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We show a beyond 200Gb/s VCSEL transmission experiment. Results are based on 35GHz VCSEL and advanced DSP. We show an AIR of 245Gb/s PAM-6 back-to-back, and 200Gb/s PAM-4 over 60m OM4 fiber assuming KP4-FEC.

Probabilistic constellation shaping has been used in long-haul optically amplified coherent systems for its capability to approach the Shannon limit and realize fine rate granularity. The availability of high-bandwidth optical-electronic components and the previously mentioned advantages have invigorated researchers to explore probabilistic shaping (PS) in intensity-modulation and direct-detection (IM/DD) systems. This article presents an extensive comparison of uniform 8-ary pulse amplitude modulation (PAM) with PS PAM-8 using cap and cup Maxwell-Boltzmann (MB) distributions as well as MB distributions of different Gaussian orders. We report that in the presence of linear equalization, PS-PAM-8 outperforms uniform PAM-8 in terms of bit error ratio, achievable information rate and operational net bit rate indicating that cap-shaped PS-PAM-8 shows high tolerance against nonlinearities. In this paper, we have focused our investigations on O-band electro-absorption modulated laser unamplified IM/DD systems, which are operated close to the zero dispersion wavelength., Comment: 9 pages, 12 figures

Neuromorphic computing implementing spiking neural networks (SNN) is a promising technology for reducing the footprint of optical transceivers, as required by the fast-paced growth of data center traffic. In this work, an SNN nonlinear demapper is designed and evaluated on a simulated intensity-modulation direct-detection link with chromatic dispersion. The SNN demapper is implemented in software and on the analog neuromorphic hardware system BrainScaleS-2 (BSS-2). For comparison, linear equalization (LE), Volterra nonlinear equalization (VNLE), and nonlinear demapping by an artificial neural network (ANN) implemented in software are considered. At a pre-forward error correction bit error rate of 2e-3, the software SNN outperforms LE by 1.5 dB, VNLE by 0.3 dB and the ANN by 0.5 dB. The hardware penalty of the SNN on BSS-2 is only 0.2 dB, i.e., also on hardware, the SNN performs better than all software implementations of the reference approaches. Hence, this work demonstrates that SNN demappers implemented on electrical analog hardware can realize powerful and accurate signal processing fulfilling the strict requirements of optical communications., Comment: 9 pages, 5 figures, accepted for publication by the IEEE/Optica Publishing Group Journal of Lightwave Technology

Concatenated forward error correction is studied using an outer KP4 Reed-Solomon code with hard-decision decoding and inner single parity check (SPC) codes with Chase/Wagner soft-decision decoding. Analytical expressions are derived for the end-to-end frame and bit error rates for transmission over additive white Gaussian noise channels with binary phase-shift keying (BPSK) and quaternary amplitude shift keying (4-ASK), as well as with symbol interleavers and quantized channel outputs. The BPSK error rates are compared to those of two other inner codes: a two-dimensional product code with SPC component codes and an extended Hamming code. Simulation results for unit-memory inter-symbol interference channels and 4-ASK are also presented. The results show that the coding schemes achieve similar error rates, but SPC codes have the lowest complexity and permit flexible rate adaptation., Comment: Submitted to IEEE Journal of Lightwave Technology on December 20, 2022; revised March 29, 2023; accepted April 5, 2023

The maximum information rates for bandlimited channels with direct detection are achieved with joint detection and decoding (JDD), but JDD is often too complex to implement. Two receiver structures are studied to reduce complexity: separate detection and decoding (SDD) and successive interference cancellation (SIC). For bipolar modulation, frequency-domain raised-cosine pulse shaping, and fiber-optic channels with chromatic dispersion, SIC achieves rates close to those of JDD, thereby attaining significant energy gains over SDD and intensity modulation. Gibbs sampling further reduces the detector complexity and achieves rates close to those of the forward-backward algorithm at low to intermediate signal-to-noise ratio (SNR) but stalls at high SNR. Simulations with polar codes, higher-order modulation, and multi-level coding confirm the predicted gains., Comment: Submitted to IEEE Journal of Lightwave Technology on December 15, 2022; Resubmitted to IEEE Transactions on Communications on September 9, 2023; accepted November 17, 2023

For 200Gb/s net rates, cap probabilistic shaped PAM-8 with different Gaussian orders are experimentally compared against uniform PAM-8. In back-to-back and 5km measurements, cap-shaped 85-GBd PAM-8 with Gaussian order of 5 outperforms 71-GBd uniform PAM-8 by up to 2.90dB and 3.80dB in receiver sensitivity, respectively., Comment: submitted to 2022 European Conference on Optical Communication (ECOC)

An entropy-regularized mean square error (MSE-X) cost function is proposed for nonlinear equalization of short-reach optical channels. For a coherent optical transmission experiment, MSE-X achieves the same bit error rate as the standard MSE cost function and a significantly higher achievable information rate.

A spiking neural network (SNN) non-linear equalizer model is implemented on the mixed-signal neuromorphic hardware system BrainScaleS-2 and evaluated for an IM/DD link. The BER 2e-3 is achieved with a hardware penalty less than 1 dB, outperforming numeric linear equalization.

For 200Gbit/s net rates, uniform PAM-4, 6 and 8 are experimentally compared against probabilistic shaped PAM-8 cap and cup variants. In back-to-back and 20km measurements, cap shaped 80GBd PAM-8 outperforms 72GBd PAM-8 and 83GBd PAM-6 by up to 3.50dB and 0.8dB in receiver sensitivity, respectively, Comment: Originally published in ECOC-2021. We have updated Figure 3. The change also affects the overall outcome. In contrast to the published version, compared to uniform PAM-8 72 GBd, PS-PAM-8 80 GBd performance is updated to 3.50 dB instead of 5.17 dB, while for PAM-6 83 GBd the gain becomes 0.8 dB instead of 2.17 dB. The changes are adapted in all sections except the experimental setup and DSP section

PAM-6 transmission is considered for short-reach fiber-optic links with intensity modulation and direct detection. Experiments show that probabilistically-shaped PAM-6 and a framed-cross QAM-32 constellation outperform conventional cross QAM-32 under a peak power constraint., Comment: submitted to European Conference on Optical Communication (ECOC) 2022

Achievable information rates of bipolar 4- and 8-ary constellations are experimentally compared to those of intensity modulation (IM) when using an oversampled direct detection receiver. The bipolar constellations gain up to 1.8 dB over their IM counterparts., Comment: submitted to ECOC 2022

A spiking neural network (SNN) equalizer model suitable for electronic neuromorphic hardware is designed for an IM/DD link. The SNN achieves the same bit-error-rate as an artificial neural network, outperforming linear equalization.

Spectrally efficient communication is studied for short-reach fiber-optic links with chromatic dispersion (CD) and receivers that employ direction-detection and oversampling. Achievable rates and symbol error probabilities are computed by using auxiliary channels that account for memory in the sampled symbol strings. Real-alphabet bipolar and complex-alphabet symmetric modulations are shown to achieve significant energy gains over classic intensity modulation. Moreover, frequency-domain raised-cosine (FD-RC) pulses outperform time-domain RC (TD-RC) pulses in terms of spectral efficiency for two scenarios. First, if one shares the spectrum with other users then inter-channel interference significantly reduces the TD-RC rates. Second, if there is a transmit filter to avoid interference then the detection complexity of FD-RC and TD-RC pulses is similar but FD-RC achieves higher rates., Comment: Submitted to J. Lightw. Technol. on November 15, 2021; revised January 7, 2022; accepted January 22, 2022

We report an industry leading optical dense wavelength division multiplexing (DWDM) field trial with line rates per channel exceeding 1.66 Tb/s using 130 GBaud dual-polarization probabilistic constellation shaping 256-ary quadrature amplitude modulation (DP-PCS256QAM) in a high capacity data center interconnect (DCI) scenario. This research trial was performed on 96.5 km of field-deployed standard single mode G.652 fiber infrastructure of Deutsche Telekom in Germany employing Erbium-doped fiber amplifier (EDFA)-only amplification. A total of 34 channels were transmitted with 150 GHz spacing for a total fiber capacity of 56.51 Tb/s and a spectral efficiency higher than 11bit/s/Hz. In the single-channel transmission scenario 1.71 Tb/s was achieved over the same link. In addition, we successfully demonstrate record net bitrates of 1.88 Tb/s in back-to-back (B2B) using 130 GBaud DP-PCS400QAM., Comment: This work has been submitted to the IEEE Photonics Technology Letters (PTL) for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible

Coded modulation with probabilistic amplitude shaping (PAS) is considered for intensity modulation/direct detection channels with a transmitter peak-power constraint. PAS is used to map bits to a uniform PAM-6 distribution and outperforms PAM-8 for rates up to around 2.3 bits per channel use. PAM-6 with PAS also outperforms a cross-shaped QAM-32 constellation by up to 1 dB and 0.65 dB after bit-metric soft- and hard decoding, respectively. An alternative PAM-6 scheme based on a framed cross-shaped QAM-32 constellation is proposed that shows similar gains., Comment: submitted to 11th International Symposium on Topics in Coding

We investigate approaches to reduce the computational complexity of Volterra nonlinear equalizers (VNLEs) for short-reach optical transmission systems using intensity modulation and direct detection (IM/DD). In this contribution we focus on a structural reduction of the number of kernels, i.e. we define rules to decide which terms need to be implemented and which can be neglected before the kernels are calculated. This static complexity reduction is to be distinguished from other approaches like pruning or L1 regularization, that are applied after the adaptation of the full Volterra equalizer e.g. by thresholding. We investigate the impact of the complexity reduction on 90 GBd PAM6 IM/DD experimental data acquired in a back-to-back setup as well as in case of transmission over 1 km SSMF. First, we show, that the third-order VNLE terms have a significant impact on the overall performance of the system and that a high number of coefficients is necessary for optimal performance. Afterwards, we show that restrictions, for example on the tap spacing among samples participating in the same kernel, can lead to an improved tradeoff between performance and complexity compared to a full third-order VNLE. We show an example, in which the number of third-order kernels is halved without any appreciable performance degradation.