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Norbert Hanik

Publications and source records attributed to Norbert Hanik.

At least 19 recordsLinked to original sources
arXiv2025

Low-Cost Phase Precoding for Short-Reach Fiber Links with Direct Detection

Low-cost analog phase precoding is used to compensate chromatic dispersion (CD) in fibers with intensity modulation and direct detection (IM/DD). In contrast to conventional precoding with an in-phase and quadrature (IQ) Mach-Zehnder modulator (MZM), only a single additional phase modulator (PM) is required at the transmitter. Depending on the CD, the PM generates a periodic phase modulation that is modelled by a Fourier series and optimized via a mean squared error (MSE) cost criterion. Numerical results compare achievable information rates (AIRs) for 4- and 6-PAM. With the additional PM, energy gains of up to 3 dB are achieved for moderate fiber lengths.

eess.SP↗
arXiv2024

Neural Network Equalizers and Successive Interference Cancellation for Bandlimited Channels with a Nonlinearity

Neural networks (NNs) inspired by the forward-backward algorithm (FBA) are used as equalizers for bandlimited channels with a memoryless nonlinearity. The NN-equalizers are combined with successive interference cancellation (SIC) to approach the information rates of joint detection and decoding (JDD) with considerably less complexity than JDD and other existing equalizers. Simulations for short-haul optical fiber links with square-law detection illustrate the gains.

cs.IT↗
arXiv2024

Closed-Form Expressions for Nonlinearity Coefficients in Multimode Fibers

We derive novel approximate closed-form expressions for the nonlinear coupling coefficients appearing in the Manakov equations for multimode fibers for space-division multiplexing in the two regimes of strong and weak coupling. The expressions depend only on few fiber design parameters. In particular, the Manakov coefficients are shown to be simple rational numbers which depend solely on the number of guided modes. The overall nonlinearity coefficients are found to decrease with increasing core radius and to stay nearly constant with increasing refractive index difference between core and cladding. Validation is performed through a numerical approach. The consequences of the findings onto fiber design are discussed in terms of achievable data rates. The analysis is mainly focused on the trenchless parabolic graded-index profile, but considerations on the use of realistic trenches and non-parabolic indices, and on the step-index profile are given.

physics.optics↗
arXiv2024

Neural Network-Based Successive Interference Cancellation for Non-Linear Bandlimited Channels

Reliable communication over bandlimited and non-linear channels usually requires equalization to simplify receiver processing. Equalizers that perform joint detection and decoding (JDD) achieve the highest information rates but are often too complex to implement. To address this challenge, model-based neural network (NN) equalizers that perform successive interference cancellation (SIC) are shown to approach JDD information rates for bandlimited channels with a memoryless nonlinearity and additive white Gaussian noise. The NNs are chosen to have a periodically time-varying and recurrent structure that imitates the forward-backward algorithm (FBA) in every SIC stage. Simulations for short-haul fiber-optic links with square-law detection show that NN-SIC nearly doubles current spectral efficiencies, and bipolar or complex-valued modulations achieve energy gains of up to 3dB compared to state-of-the-art intensity modulation. Moreover, NN-SIC is considerably less complex than equalizers that perform JDD, mismatched FBA processing, and Gibbs sampling.

cs.IT↗
arXiv2022

Successive Interference Cancellation for Bandlimited Channels with Direct Detection

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.

cs.IT↗
arXiv2022

Phase Matching for Multimode Four-Wave Mixing in Few-Mode Fibers and Nano-Rib Waveguides

We compare phase matching for four-wave mixing using one, two, three, and four waveguide modes. For the comparison, we use numerical optimizations and an estimate of the generated idler power. We present results for few-mode fibers and nano-rib waveguides and show that for both waveguide types, four-wave mixing bandwidths and idler powers are best for one- and two-mode operation and that four-mode four-wave mixing is not feasible at all. Some nano-rib waveguides support three-mode four-wave mixing, albeit with much reduced bandwidth and reduced idler power.

physics.optics↗
arXiv2022

Experiments on Bipolar Transmission with Direct Detection

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.

cs.IT↗
arXiv2021

Achievable Rates for Short-Reach Fiber-Optic Channels with Direct Detection

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.

cs.IT↗
arXiv2020

Wiener Filter for Short-Reach Fiber-Optic Links

Analytic expressions are derived for the Wiener filter (WF), also known as the linear minimum mean square error (LMMSE) estimator, for an intensity-modulation/direct-detection (IM/DD) short-haul fiber-optic communication system. The link is purely dispersive and the nonlinear square-law detector (SLD) operates at the thermal noise limit. The achievable rates of geometrically shaped PAM constellations are substantially increased by taking the SLD into account as compared to a WF that ignores the SLD.

cs.IT↗
arXiv2017

Experimental Comparison of Probabilistic Shaping Methods for Unrepeated Fiber Transmission

This paper studies the impact of probabilistic shaping on effective signal-to-noise ratios (SNRs) and achievable information rates (AIRs) in a back-to-back configuration and in unrepeated nonlinear fiber transmissions. For back-to-back, various shaped quadrature amplitude modulation (QAM) distributions are found to have the same implementation penalty as uniform input. By demonstrating in transmission experiments that shaped QAM input leads to lower effective SNR than uniform input at a fixed average launch power, we experimentally confirm that shaping enhances the fiber nonlinearities. However, shaping is ultimately found to increase the AIR, which is the most relevant figure of merit as it is directly related to spectral efficiency. In a detailed study of these shaping gains for the nonlinear fiber channel, four strategies for optimizing QAM input distributions are evaluated and experimentally compared in wavelength division multiplexing (WDM) systems. The first shaping scheme generates a Maxwell-Boltzmann (MB) distribution based on a linear additive white Gaussian noise channel. The second strategy uses the Blahut-Arimoto algorithm to optimize an unconstrained QAM distribution for a split-step Fourier method based channel model. In the third and fourth approach, MB-shaped QAM and unconstrained QAM are optimized via the enhanced Gaussian noise (EGN) model. Although the absolute shaping gains are found to be relatively small, the relative improvements by EGN-optimized unconstrained distributions over linear AWGN optimized MB distributions are up to 59%. This general behavior is observed in 9-channel and fully loaded WDM experiments.

cs.IT↗
arXiv2016

On Probabilistic Shaping of Quadrature Amplitude Modulation for the Nonlinear Fiber Channel

Different aspects of probabilistic shaping for a multi-span optical communication system are studied. First, a numerical analysis of the additive white Gaussian noise (AWGN) channel investigates the effect of using a small number of input probability mass functions (PMFs) for a range of signal-to-noise ratios (SNRs), instead of optimizing the constellation shaping for each SNR. It is shown that if a small penalty of at most 0.1 dB SNR to the full shaping gain is acceptable, just two shaped PMFs are required per quadrature amplitude modulation (QAM) over a large SNR range. For a multi-span wavelength division multiplexing (WDM) optical fiber system with 64QAM input, it is shown that just one PMF is required to achieve large gains over uniform input for distances from 1,400 km to 3,000 km. Using recently developed theoretical models that extend the Gaussian noise (GN) model and full-field split-step simulations, we illustrate the ramifications of probabilistic shaping on the effective SNR after fiber propagation. Our results show that, for a fixed average optical launch power, a shaping gain is obtained for the noise contributions from fiber amplifiers and modulation-independent nonlinear interference (NLI), whereas shaping simultaneously causes a penalty as it leads to an increased NLI. However, this nonlinear shaping loss is found to have a relatively minor impact, and optimizing the shaped PMF with a modulation-dependent GN model confirms that the PMF found for AWGN is also a good choice for a multi-span fiber system.

cs.IT↗
arXiv2015

Impact of 4D channel distribution on the achievable rates in coherent optical communication experiments

We experimentally investigate mutual information and generalized mutual information for coherent optical transmission systems. The impact of the assumed channel distribution on the achievable rate is investigated for distributions in up to four dimensions. Single channel and wavelength division multiplexing (WDM) transmission over transmission links with and without inline dispersion compensation are studied. We show that for conventional WDM systems without inline dispersion compensation, a circularly symmetric complex Gaussian distribution is a good approximation of the channel. For other channels, such as with inline dispersion compensation, this is no longer true and gains in the achievable information rate are obtained by considering more sophisticated four-dimensional (4D) distributions. We also show that for nonlinear channels, gains in the achievable information rate can also be achieved by estimating the mean values of the received constellation in four dimensions. The highest gain for such channels is seen for a 4D correlated Gaussian distribution.

cs.IT↗
arXiv2015

Sensitivity Gains by Mismatched Probabilistic Shaping for Optical Communication Systems

Probabilistic shaping of quadrature amplitude modulation (QAM) is used to enhance the sensitivity of an optical communication system. Sensitivity gains of 0.43 dB and 0.8 dB are demonstrated in back-to-back experiments by shaping of 16QAM and 64QAM, respectively. Further, numerical simulations are used to prove the robustness of probabilistic shaping to a mismatch between the constellation used and the signal-to-noise ratio (SNR) of the channel. It is found that, accepting a 0.1 dB SNR penalty, only four shaping distributions are required to support these gains for 64QAM.

cs.IT↗
arXiv2015

On Achievable Rates for Long-Haul Fiber-Optic Communications

Lower bounds on mutual information (MI) of long-haul optical fiber systems for hard-decision and soft-decision decoding are studied. Ready-to-use expressions to calculate the MI are presented. Extensive numerical simulations are used to quantify how changes in the optical transmitter, receiver, and channel affect the achievable transmission rates of the system. Special emphasis is put to the use of different quadrature amplitude modulation formats, channel spacings, digital back-propagation schemes and probabilistic shaping. The advantages of using MI over the prevailing $Q$-factor as a figure of merit of coded optical systems are also highlighted.

cs.IT↗
arXiv2014

Mutual Information as a Figure of Merit for Optical Fiber Systems

Advanced channel decoders rely on soft-decision decoder inputs for which mutual information (MI) is the natural figure of merit. In this paper, we analyze an optical fiber system by evaluating MI as the maximum achievable rate of transmission of such a system. MI is estimated by means of histograms for which the correct bin number is determined in a blind way. The MI estimate obtained this way shows excellent accuracy in comparison with the true MI of 16-state quadrature amplitude modulation (QAM) over an additive white Gaussian noise channel with additional phase noise, which is a simplified model of a nonlinear optical fiber channel. We thereby justify to use the MI estimation method to accurately estimate the MI of an optical fiber system. In the second part of this work, a transoceanic fiber system with 6000 km of standard single-mode fiber is simulated and its MI determined. Among rectangular QAMs, 16-QAM is found to be the optimal modulation scheme for this link as to performance in terms of MI and requirements on components and digital signal processing. For the reported MI of 3.1 bits/symbol, a minimum coding overhead of 29% is required when the channel memory is not taken into account. By employing ideal single-channel digital back-propagation, an increase in MI by 0.25 bits/symbol and 0.28 bits/symbol is reported for 16-QAM and 64-QAM, respectively, lowering the required overhead to 19% and 16%. When the channel spacing is decreased to be close to the Nyquist rate, the dual-polarization spectral efficiency is 5.7 bits/s/Hz, an increase of more than 2 bits/symbol compared to a 50 GHz spacing.

cs.IT↗