Overhead Hard-decision Forward Error Correction Research Articles

High Spectral Efficiency Long-Wave Infrared Free-Space Optical Transmission With Multilevel Signals

This study explores the potential of long-wave infrared free-space optical (FSO) transmission that leverages multilevel signals to attain high spectral efficiency. The FSO transmission system consists of a directly modulated-quantum cascade laser (DM-QCL) operating at 9.15 μm and a mercury cadmium telluride (MCT) detector. To fully understand the system, we conduct measurements on the DM-QCL chip and MCT detector and assess the overall amplitude response of the DM-QCL, MCT detector, and all electrical components. We apply various signals, including on-off keying (OOK), 4-level pulse amplitude modulation (PAM4), 6-level PAM (PAM6), and 8-level PAM (PAM8) to maximize the bit rate and spectral efficiency of the FSO transmission. Through a two-dimensional sweeping of the laser bias current and MCT detector photovoltage, we optimize the transmission performance. At the optimal operation point, the FSO system achieved impressive results which are up to 6 Gbaud OOK, 3.5 Gbaud PAM4, 3 Gbaud PAM6, and 2.7 Gbaud PAM8 signal transmissions, with a bit error rate performance below 6.25% overhead hard decision-forward error correction limit when the DM-QCL operates at 10°C. We also evaluate the eye diagrams and stability of the system to showcase its remarkable transmission performance. Our findings suggest that the DM-QCL and MCT detector-based FSO transceivers offer a highly competitive solution for the next generation of optical wireless communication systems.

Long-Wave Infrared Discrete Multitone Free-Space Transmission Using a 9.15-μm Quantum Cascade Laser

A free-space optical (FSO) transmission system is experimentally demonstrated in the long-wave infrared (LWIR, 9.15 μm) using a directly modulated quantum cascade laser (DM-QCL) and a commercial mercury-cadmium-telluride infrared photovoltaic detector. At room temperature, the DM-QCL is current-modulated by discrete multitone signals pre-processed with bit-/power-loading. Up to 5.1 Gbit/s data rate is achieved with bit error rate performance below the 6.25% overhead hard-decision forward error correction limit of 4.5 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> , enabled by a frequency domain equalizer. The stability study of the FSO system is also performed at multiple temperature values. This study can provide a valuable reference for future terrestrial and space communications.

Optical amplification-free deep reservoir computing-assisted high-baudrate short-reach communication.

An optical amplification-free deep reservoir computing (RC)-assisted high-baudrate intensity modulation direct detection (IM/DD) system is experimentally demonstrated using a 100G externally modulated laser operated in C-band. We transmit 112 Gbaud 4-level pulse amplitude modulation (PAM4) and 100 Gbaud 6-level PAM (PAM6) signals over a 200-m single-mode fiber (SMF) link without any optical amplification. The decision feedback equalizer (DFE), shallow RC, and deep RC are adopted in the IM/DD system to mitigate impairment and improve transmission performance. Both PAM transmissions over a 200-m SMF with bit error rate (BER) performance below 6.25% overhead hard-decision forward error correction (HD-FEC) threshold are achieved. In addition, the BER of the PAM4 signal is below the KP4-FEC limit after 200-m SMF transmission enabled by the RC schemes. Thanks to the use of a multiple-layer structure, the number of weights in deep RC has been reduced by approximately 50% compared with the shallow RC, whereas the performance is comparable. We believe that the optical amplification-free deep RC-assisted high-baudrate link has a promising application in intra-data center communications.

Master–slave carrier phase recovery using optical phase conjugation for frequency comb-based long-haul coherent communication systems

Taking optical frequency combs as WDM laser sources for coherent optical communication systems has great potential in low-cost, low-complexity, and large-capacity communications. Master–slave carrier phase recovery (MS-CPR) utilizes the phase coherence of received signals to reduce the computational complexity (CC) in frequency comb-based communication systems. In long-haul systems, chromatic dispersion (CD) weakens the phase coherence and makes MS-CPR ineffective. Besides, nonlinear effects greatly degrade the quality of received signals. A master–slave carrier phase recovery method using optical phase conjugation (OPC) is proposed for frequency comb-based long-haul coherent optical communication systems. By placing the OPC module in the middle of the link, not only the weakening of phase coherence caused by CD is solved, but also nonlinear effects are mitigated. The simulation results show that the proposed method has better performance than conventional MS-CPR and independent carrier phase recovery (ICPR). In the 1000 km long system with 16 quadrature amplitude modulation (QAM) signals, the BER of proposed method is 9.3% of conventional MS-CPR and even 40% lower than ICPR, and the BER of all channels is below the threshold for 7% overhead hard-decision forward error correction (7% HD-FEC).

Optical Amplification-Free High Baudrate Links for Intra-Data Center Communications

The enormous traffic growth sets a stringent requirement to upgrade short-reach optical links to 1.6 TbE capacity in an economically viable way. The power consumption and latency in these links should be as low as possible, especially for high-speed computing. This is possible to achieve using high baudrate on-off keying links thanks to a better noise tolerance and a relaxed requirement on linearity for electronics and photonics. In this regard, we demonstrate a 200 Gbaud on-off keying link without any optical amplification using an externally modulated laser with 3.3 dBm of modulated output power operating at 1541.25 nm wavelength. We achieve transmission over 200 meters of single-mode fiber with performance below 6.25% overhead hard-decision forward error correction threshold for each baudrate and all selection of modulation formats. We also show 108 Gbaud on-off keying link with superior performance without decision feedback equalizer up to 400 meters of single-mode fiber. In addition, we benchmark the short-reach optical link with 112 Gbaud four-level pulse amplitude modulation and 100 Gbaud six-level pulse amplitude modulation. For 108 Gbaud on-off keying and 112 Gbaud four-level pulse amplitude modulation, we can achieve an even lower bit error rate.

High bitrate data transmission in the 8-14 µm atmospheric window using an external Stark-effect modulator with digital equalization.

High bitrate mid-infrared links using simple (NRZ) and multi-level (PAM-4) data coding schemes have been realized in the 8 µm to 14 µm atmospheric transparency window. The free space optics system is composed of unipolar quantum optoelectronic devices, namely a continuous wave quantum cascade laser, an external Stark-effect modulator and a quantum cascade detector, all operating at room-temperature. Pre- and post-processing are implemented to get enhanced bitrates, especially for PAM-4 where inter-symbol interference and noise are particularly detrimental to symbol demodulation. By exploiting these equalization procedures, our system, with a full frequency cutoff of 2 GHz, has reached transmission bitrates of 12 Gbit/s NRZ and 11 Gbit/s PAM-4 fulfilling the 6.25 % overhead hard-decision forward error correction threshold, limited only by the low signal-to-noise ratio of our detector.

Design, analysis, and characterization of a compact silicon photonic modulator with meandered phase shifters.

We present a C-band Mach-Zehnder modulator with meandered phase shifters and a compact footprint of 432 × 260 μm2 on the silicon-on-insulator platform. Electrode, p-n junction, and optical transit time are considered when performing the electro-optic bandwidth (EO BW) simulations. The simulation results prove that the dominant bandwidth limiting factor for this type of modulator is optical transit time. The insertion loss of the modulator without bias is 2.1 dB. The measured half-wave voltage (V π ) and 3-dB EO BW at -0.5 V bias are 6.4 V and 7.7 GHz, respectively. 53 Gbaud PAM-4 transmission over 2 km of standard single-mode fiber is achieved at a bit error rate (BER) below the 6.7% overhead hard-decision forward error correction BER threshold of 3.8×10 -3.

Optical Multipath Interference Mitigation for High-Speed PAM4 IMDD Transmission System

Multipath interference (MPI) noise suppression is crucial for high-speed 4-level pulse amplitude modulation (PAM4) intensity modulation direct detection (IMDD) transmission systems. In this paper, two algorithms are proposed to eliminate the MPI noise, and these algorithms can be realized in the receiver digital signal processing (DSP) module without changing the existing IMDD system architecture. The first algorithm (A1) suppresses the MPI noise by removing the fluctuation of MPI-impaired PAM4 signals. The second algorithm (A2) can estimate the MPI noise which is intensity-dependent, and then the estimated MPI noise is subtracted from the impaired signal. The complexity of the proposed algorithms is lower than that of the traditional high-pass filter (HPF) scheme. Simulation results indicate that the proposed schemes can effectively suppress the MPI noise and improve the transmission performance under different signal-interference ratios (SIR), different laser linewidth, and random optical delay of the reflected signal. Besides, the cascade of A1 and A2 can further improve the transmission performance, and it has a higher tolerance for laser linewidth compared to the traditional HPF scheme. With the help of the proposed scheme, 56 Gb/s PAM4 signals are experimentally transmitted over 15.5 km standard single-mode fiber under the SIR of 18 dB and the laser linewidth of 100 kHz, and the measured bit error rate (BER) can be below the 7% overhead hard-decision forward error correction limit. When the laser linewidth is increased to 4 MHz, the traditional HPF scheme becomes less effective and may degrade the transmission performance, but the proposed schemes are still effective and the SIR tolerance can be improved by about 3 dB. 100 Gb/s PAM4 under optical back-to-back transmission with 24 dB SIR can be achieved, and the BER performance can be increased from 4.63e-3 to 2.06e-3 with the help of the proposed schemes.

Experimental demonstration of secure 100 Gb/s IMDD transmission over a 50 km SSMF using a quantum noise stream cipher and optical coarse-to-fine modulation.

In this paper, we experimentally demonstrate a secure 100 Gb/s 214-level intensity modulation and direct detection transmission over a 50 km standard single-mode fiber (SSMF) using a quantum noise stream cipher (QNSC) technique and 8-bit digital to analog converters. Optical coarse-to-fine modulation (CTFM) has been proposed to simultaneously enhance the security and overcome the weakness of low modulation depth in the traditional CTFM scheme. The optical power instead of the radio-frequency signal power is adjusted to satisfy the required peak-to-peak relation for CTFM, and thus the coarse and fine modulation has the same modulation depth. Two optical CTFM schemes based on an optical coupler and a polarizing beam combiner (PBC) are proposed and their pros and cons are analyzed and compared. Considering the trade-off of transmission performance and security performance, the optical CTFM scheme based on PBC is preferred in our experiment. 214-level pulse amplitude modulation (PAM) is achieved using two dual-drive Mach-Zehnder modulators (DD-MZM). Simultaneously, each DD-MZM is also used to achieve single-sideband (SSB) modulation to eliminate the power fading induced by fiber dispersion. By these means, 100 Gb/s 214-level PAM-QNSC signal transmission over 50 km SSMF with the bit error rate below the 7% overhead hard-decision forward error correction threshold of 3.8×10-3 is achieved. The results validate that the proposed scheme is effective to realize low-cost, high-speed, and highly secure optical transmission in the data center.

Experimental Demonstration of 600 Gb/s Net Rate PAM4 Transmissions over 2 km and 10 km with a 4-λ CWDM TOSA

We propose to introduce a controlled amount of inter-symbol interference (ISI) during pulse shaping in a high symbol rate intensity modulation direct detection (IM/DD) system to increase the alternating current (AC) power of the received electrical signal after photo-detection and transimpedance amplification. We experimentally demonstrate high-speed 4-level pulse amplitude modulation (PAM4) transmissions with a 4-λ coarse wavelength division multiplexing (CWDM) transmitter optical sub-assembly (TOSA) using the proposed scheme. The intentionally introduced ISI is mitigated using either transmitter-side Tomlinson Harashima precoding (THP) or receiver-side feed forward equalization (FFE) aided with a 2-tap post filter and maximum likelihood sequence estimation (MLSE). Both methods enable 4 × 81 Gbaud PAM4 transmission over 2 km of single mode fiber (SMF), with a bit error rate (BER) below the 7% overhead hard-decision forward error correction (HD-FEC) threshold of 3.8 × 10−3, which corresponds to a net rate of >600 Gb/s. We also explore the limit of our system at 10 km. The result shows that an aggregated net rate of 600 Gb/s excluding the HD-FEC overhead can still be achieved by loading different symbol rates onto different wavelength channels.

180 Gb/s PAM8 Signal Transmission in Bandwidth-Limited IMDD System Enabled by Tap Coefficient Decision Directed Volterra Equalizer

In this paper, we have explored the feasibility of 8-level pulse amplitude modulation (PAM8) format for realizing beyond 100 Gb/s transmission in a bandwidth-limited intensity modulation and direct-detection (IMDD) system. Generally, Volterra equalizer is a practical algorithm which can be used in bandwidth-limited system to combat the linear and nonlinear impairments. However, we observe that the performance of Volterra equalizer would be restricted by a phenomenon of level-dependent equalized effect, especially in low optical signal-to-noise ratio case. To cope with this problem, a tap coefficient decision directed Volterra equalizer (TDD-Volterra) with multiple sets of tap coefficients is proposed. The optimal set of tap coefficients is selected according to the decision results of input symbols before equalization. By this means, the TDD-Volterra is effective for overcoming the level-dependent equalized effect. By using the proposed TDD-Volterra, 180 Gb/s PAM8 signal is successfully transmitted over 2 km standard single mode fiber in an IMDD system with the 10-dB bandwidth of 17.5 GHz for the first time. The achieved bit error rate (BER) value is below the 7% overhead hard-decision forward error correction threshold of $3.8\times 10 ^{-3}$ . Moreover, the performance comparison among decision-directed least-mean square equalizer, Volterra Equalizer, and TDD-Volterra are analyzed in this paper. The experimental results show that compared to the conventional Volterra equalizer, the algorithm complexity of TDD-Volterra is decreased by over 50% for achieving a given BER value. Our research may provide a solution for beyond 100 Gb/s short-reach applications using bandwidth-limited electro-optical components.

Secure 100 Gb/s IMDD Transmission Over 100 km SSMF Enabled by Quantum Noise Stream Cipher and Sparse RLS-Volterra Equalizer

In this paper, we have experimentally demonstrated a secure 100 Gb/s intensity-modulation and direct-detection transmission over 100 km standard single-mode fiber (SSMF) based on quantum noise stream cipher (QNSC) for the first time. The original 4-level pulse-amplitude modulation (PAM4) data is mapped to M-level data sequence randomly, and quantum noise such as the generated amplified spontaneous emission noise and the shot noise in the channel can mask these adjacent signal levels. The legitimate receiver needs to distinguish not M-level encrypted data but 4-level data with the shared key. In our scheme, a calculated detection failure probability of 98.72% is achieved. Apparently, more quantum noise contributes to higher security but the worse signal to noise ratio. To balance algorithm complexity, transmission performance and security performance, a sparse $\ell _{1} $ regularization based on recursive least square (RLS) algorithm is proposed and firstly used in Volterra equalizer. To eliminate the power fading induced by fiber dispersion, a dual-drive Mach-Zehnder modulator is used to achieve single-sideband modulation, and no dispersion compensation is required. By these means, 100 Gb/s PAM4-QNSC signal transmission over 100 km SSMF with the bit error rate (BER) below the 7% overhead hard-decision forward error correction threshold of $3.8 \times 10^{-3}$ is achieved, and > 59% complexity reduction of Volterra equalizer is realized. Moreover, the measured BER of 150 Gb/s PAM8-QNSC signal transmission over 50 km SSMF could go below the 20% overhead soft-decision forward error correction threshold of $2.0\times 10^{-2}$ . The results validate that the proposed scheme is effective to realize low-cost, high-speed (> 100 Gb/s), and secure optical fiber transmission in the data center.

DSP-Free and Real-Time NRZ Transmission of 50 Gb/s Over 15-km SSMF and 64 Gb/s Back-to-Back With a 1.3-μm VCSEL

We demonstrate and analyze 50 Gb/s non-return-to-zero (NRZ) transmission over 15 km of standard single-mode fiber (SSMF), 60-Gb/s NRZ transmission over 5 km of SSMF and up to 64-Gb/s NRZ back-to-back using a directly modulated short-cavity long-wavelength single-mode vertical-cavity surface-emitting laser (VCSEL) emitting at 1326 nm. Owing to an analog 6-tap transmit feedforward equalizer, the link can operate without digital signal processing. In all three cases, real-time bit error ratio measurements below the 7% overhead hard-decision forward error correction threshold are demonstrated when transmitting a pseudo-random bit sequence with a period of $2^7-1$ bits. In addition, we analyze the interplay between the residual fiber chromatic dispersion at the operating wavelength of the VCSEL and the chirp due to direct modulation. These results demonstrate how O-band, short-cavity long-wavelength single-mode VCSELs can be used in intradata center networks, as well as in interdata center networks at reaches below 15 km.

High-Speed PAM4-Based Optical SDM Interconnects With Directly Modulated Long-Wavelength VCSEL

This paper reports the demonstration of high-speed PAM-4 transmission using a 1.5-{\mu}m single-mode vertical cavity surface emitting laser (SM-VCSEL) over multicore fiber with 7 cores over different distances. We have successfully generated up to 70 Gbaud 4-level pulse amplitude modulation (PAM-4) signals with a VCSEL in optical back-to-back, and transmitted 50 Gbaud PAM-4 signals over both 1-km dispersion-uncompensated and 10-km dispersion-compensated in each core, enabling a total data throughput of 700 Gbps over the 7-core fiber. Moreover, 56 Gbaud PAM-4 over 1-km has also been shown, whereby unfortunately not all cores provide the required 3.8 $\times$ 10 $^{-3}$ bit error rate (BER) for the 7% overhead-hard decision forward error correction (7% OH HDFEC). The limited bandwidth of the VCSEL and the adverse chromatic dispersion of the fiber are suppressed with pre-equalization based on accurate end-to-end channel characterizations. With a digital post-equalization, BER performance below the 7% OH-HDFEC limit is achieved over all cores. The demonstrated results show a great potential to realize high-capacity and compact short-reach optical interconnects for data centers.

Negative Frequency-Chirped 112-Gb/s PAM-4 Using an Integrated Germanium Franz-Keldysh Modulator

Integrated germanium-on-silicon Franz–Keldysh modulators (Ge-EAMs) offer a small footprint and low-energy-per-bit performance for high-speed data communications. In this letter, we study the use of Ge-EAMs for four-level pulse amplitude modulation (PAM-4), and report on the linearity of the modulator in terms of its spurious-free dynamic range. The experimental results show that the negative frequency chirp from the modulator can improve the transmission distance of the PAM-4 signal. Using pre-equalization with a 25-GHz bandwidth-limited arbitrary waveform generator, we obtained a data rate of 112 Gb/s with a bit-error-rate of $2.5\times 10^{-3}$ under the 7% overhead hard-decision forward error correction threshold. We observed an extended transmission distance in our 112-Gb/s PAM-4 experiment on a standard single-mode fiber thanks to the negative frequency chirp of the modulator.

Nonlinearity Tolerant High-Speed DMT Transmission With 1.5-&lt;italic&gt;μ&lt;/italic&gt;m Single-Mode VCSEL and Multi-Core Fibers for Optical Interconnects

We experimentally demonstrate the generation of 107-Gbit/s net-rate optical discrete multitone signal using a 1.5- μ m single-mode vertical cavity surface emitting laser (VCSEL) with modulation bandwidth of 22 GHz. Utilizing a nonlinearity-tolerant channel equalization algorithm for digital signal processing, total net-rates of 726.6-Gbit/s over 2.5-km dispersion-uncompensated 7-core fiber and 533.1-Gbit/s over 10-km dispersion-compensated 7-core fiber below 7% overhead hard-decision forward error correction limit have been experimentally achieved with a 1.5- μ m VCSEL-based intensity-modulation direct-detection system. The features of the 1.5- μ m single-mode VCSEL, 2.5-km/10-km multi-core fibers, and fan-in/fan-out modules are presented. Besides, the Volterra series-based nonlinearity-tolerant channel equalization algorithm, which improves the signal-to-noise ratio with more than 5 dB, is mathematically described and experimentally validated. The results have demonstrated that 1.5- μ m single-mode VCSEL and multi-core-fiber-based transmission can be a promising candidate to solve the capacity challenges in short-reach optical interconnects.

Pulse-Overlapping Super-Nyquist WDM System

In this paper, a pulse-overlapping super-Nyquist (Pol-SN) wavelength-division multiplexing (WDM) scheme is proposed to improve spectral efficiency of coherent optical transmission. In this scheme, two tributaries of polarization-division multiplexing quadrature phase-shift keying (PDM-QPSK) signals at the transmitter, carried by the same wavelength, are grouped together to allow for pulse overlapping in the time domain. Then, several wavelength channels are packed tightly in the frequency domain to form a super-Nyquist WDM system. At the receiver, three partial-response detection schemes are investigated and compared: (1) constant modulus algorithm (CMA) + duobinary shaping + maximum likelihood sequence estimation (MLSE); (2) duobinary shaping + multimodulus algorithm (MMA) + MLSE; and (3) channel shortening filter. Among these schemes, the easy-to-implement duobinary shaping +MMA + MLSE is selected by virtue of its best performance and lowest complexity. A 224-Gb/s Pol-SN PDM-QPSK system is investigated through numerical simulations. The simulation results show that the channel spacing of the 224 Gb/s Pol-SN PDM-QPSK system can be reduced to 20 GHz (11.2 bit/s/Hz SE) with 7% overhead hard-decision forward-error correction (HD-FEC, 3.8 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> ). At 26-GHz channel spacing, Pol-SN PDM-QPSK signals show 5.5-dB OSNR improvement, as compared with the signals of 224-Gb/s super-Nyquist PDM-16QAM. The simulation results also show that 224-Gb/s Pol-SN PDM-QPSK system, with 20-GHz spacing, can transmit up to 1000-km SSMF with 7% overhead HD-FEC.

High-Speed DMT and VCSEL-Based MMF Transmission Using Pre-Distortion

We present high-speed single-channel discrete multitone (DMT) operations of directly modulated 850-nm vertical-cavity surface-emitting lasers (VCSEL). Successful transmission of 135 Gb/s over 10 m of OM4 multi-mode fiber (MMF) and 114 Gb/s over 550 m is demonstrated below the 7 % overhead hard-decision forward error correction (FEC) bit error rate (BER) limit. At higher BER limits, i.e. 20 % overhead soft-decision FEC, which are of arising interest for these high-speed short-range links, data rates of up to 161 Gb/s are presented. This is enabled by high-bandwidth low-noise VCSEL, which operate in quasi-single mode to overcome the mode dispersion limitations of the MMF. The applied modulation format is DMT in combination with a Volterra-filter-based pre-distortion approach, which pre-compensates the linear and nonlinear behavior of the transmission system, primarily the digital-analog converter, the VCSEL, the MMF, and the photoreceiver. Furthermore, a detailed investigation of the pre-distortion is given by experimental means, showing that the optimum amount of pre-distortion depends on the applied components and the signal bandwidth. This makes it challenging to predict the optimum; however, a pure electrical pre-distortion offers already a fair gain in performance.

Calibrated Link Budget of a Silicon Photonics WDM Transceiver with SOA and Semiconductor Mode-Locked Laser

Based on the single channel characterization of a Silicon Photonics (SiP) transceiver with Semiconductor Optical Amplifier (SOA) and semiconductor Mode-Locked Laser (MLL), we evaluate the optical power budget of a corresponding Wavelength Division Multiplexed (WDM) link in which penalties associated to multi-channel operation and the management of polarization diversity are introduced. In particular, channel cross-talk as well as Cross Gain Modulation (XGM) and Four Wave Mixing (FWM) inside the SOA are taken into account. Based on these link budget models, the technology is expected to support up to 12 multiplexed channels without channel pre-emphasis or equalization. Forward Error Correction (FEC) does not appear to be required at 14 Gbps if the SOA is maintained at 25 °C and MLL-to-SiP as well as SiP-to-SOA interface losses can be maintained below 3 dB. In semi-cooled operation with an SOA temperature below 55 °C, multi-channel operation is expected to be compatible with standard 802.3bj Reed-Solomon FEC at 14 Gbps provided interface losses are maintained below 4.5 dB. With these interface losses and some improvements to the Transmitter (Tx) and Receiver (Rx) electronics, 25 Gbps multi-channel operation is expected to be compatible with 7% overhead hard decision FEC.

Direct Modulation of a Laser Using 112-Gb/s 16-QAM Nyquist Subcarrier Modulation

A 112-Gb/s single-carrier, single-polarization short reach transmission system using a high bandwidth 1310 nm directly modulated laser is demonstrated. Spectrally efficient signal generation is achieved by using: 1) half-cycle Nyquist subcarrier modulation with 16-ary quadrature-amplitude-modulation; 2) pre-compensation for the frequency response of the end-to-end system; and 3) and a Volterra nonlinear equalizer to post-compensate for the nonlinear modulation dynamics of the laser. Digital signal processing techniques for signal recovery enable transmission over 20 km of standard single mode fiber with a bit error ratio below the 7% overhead hard-decision forward error correction coding threshold of $4.6\times 10^{-3}$ at a received optical power of −5.25 dBm.