Forward Error Correction Overhead Research Articles

Complex-valued recurrent neural network equalizer with low complexity for a 120-Gbps 50-km optical PAM-4 IM/DD system

This paper introduces a novel complex-valued recurrent neural networks equalizer (RNNE) designed for a 120-Gbps, 50-km optical 4-level pulse-amplitude modulation (PAM-4) intensity modulation and direct detection (IM/DD) system. By mapping adjacent symbols of PAM-4 signals onto the complex domain, the correlation between two adjacent symbols of PAM-4 signals can be preserved. Based on experimental results, the proposed complex-valued RNNE outperforms the traditional real-valued RNNE with a 1.38-dB system power budget gain at the 7% overhead forward error correction BER threshold of 3.8 × 10−3. We believe that complex-valued RNNE has an advantage over real-valued RNNE in processing real-valued signals in IM/DD systems.

Segmented Silicon Modulator With a Bandwidth Beyond 67 GHz for High-Speed Signaling

We demonstrate an all-silicon segmented modulator with traveling-wave electrodes, achieving an electro-optic bandwidth beyond 67 GHz and a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$V_\pi$</tex-math></inline-formula> of 5V. We show that dividing a long optical modulator into shorter segments can help achieve a higher bandwidth without compromising modulation efficiency or optical loss. We analyze the bandwidth limitation due to the delay mismatch between the driving and optical signals. We show that the impact of misalignment of driving delays between segments on the overall bandwidth of the modulator can be described by a finite impulse response filter. Using this modulator, we achieve optical transmission of 120 Gbaud 8-level amplitude shift keying with coherent detection. Taking into account the forward error correction overhead, this yields 336.4 Gb/s net on a single polarization. Our design has the potential for achieving 1 Tb/s using dual-polarization IQ modulation.

Statistical Analysis of 100 Gbps per Wavelength SWDM VCSEL-MMF Data Center Links on a Large Set of OM3 and OM4 Fibers

We present a detailed statistical study on achievable reach of 100 Gbps data center optical links based on vertical cavity surface emitting lasers (VCSEL) and multimode fibers (MMF). Based on the characterization of the spectral and spatial properties of eight lasers and of the modal and dispersion behavior of a large set of 20233 OM3 and OM4 modeled fibers (obtained by properly extending an initial set of 500 measured fibers), we compute the resulting frequency responses of all of the VCSEL-MMF combinations. Then, we feed them to a numerical tool modeling PAM-4 transmission at 100 Gbps net bit rate per wavelength. Our model analyzes performance at distances up to 400 meters, using three different adaptive equalizers at the receiver and considering two forward error correction overheads. We show that 100 Gbps operation is feasible for 99% of the simulated links reaching up to 120 m over OM4 at 850 nm and using a decision feedback equalizer (DFE). Aggregated data rates of 200 Gbps and 400 Gbps per fiber using Shortwave Wavelength Division Multiplexing (SWDM) are achievable for 99% of the links reaching 80 m over OM4 using two wavelengths and feed-forward equalizer (FFE) and four wavelengths and maximum likelihood sequence estimation (MLSE)-based equalizer, respectively.

Power Efficient Communications Employing Phase Sensitive Pre-Amplified Receiver

The receiver sensitivity is a very important metric in optical communication links operating at low received signal powers. Phase sensitive optical amplifiers (PSAs) can amplify optical signals without excess noise, thus providing a fundamental sensitivity improvement of 3 dB when employed as a pre-amplifier compared to conventional erbium doped fiber amplifiers (EDFA). In this letter, we investigate, both theoretically and experimentally, the sensitivities achieved using power efficient multi-dimensional modulation formats such as M-ary pulse position modulation format (M-PPM) and M-PPM combined with quadrature phase shift keying (QPSK) along with a near-noiseless PSA pre-amplified coherent intradyne receiver. We find that at high signal to noise ratios (SNRs) corresponding to low bit-error-rates (BER), M-PPM+QPSK results in the best sensitivity, which is improved with the order M, while at low SNRs corresponding to high BER (~14% where 100% overhead forward error correction codes (FEC) would be needed to recover the data), QPSK is the most sensitive format, while at the same time providing the best spectral efficiency. We report experimental sensitivities of 2.1 photons per information bit (PPB) at a pre-FEC BER = 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup> using 64-PPM+QPSK and assuming 7% FEC, and 0.8 PPB at a pre-FEC BER = 0.14 using QPSK and assuming 100% FEC.

A 100 Gbaud On-off-Keying Silicon-Polymer Hybrid Modulator Operating at up to 110°C

We demonstrate 100-Gbaud on-off-keying (OOK) transmission driven at a low voltage using an electro-optic (EO) polymer modulator combined with a silicon Mach-Zehnder interferometer waveguide. Various types of organic- and polymer-based modulators have been reported to perform efficient EO modulation and high-speed data transmission at over 100 Gbaud. However, there are critical concerns regarding the practical application of polymer devices in terms of environmental stability. In particular, long-term thermal storage and stability during operation require improvements before EO polymer modulators can be applied in practical systems. We have developed an EO polymer with enhanced thermophysical stability and used it to fabricate an efficient EO polymer modulator. In this study we extend our earlier work on high-speed EO polymer modulators by performing fiber-link 100-Gbaud OOK transmission at various operating temperatures. A thermal stability test revealed that the EO polymer modulator can survive high-temperature exposure up to 110°C. Error-free signal transmissions over a distance of 2.0 km was successfully demonstrated with a driving voltage of 1.9 V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">pp</sub> and a bit error rate below the 7% overhead forward error correction threshold. The driving voltage, bandwidth, bit error rate, and fiber-link performance of the device are presented.

Beyond 200-Gb/s/λ DMT Signal Transmission With NGMI Optimization and Volterra Equalization

The band-limited and power fading effects are two main limitations to intensity-modulation direct-detection (IM-DD) transmission systems due to the low-cost transceivers and interactions from fiber dispersion. Entropy loading (EL) has the ability to squeeze out the last bit by continuous adjustment of entropy. However, it is a passively process to adapt to the channel response. Moreover, the normalized generalized mutual information (NGMI) target based EL may be overestimated because the practical binary forward error correction (FEC) codes have a gap to the theoretic limit, which may result in unsatisfied transmission capacity or post-FEC performance. To optimize the NGMI, we analyze the NGMI upper and lower boundaries defined by the achievable information rate (AIR) and FEC overhead (OH). We propose to use the AIR as target and optimize the NGMI with the FEC OH as constraint. We conduct an experiment to target the beyond 200-Gb/s discrete multi-tone signal transmission over 2-km or 10-km single mode fiber using a 32-GHz electro-absorption modulated laser (EML). However, we find that the channel response and generalized mutual information (GMI) cannot support the target AIR even with NGMI optimization. We propose a joint EL and second-order Volterra filter (VF) to alleviate the power fading effects and maximize the transmission capacity. To achieve the AIR target and use below 20% SD-FEC, we find the optimized NGMI is 0.92 to simultaneously meet the 2-km and 10-km transmission requirement. We successfully transmit beyond 200-Gb/s DMT signal over 2-km or 10-km single mode fiber with BER below 2.6 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−2</sup> in the EML-based direct-detection system.

Independent and mixed transmission of 166.5 Gb/s PM‐8QAM and 222 Gb/s PM‐16QAM Nyquist‐wavelength division multiplexed superchannel for long‐haul metro network

SummaryThis paper investigates the Nyquist‐wavelength division multiplexed (Nyquist‐WDM) terabit superchannel by employing independent and mixed line rate (MLR) transmission of different polarization‐multiplexed quadrature amplitude modulation (PM‐QAM) subcarriers. Here, terabit superchannel transmission including forward error correction overhead is successfully achieved by employing either 7 × 166.5 Gb/s PM‐8QAM or 5 × 222 Gb/s PM‐16QAM or both 2 × 166.5 Gb/s PM‐8QAM and 3 × 222 Gb/s PM‐16QAM simultaneous transmission. Considering linear filtering penalties and nonlinear propagation effects, the proposed superchannel is transmitted over standard single‐mode fiber (SSMF) and pure silica core fiber (PSCF) along with erbium‐doped fiber amplifier (EDFA) at 19.8‐ and 15.12‐dB span loss for SSMF and PSCF, respectively. The performance of both terabit superchannels is analyzed in terms of maximum reach, good spectral efficiency, highest transmission capacity, and optimum launch power with variation in channel spacing from 50‐GHz fixed ITU‐T grid to 29 GHz, at an acceptable bit error rate (BER). To achieve BER 4 × 10−3, MLR‐based 166.5 Gb/s PM‐8QAM and 222 Gb/s PM‐16QAM suffer a penalty of 5.5‐ and 9.2‐dB OSNR over Nyquist‐only 7 × 166.5 Gb/s PM‐8QAM and 5 × 222 Gb/s PM‐16QAM transmission at the advent of a flexible multi‐flow transponder. It is observed that at 33.33‐GHz Nyquist spacing over PSCF, 5 × 222 Gb/s PM‐16QAM and 7 × 166.5 Gb/s PM‐8QAM superchannels deliver a reach up to 1800 and 2970 km, while MLR approach results in extreme reach of 2250 and 3600 km over PSCF as per MLR PM‐16QAM and PM‐8QAM subcarriers, respectively. Hence, an appreciable spectral efficiency–distance product (SEDP) is achieved due to PSCF at Nyquist spacing of 33.33 GHz with 5.25 bit/s/Hz spectral efficiency. A good link power budget is also calculated for the proposed MLR‐based Nyquist‐WDM superchannel. MLR‐based PM‐16QAM and PM‐8QAM subcarriers deliver excellent SEDP of 11,812 and 18,900 bit/s/Hz·km, respectively, which is, to the best of author's knowledge, better on comparing with the other existing literature for single‐core channel explorations.

Soft-Demapping for Short Reach Optical Communication: A Comparison of Deep Neural Networks and Volterra Series

In optical fiber communication, optical and electrical components introduce nonlinearities, which require effective compensation to attain highest data rates. In particular, in short reach communication, components are the dominant source of nonlinearities. Volterra series are a popular countermeasure for receiver-side equalization of nonlinear component impairments and their memory effects. However, Volterra equalizer architectures are generally very complex. This article investigates soft deep neural network (DNN) architectures as an alternative for nonlinear equalization and soft-decision demapping. On coherent 92GBd dual polarization 64QAM back-to-back measurements performance and complexity is experimentally evaluated. The proposed bit-wise soft DNN equalizer (SDNNE) is compared to a 5th order Volterra equalizer at a 15% overhead forward error correction (FEC) limit. At equal performance, the computational complexity is reduced by 65%. At equal complexity, the performance is improved by 0.35 dB gain in optical signal-to-noise-ratio (OSNR).

On the performance of all-optical OFDM based PM-QPSK and PM-16QAM

A polarization multiplexed all-optical orthogonal frequency division multiplexing (AO-OFDM) system is investigated analytically and numerically, with 12.5 Gbaud symbol rate, that is compatible with the International Telecommunication Union flexible grid. We demonstrate that fast adaptive filtering is not require at the receiver and chromatic dispersion with polarization mode dispersion can be compensated without the cyclic prefix insertion, with the maximum spectral efficiency by using proper optical filter. System performance are numerically and analytically evaluated considering nonlinear effects and power consumption, evidencing a good agreement between the theoretical model and numerical results. We compare AO-OFDM performance with coherent OFDM scheme using the derived theoretical formula and numerical results. 21 subcarriers are investigated with quadrature phase shift keying modulation and 7 subcarriers in case of 16-quadrature amplitude modulation, with a total capacity of 976.5 Gb/s and 651 Gb/s, respectively, considering 7% forward error correction overhead.

Mach-Zehnder Silicon Photonic Modulator Assisted by Phase-Shifted Bragg Gratings

We experimentally demonstrate a silicon photonic Mach-Zehnder modulator (MZM) assisted by phase-shifted Bragg gratings. Coupled resonators are inserted in the Bragg grating structure to significantly enhance the phase modulation efficiency, while maintaining a wide optical bandwidth compared to other resonator-based modulators. Fabricated using a CMOS-compatible foundry process, the device achieved a small-signal V π × L of 0.18 V.cm, which is seven times lower than a conventional silicon MZM fabricated with the same process. The device has a compact footprint, with a length of only 162 μm, and shows a modulation bandwidth of 28 GHz at a reverse bias of 1 V. Non-return-to-zero modulation is demonstrated at 30 Gb/s with a bit-error-rate (BER) below the 7%-overhead forward error correction (FEC) threshold over a bandwidth of 3.5 nm. This bandwidth should translate into an operating temperature range greater than 40 °C.

Ultrahigh-speed Nyquist pulse transmission beyond 10 Tbit/s

This paper presents recent progress toward the realization of ultrahigh-speed optical time-division multiplexed transmission with a single-channel bit rate of more than 10 Tbit/s using a Nyquist pulse. We first describe non-coherent Nyquist pulse transmission with differential quadrature phase-shift keying (DQPSK). We present a single-channel 10.2 Tbit/s, DQPSK-300 km transmission, where the highest symbol rate of 2.56 Tbaud was demonstrated with an ultrashort Nyquist pulse train and an ultrafast demultiplexer using a nonlinear optical loop mirror. We then present a recent demonstration of a 1.28 Tbit/s/ch × 10 channel (total 12.8 Tbit/s) DQPSK transmission, where the transmission distance was successfully extended to 1500 km by employing a wavelength division multiplexing scheme and reducing the symbol rate to 320 Gbaud while retaining a total transmission capacity of more than 10 Tbit/s. Next, we describe coherent Nyquist pulse transmission with quadrature amplitude modulation (QAM). We present a single-channel polarization-multiplexed 1.28 Tbaud, 64 QAM-150 km transmission, where the highest transmission speed of 15.3 Tbit/s was achieved with a homodyne detection scheme using an optically phase-locked LO Nyquist pulse. Furthermore, we present recent results related to BER performance improvement in a 15.3 Tbit/s coherent Nyquist pulse transmission by newly constructing a low-nonlinearity, dispersion-compensated transmission line using a chirped fiber Bragg grating and a liquid crystal on silicon device. As a result, the required forward-error correction overhead was successfully reduced from 25.5% to 20%, and the spectral efficiency reached as high as 8.7 bit/s/Hz.

System Optimization of an All-Silicon IQ Modulator: Achieving 100-Gbaud Dual-Polarization 32QAM

We experimentally demonstrate the highest, to the best of our knowledge, reported net rate in a SiP IQ modulator. At 100 Gbaud 32QAM (quadrature amplitude modulation), and assuming 20% FEC (forward error correction) overhead, we achieved a dual polarization net rate of 833 Gb/s. This record was achieved by adapting digital signal processing to the challenging pattern dependent distortion encountered in the nonlinear and bandwidth limited regime. First the Mach Zehnder modulator (MZM) operating point (trading off modulation efficiency and 3 dB bandwidth) and linear compensation (electrical and optical) are jointly optimized. Next, the key application of nonlinear pre- and post-compensation are explored. We show that nonlinear processing at the transmitter, in our case an iterative learning control (ILC) method, is essential as post-processing alone could not achieve reliable communications at 100 Gbaud. Nonlinear post-compensation algorithms pushed the performance under the FEC threshold with the introduction of structured intersymbol interference in post processing and a simple one-step maximum likelihood sequence detector. We provide detailed descriptions of our methodology and results.

Suppression of large error floor in 1024 QAM digital coherent transmission by compensating for GAWBS phase noise.

There is a large error floor in an ultra multi-level digital coherent transmission signal of 1024 QAM or higher, and we have yet to determine its origin. In this paper, we show that this large error floor results from guided acoustic-wave Brillouin scattering (GAWBS) phase noise. We prove experimentally that such an error floor can be greatly reduced by compensating for the GAWBS noise with a phase modulation technique. We show that the BER of a 1024 QAM signal was reduced from 8.7 × 10-4 to 2.7 × 10-4 after a 160 km transmission with GAWBS noise compensation. Furthermore, we successfully extend the transmission distance from 160 to 240 km with a 7% overhead forward error correction.

200 G Outdoor Free-Space-Optics Link Using a Single-Photodiode Receiver

We experimentally evaluate the performance of Kramers–Kronig (KK) receivers for free-space optical transmission. We transmit a dual-carrier signal, each carrier modulated as a 25 Gbaud 16/32 quadrature-amplitude modulation (QAM) signal. This dual-carrier signal, with overall symbol rate of 50 Gbaud, is detected in a single receiver with about 35 GHz bandwidth. Key parameters such as the carrier-to-signal power ratio, the frequency allocation of the pilot tone, and the frequency separation between both modulated carriers are optimized. In addition, we also study the effect of the receiver bandwidth limitations on the KK technique. We perform long-term measurements, beyond one hour, for both 16 and 32 QAM signals in a 55 m outdoor free-space link during daylight with sunny weather conditions. Our measurements demonstrate that the link operates below the BER threshold assuming 20% forward-error correction (FEC) for the 32QAM signal and 7% FEC overhead for the 16QAM signal. The resulting net data rates are 208 and 184 Gbit/s for the 32 and 16 QAM signals, respectively.

Mitigation for turbulence effects in a 40-Gbit/s orbital-angular-momentum-multiplexed free-space optical link between a ground station and a retro-reflecting UAV using MIMO equalization.

We experimentally demonstrate turbulence effect mitigation in a 100-m round-trip orbital-angular-momentum (OAM)-multiplexed free-space optical communication link between a ground transmitter and a ground receiver via a retro-reflecting hovering unmanned aerial vehicle (UAV) using multiple-input-multiple-output (MIMO) equalization. In our demonstration, two OAM beams at 1550nm are transmitted to the UAV through emulated atmospheric turbulence, each carrying a 20-Gbit/s signal. 2×2 MIMO equalization is used to mitigate turbulence-induced crosstalk between the two OAM channels. Bit error rates below the 7% overhead forward error correction limit of 3.8×10-3 are achieved for both channels.

Single-carrier 72 GBaud 32QAM and 84 GBaud 16QAM transmission using a SiP IQ modulator with joint digital-optical pre-compensation.

We establish experimentally the suitability of an all-silicon optical modulator to support future ultra-high-capacity coherent optical transmission links beyond 400 Gb/s. We present single-carrier data transmission from 400 Gb/s to 600 Gb/s using an all-silicon IQ modulator produced with a generic foundry process. The operating point of the silicon photonic transmitter is carefully optimized to find the best efficiency bandwidth trade-off. We present a methodology to split pre-compensation between digital and optical stages. For the 400 Gb/s transmission, we achieved 60 Gbaud dual-polarization (DP)-16QAM, reaching a distance of 1,520 km. Transmission of 500 Gb/s was further tested using 75 Gbaud 16QAM and 60 Gbaud 32QAM, reaching 1,120 km and 480 km, respectively. We finally demonstrated 72 Gbaud DP-32QAM (720 Gb/s) transmitted over 160 km and 84 Gbaud DP-16QAM (672 Gb/s) transmitted over 720 km, meeting the threshold for 20% forward error correction overhead and achieving net rates of 600 Gb/s and 576 Gb/s, respectively. To the best of our knowledge, these are the highest baud-rate coherent transmission results achieved using an all-silicon IQ modulator. We have demonstrated that we can reap the myriad advantages of SiP integration for transmission at extreme bit rates.

Homodyne coherent optical receiver for intersatellite communication.

For increasing the data rate and reducing the power consumption in satellite communication systems, free-space optical communication technology has been verified as an attractive alternative to traditional radiofrequency communication systems. In this study, a high-sensitivity homodyne coherent optical receiver was demonstrated. A sensitivity of -59.2 dBm was achieved with an unencoded bit-error rate below 10-3 at a bit rate of 1Gbps (9.4photons/bit does not include any overhead for forward error correction). To achieve homodyne detection, a modified decision-driven Costas optical phase-locked loop and a digital control algorithm were used to suppress the phase error and track the Doppler shift. Test experiments show that the receiver sensitivity penalty caused by the phase error is approximately 1dB and that the receiver can track a Doppler shift at the speed of 100MHz/s. Test experiments demonstrate that the receiver has a robust adaptive capacity to received-power fluctuation. The theoretical analysis and experimental results are presented in this paper.

Frequency Comb Generation Using a CMOS Compatible SiP DD-MZM for Flexible Networks

On-chip frequency comb generation is a promising solution for seeding a chip-scale optical transmitter for both Nyquist wavelength-division multiplexing (WDM) and orthogonal frequency-division multiplexing. We demonstrate flexible frequency comb generation using a silicon photonic dual-drive Mach–Zehnder modulator fabricated on a CMOS-compatible process. Our on-chip comb has five lines spaced at 20 GHz with a high tone-to-noise ratio of about 40 dB after one stage optical amplification. Our back-to-back transmission achieves bit error rates (BERs) well below 2e-2, the threshold for 20% overhead forward error correction (FEC), for 800 Gb/s using 16-GBd 32QAM on five WDM channels. We also test a seamless 800-Gb/s super-channel using $5\times 20$ GBd 16QAM, with BER below the 7% overhead FEC threshold of 3.8e-3. To the best of our knowledge, this is the first demonstration of high-spectral-efficiency data carried by an all-silicon optical frequency comb. This establishes that a silicon optical frequency comb has sufficient optical signal-to-noise ratio for high-order QAM, as well as excellent stability for super-channels without guard bands, paving the way to an integrated high-spectral-efficiency multi-carrier optical transmitter.

40 km amplifier-less transmission of single wavelength 90 Gbps four-level pulse amplitude modulation signals enabled by an ultrabroadband directly modulated laser.

An ultrabroadband, high linearity directly modulated laser (DML) module operated at the O-band is proposed. The effect of the package network on the DML module is first investigated. In the package network, a wire bonding compensation method is used to improve the resonance at high frequency, which can be equivalent to the channel equalization technique. Without any optical amplification, we experimentally demonstrated 90Gb/s four-level pulse amplitude modulation transmission over 40km standard single mode fiber, which is the longest reach to the best of our knowledge. A bit error rate of 6.74×10-4 is achieved at a received optical power of -2.5 dBm. A receiver sensitivity of -4.5 dBm at 7% overhead forward error correction limit (3.8×10-3) is obtained for back-to-back with a power margin of more than 8.5dB.

High Spectral Efficiency PM-128QAM Comb-Based Superchannel Transmission Enabled by a Single Shared Optical Pilot Tone

We exploit the coherence of frequency combs for high spectral efficiency superchannel transmission via effective sharing of a single pilot tone. By phase-locking the receiver comb to the transmitted pilot tone, carrier offsets are suppressed while both the overhead and complexity associated with the pilot tone are reduced. We form a 55 carrier superchannel using a 25-GHz spaced electro-optic frequency comb seeded by a 100-kHz linewidth laser. At a pilot tone overhead of $ 2%, the reduction in carrier offsets is shown to facilitate blind DSP-based carrier recovery of all 54 $\times$ 24 Gbaud PM-128QAM data channels. The resulting superchannel spectral efficiency is 10.3 bits/s/Hz assuming a 28% overhead for forward error correction. Our results show the potential for optical pilot tones to reduce both overhead and complexity in systems using comb-based superchannels together with high-order modulation formats.