbstractQuantum error mitigation aims to reduce errors in quantum systems and improve accuracy. Zero‐noise extrapolation (ZNE) is a commonly used method, where noise is amplified, and the target expectation is extrapolated to a noise‐free point. However, ZNE relies on assumptions about error rates based on the error model. In this study, a purity‐assisted zero‐noise extrapolation (pZNE) method is utilized to address limitations in error rate assumptions and enhance the extrapolation process. The pZNE is based on the Pauli diagonal error model implemented using the Pauli twirling technique. Although this method does not significantly reduce the bias of routine ZNE, it extends its effectiveness to a wider range of error rates where routine ZNE may face limitations. In addition, the practicality of the pZNE method is verified through numerical simulations and experiments on the online quantum computation platform, Quafu. Comparisons with routine ZNE and virtual distillation methods show that biases in extrapolation methods increase with error rates and may become divergent at high error rates. The bias of pZNE is slightly lower than routine ZNE, while its error rate threshold surpasses that of routine ZNE. Furthermore, for full density matrix information, the pZNE method is more efficient than the routine ZNE.

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.

Joint constellation shaping optical modulation scheme based on a pair of common-bottomed trigonal cones.

A joint constellation shaping (JCS) three-dimensional (3D) 16-ary modulation scheme constructed with a pair of common-bottomed trigonal cones (CBTC) as primitives is proposed. Compared to the 3D traditional constellation (TC) and the 3D geometric constellation shaping (GS) structure previously proposed by our group (GGS), the constellation figure of merit (CFM) is improved by 0.3906 and 0.0097, respectively. Meanwhile, probabilistic shaping (PS) is employed to optimize the 3D-CBTC-16CAP constellation structure for the second time to enhance the CFM of the constellation further. Compared to the 3D-CBTC-16CAP, after PS the 3D-JCS-16CAP has a CFM improvement of 0.5014. Experiments are carried out to transmit the signals across a 2 km seven-core fiber. At the bit error rate (BER) threshold ∼3.8 × 10-3, the 3D-CBTC-16CAP scheme demonstrates an improvement in the receiver sensitivity by 0.76 and 0.39 dB compared with 3D-TC-16CAP and 3D-GGS-16CAP. In addition, the transmission effect of the signals after joint PS is verified. Experiments show that the proposed 3D-JCS-16CAP scheme has the most significant enhancement effect when used in conjunction with PS, and the receiver sensitivity is improved by about 0.97 and 0.34 dB compared with the 3D-JTC-16CAP (3D-TC-16CAP signal after joint PS) and 3D-JGGS-16CAP (3D-GGS-16CAP signal after the joint PS).

Mitigating Temporal Fragility in the XY Surface Code

An important outstanding challenge that must be overcome in order to fully utilize the XY surface code for correcting biased Pauli noise is the phenomenon of fragile temporal boundaries that arises during the standard logical state-preparation and measurement protocols. To address this challenge we propose a new logical state-preparation protocol based on locally entangling qubits into small Greenberger-Horne-Zeilinger-like states prior to making the stabilizer measurements that place them in the XY-code state. We prove that in this new procedure O(n) high-rate errors along a single lattice boundary can cause a logical failure, leading to an almost quadratic reduction in the number of fault configurations compared to the standard state-preparation approach. Moreover, the code becomes equivalent to a repetition code for high-rate errors, guaranteeing a 50% code-capacity threshold during state preparation for infinitely biased noise. With a simple matching decoder we confirm that our preparation protocol outperforms the standard protocol in terms of both threshold and logical error rate in the fault-tolerant regime where measurements are unreliable and at experimentally realistic biases. We also discuss how our state-preparation protocol can be inverted for similar fragile-boundary-mitigated logical-state measurement. Published by the American Physical Society 2024

Artificial neural network syndrome decoding on IBM quantum processors

Syndrome decoding is an integral but computationally demanding step in the implementation of quantum error correction for fault-tolerant quantum computing. Here, we report the development and benchmarking of Artificial Neural Network (ANN) decoding on IBM quantum processors. We demonstrate that ANNs can efficiently decode syndrome measurement data from heavy-hexagonal code architecture and apply appropriate corrections to facilitate error protection. The current physical error rates of IBM devices are above the code's threshold and restrict the scope of our ANN decoder for logical error rate suppression. However, our work confirms the applicability of ANN decoding methods of syndrome data retrieved from experimental devices and establishes machine learning as a promising pathway for quantum error correction when quantum devices with below threshold error rates become available in the near future. Published by the American Physical Society 2024

Dynamic updated key distribution encryption scheme with the wireless rate of 102 Gb/s based on a syncretic W band-PON transmission system.

In this paper, a dynamic updated key distribution encryption scheme based on syncretic W band-passive optical network (PON) is proposed. The 102 Gb/s encrypted data rate using 64QAM is successfully transmitted over the 50 m wireless distance under 15% soft-decision forward error correction (SD-FEC) for a pre-FEC bit error rate (BER) threshold of 1.56 × 10-2. The scheme can realize an error-free public key transmission and public key updates up to 1014 times. In the encryption transmission system, there is a small deviation of the private key, and the received BER is more than 0.45. As far as we know, this is the first time to complete a dynamic key distribution based on a syncretic W band-PON system.

Secure high-density constellation mapping OTFS modulation scheme with low PAPR

In this paper, a secure orthogonal time-frequency space (OTFS) modulation transmission system based on 3D dense constellation mapping (DCM) geometric shaping is proposed, and a selective reduction amplitude algorithm (SRA) for DCM to reduce peak average power ratio (PAPR) is presented. The DCM is based on regular tetrahedron construction to improve its space utilization efficiency. The proposed SRA involves reducing high PAPRs transmitter and restoring them at the receiving end, which only requires an additional 0.57% of the total transmission capacity. The algorithm reduces PAPR while ensuring the bit error rate performance of the system, so it is suitable for systems that need to process large amounts of transmitted data quickly. By verifying the actual transmission performance on a 2 km of 7-core optical fiber transmission system, the optical transmission with a bit rate of 33.93Gb/s is achieved. The experimental results show that when the bit error rate (BER) reaches the 3.8×10−3 threshold, the OTFS system using DCM and SRA could improve the receiver sensitivity by 3.7 dB compared with the OTFS system using concentric cube mapping and SRA, and 2.7 dB compared with the OFDM system using DCM. After adding the SRA, the PAPR of the OTFS system is reduced by more than 2.2 dB. When the received optical power reaches near the bit error rate threshold, the SRA valid data can be fully recovered by optimizing the SRA.

Neural-network-based carrier-less amplitude phase modulated signal generation and end-to-end optimization for fiber-terahertz integrated communication system.

In fiber-terahertz integrated communication systems, nonlinear distortion and inter-symbol interference (ISI) will degrade transmission performance. Pre-compensation is an efficient method to handle the channel distortion as it can avoid noise boosting during channel compensation and reduce receiver side signal processing algorithmic complexity at user-end (UE) considering the asymmetric access scenario. In this paper, we propose and experimentally demonstrate a neural-network (NN)-based carrier-less amplitude phase (CAP) modulated signal generation and end-to-end optimization method for a fiber-terahertz integrated communication system. The CAP signal is generated directly from quadrature amplitude modulation symbols and pre-compensated through a transmitter NN, which allows the receiver to demodulate the signal with simple linear digital signal process (DSP). In generating the CAP signal, the NN based transmitter learns a group of filters, which can generate, up-convert, and pre-compensate the signals. Based on the proposed method, a fiber-terahertz integration access system at 220 GHz is demonstrated and a sensitivity gain of 1.2 dB is achieved at a transmission speed of 50 Gbps and the forward error correction (FEC) bit error rate (BER) threshold of 1 × 10-2 compared with the baseline after 10-km fiber transmission and 1-m wireless delivering.

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.

Coherent errors and readout errors in the surface code

We consider the combined effect of readout errors and coherent errors, i.e., deterministic phase rotations, on the surface code. We use a recently developed numerical approach, via a mapping of the physical qubits to Majorana fermions. We show how to use this approach in the presence of readout errors, treated on the phenomenological level: perfect projective measurements with potentially incorrectly recorded outcomes, and multiple repeated measurement rounds. We find a threshold for this combination of errors, with an error rate close to the threshold of the corresponding incoherent error channel (random Pauli-Z and readout errors). The value of the threshold error rate, using the worst case fidelity as the measure of logical errors, is 2.6%. Below the threshold, scaling up the code leads to the rapid loss of coherence in the logical-level errors, but error rates that are greater than those of the corresponding incoherent error channel. We also vary the coherent and readout error rates independently, and find that the surface code is more sensitive to coherent errors than to readout errors. Our work extends the recent results on coherent errors with perfect readout to the experimentally more realistic situation where readout errors also occur.

Partial response THP for high-speed PAM-4 transmission

Intensity-modulation direct-detection (IM/DD) pulse-amplitude modulation (PAM-4) signals are promising for high-speed data center networks. However, high-speed PAM-4 signals always are subject to critical impairments due to the bandwidth constraint. In the conventional PAM-4 system, a direct detection-faster than Nyquist (DD-FTN) with high complexity is usually appended to the feed-forward equalizer (FFE) for colored noise suppression to maximize transmission performance. In order to yield a simple PAM-4 scheme with similar performance as that of the DD-FTN, we proposed a nonlinear differential coding-generalized Tomlinson-Harashima Precoding (NLDC-GTHP) PAM-4 system. The proposed system consists of a NLDC-GTHP at the transmitter and a simplified two-dimensional constellation distortion (S2DCD) module at the receiver. We experimentally demonstrated the proposed NLDC-GTHP PAM-4 system for 62.5-Gb/s PAM-4 signal transmission over 2-km standard single mode fiber (SSMF) with the 10-dB bandwidth of about 12 GHz. By introducing the NLDC-GTHP and S2DCD, we achieved the similar receiver sensitivity as that of the DD-FTN at the hard-decision forward-error-correction (HD-FEC) bit error rate (BER) threshold, with the decrease of 86% computational complexity.

A Decision Feedback Equalization Algorithm Based on Simplified Volterra Structure for PAM4 IM-DD Optical Communication Systems

A novel simplifying Volterra structure algorithm is proposed for an intensity modulation direct detection (IM-DD) optical fiber short distance communication system using the decision feedback equalization algorithm (DFE). Based on this algorithm, the signal damage for the four-level pulse amplitude modulation signal (PAM-4) is compensated, which is caused by device bandwidth limitation and dispersion during transmission. Experiments have been carried out using a 25 GHz Electro-absorption Modulated Laser (EML), showing that PAM-4 signals can transmit over 10 km in standard single-mode fiber (SSMF). The 112 Gbps and 128 Gbps signals can reach the error rate threshold of KP4-FEC (BER = 2 × 10−4) and HD-FEC (BER = 3.8 × 10−3), respectively. The simplified principle and process of the proposed Volterra-based equalization algorithm are presented. Experimental results show that the algorithm complexity is greatly reduced by 75%, which provides effective theoretical support for the commercial application of this algorithm.

Bi-Directional Free-Space Visible Light Communication Supporting Multiple Moveable Clients Using Light Diffusing Optical Fiber.

In this work, we put forward and demonstrate a bi-direction free-space visible light communication (VLC) system supporting multiple moveable receivers (Rxs) using a light-diffusing optical fiber (LDOF). The downlink (DL) signal is launched from a head-end or central office (CO) far away to the LDOF at the client side via a free-space transmission. When the DL signal is launched to the LDOF, which acts as an optical antenna to re-transmit the DL signal to different moveable Rxs. The uplink (UL) signal is sent via the LDOF towards the CO. In a proof-of-concept demonstration, the LDOF is 100 cm long, and the free space VLC transmission between the CO and the LDOF is 100 cm. 210 Mbit/s DL and 850 Mbit/s UL transmissions meet the pre-forward-error-correction bit error rate (pre-FEC BER = 3.8 × 10-3) threshold.

Design and analysis of factorial clinical trials: The impact of one treatment's effectiveness on the statistical power and required sample size of the other.

Factorial trials allow for the simultaneous evaluation of more than one treatment, by randomizing patients to their possible combinations, including control. However, the statistical power of one treatment can be influenced by the effectiveness of the other, a matter that has not been widely recognized. In this paper, we evaluate the relationship between the observed effectiveness of one treatment and the implied power for a second treatment in the same trial, under a range of conditions. We provide analytic and numerical solutions for a binary outcome, under the additive, multiplicative, and odds ratio scales for treatment interaction. We demonstrate how the minimum required sample size for a trial depends on the two treatment effects. Relevant factors include the event rate in the control group, sample size, treatment effect sizes, and Type-I error rate thresholds. We show that that power for one treatment decreases as a function of the observed effectiveness of the other treatment if there is no multiplicative interaction. A similar pattern is observed with the odds ratio scale at low control rates, but at high control rates, power may increase if the first treatment is moderately more effective than its planned value. When treatments do not interact additively, power may either increase or decrease, depending on the control event rate. We also determine where the maximum power occurs for the second treatment. We illustrate these ideas with data from two actual factorial trials. These results can benefit investigators in planning the analysis of factorial clinical trials, in particular, to alert them to the potential for losses in power when one observed treatment effect differs from its originally postulated value. Updating the power calculation and modifying the associated required sample size can then ensure sufficient power for both treatments.

Experimental demonstration of real-time optical DFT-S DMT signal transmission for a blue-LED-based UWOC system using spatial diversity reception.

Underwater wireless optical communication (UWOC) has broad prospects in underwater real-time applications. We design and experimentally demonstrate a real-time discrete Fourier transform spread discrete multi-tone (DFT-S DMT) signal transmission based on a field programmable gate array for a blue-LED-based UWOC system with a data rate of up to 30Mbps over a 15-m underwater channel. The architecture and usage of an on-chip resource as well as power consumption are analyzed and discussed. To reduce the impacts of multipath fading and received intensity fluctuation, spatial diversity reception is also introduced. Furthermore, the receiver sensitivity at a specified bit error rate (BER) threshold and the quality of the images are evaluated using three types of Reed-Solomon (RS) codes. At the BER threshold of 10-4, over 2.8-dB receiver sensitivity improvement is obtained by the DFT-S DMT scheme with the RS (64, 56) code as compared to the uncoded one at the data rate of 30 Mbps. The performance of BER, color difference, and structural similarity in the image transmission of DFT-S DMT is superior to that of the conventional hard clipping quadrature amplitude modulation DMT in a high-data-rate region because of the low peak-to-average-power ratio and ability to mitigate high-frequency fading in a band-limited UWOC system. With schemes of the RS code, DFT-S, and diversity reception, error-free transmission of images is achieved over a 15-m water channel. The proposed UWOC system has the advantages of low power consumption and portability, which foresees a bright future in underwater applications over short to moderate distances.

Net 400-Gbps/λ IMDD transmission using a single-DAC DSP-free transmitter and a thin-film lithium niobate MZM.

The insatiable growth of datacenter traffic mandates increasing the capacity of cost-effective intensity modulation direct detection (IMDD) systems to meet the foreseen demand. This Letter demonstrates the first, to the best of our knowledge, single-digital-to-analog converter (DAC) IMDD system achieving a net 400-Gbps transmission using a thin-film lithium niobate (TFLN) Mach-Zehnder modulator (MZM). Employing a driver-less DAC channel (128 GSa/s, 800 mVpp) with neither pulse-shaping nor pre-emphasis filtering, we transmit (1) 128-Gbaud PAM16 below the 25% overhead soft-decision forward error correction (SD-FEC) bit error rate (BER) threshold and (2) 128-Gbaud probabilistically shaped (PS)-PAM16 under the 20% overhead SD-FEC threshold, which respectively correspond to record net rates of 410 and 400 Gbps for single-DAC operation. Our results highlight the promise of operating 400-Gbps IMDD links with reduced digital signal processing (DSP) complexity and driving swing requirements.

Imperceptible Flicker Noise Reduction Using Pseudo-Flicker Weight Functionalized Derivative Equalization in Light-Fidelity Transmission Link.

A new technique to reduce flicker noise generated in light-fidelity (Li-Fi) transmission links based on the white light-emitting diode (LED) is proposed. Here, flicker noise with a frequency of 120 Hz, which is twice the frequency of AC power (60 Hz), is generated. The proposed technique is implemented in the receiver of the Li-Fi link. It can reduce flicker noise regardless of various digital modulation formats. In addition, there is no need to change the structure of the electrical circuit driving the LED to reduce the flicker noise. As a result, the non-return to-zero-on-off-keying (NRZ-OOK) signal waveform is tilted according to the flicker noise waveform. We implement the derivative equalization with a pseudo-flicker weight function to reduce the flicker noise. The derivative value of the NRZ-OOK signal mixed with flicker noise becomes larger than that without the flicker noise. In the proposed technique, the derivative value between adjacent sampling points is suppressed below the preset thresholds when it is greater than the preset threshold. Furthermore, a pseudo-flicker weight function is applied to accelerate the flicker noise reduction. As a result, using the proposed technique, a 2 dB signal-to-noise ratio (SNR) gain is obtained based on the bit error rate (BER) threshold (3.5 × 10-5) corresponding to 10% flicker modulation, which is known to have no serious effect on human health. This means that it is possible to implement a Li-Fi transmission link based on an illumination environment with a flicker modulation reduced from 10% to 7%.

Simultaneous optical access transmission of sparse local sampled discrete multitone and on-off keying signal using L1-minimization and adaptive subtractive differential equalization

We propose a new technique of simultaneously transmitting non–return–to–zero on–off–keying (NRZ–OOK) signal and discrete multitone (DMT) encoded by 16–quadrature amplitude modulation (QAM) signal within the same bandwidth in order to increase the transmission capacity of the optical access link. It is implemented by sequentially applying two techniques. The first proposed sparse local sampling technique compresses the length of the signal, which is mixed with the NRZ–OOK signal and the DMT signal, so that more data can be transmitted per unit time. The compressed mixed signal is recovered using the L1–minimization technique based on compressive sensing. The second proposed adaptive subtractive differential equalization (ASDE) technique recovers the NRZ–OOK signal by attenuating the portion corresponding to the DMT signal in the mixed signal after the mixed signal is transmitted. Thereafter, it recovers the DMT signal by subtracting the recovered NRZ–OOK signal from the mixed signal. A 20–km optical access link is implemented to verify the proposed technique. It is found that the mixed signal can be transmitted by reducing its length by 32 % using the sparse local sampling at the bit error rate (BER) threshold (8 × 10−5) of the 1st generic forward error correction (GFEC, RS(255,239)). In case of NRZ–OOK signal, input signal to noise ratio (SNR) gain of 14 dB is observed using two techniques at the same time. Also, input DMT signal with the SNR of greater than 35 dB can be transmitted. As a result, the transmission rate of 11.824 Gb/s (NRZ–OOK: 1 Gb/s + 0.32 Gb/s = 1.32 Gb/s, 16–QAM: 7.9576 Gb/s + 2.5464 Gb/s = 10.504 Gb/s) is achieved within 2–GHz bandwidth when the empty space is filled with other signals after sparse local sampling. These results indicate that the transmission capacity can be increased 5.912 times compared to the physical bandwidth of 2 GHz.

Complex-valued decision feedback equalizer for optical IMDD signals with adaptive manipulations in time and amplitude domains.

In this work, we innovatively equalize optical intensity-modulated and directly detected (IMDD) four-level pulse amplitude modulation (PAM-4) signals using a complex-valued decision feedback equalizer (CDFE). Through mapping adjacent symbols of PAM-4 signals onto the complex domain, the influence of strongest inter-symbol interference (ISI) can be alleviated during the decision process in a decision feedback equalizer (DFE), effectively combating burst-error propagation when signals are noisy. Moreover, signal-adaptive manipulations of DFE parameters in both the time and the amplitude domain are performed by using an ultra-stable timing recovery and level-adaptive decision. Performance evaluations are made on vertical cavity surface emitting laser (VCSEL) modulated and multimode fiber (MMF) transmitted 100-Gbit/s optical PAM-4 signals. Based on experimental results of the short-reach optical communication, the proposed DFE outperforms the traditional DFE with a 0.5-dB system power budget gain at the 7% overhead (OH) forward error correction (FEC) bit error rate (BER) threshold.