On Parameter Optimization and Reach Enhancement for the Improved Soft-Aided Staircase Decoder

The so-called improved soft-aided bit-marking algorithm was recently proposed for staircase codes (SCCs) in the context of fiber optical communications. This algorithm is known as iSABM-SCC. With the help of channel soft information, the iSABM-SCC decoder marks bits via thresholds to deal with both miscorrections and failures of hard-decision (HD) decoding. In this paper, we study iSABM-SCC focusing on the parameter optimization of the algorithm and its performance analysis, in terms of the gap to the achievable information rates (AIRs) of HD codes and the fiber reach enhancement. We show in this paper that the marking thresholds and the number of modified component decodings heavily affect the performance of iSABM-SCC, and thus, they need to be carefully optimized. By replacing standard decoding with the optimized iSABM-SCC decoding, the gap to the AIRs of HD codes can be reduced to 0.26-1.02 dB for code rates of 0.74-0.87 in the additive white Gaussian noise channel with 8-ary pulse amplitude modulation. The obtained reach increase is up to 22% for data rates between 401 Gbps and 468 Gbps in an optical fiber channel.

Radar Sensing with OTFS: Embracing ISI and ICI to Surpass the Ambiguity Barrier

Orthogonal time frequency space (OTFS) is a promising alternative to orthogonal frequency division multiplexing (OFDM) in high-mobility beyond 5G communications. In this paper, we consider the problem of radar sensing with OTFS joint radar-communications waveform and derive a novel OTFS radar signal model by explicitly taking into account the intersymbol interference (ISI) and inter-carrier interference (ICI) effects. On the basis of the new model, we show how ISI and ICI phenomena can be turned into an advantage to surpass the maximum unambiguous detection limits in range and velocity, arising in existing OFDM and OTFS radar systems. Moreover, we design a generalized likelihood ratio test based detector/estimator that can embrace ISI and ICI effects. Simulation results illustrate the potential of embracing ISI/ICI and demonstrate its superior detection and estimation performance over conventional baselines.

A Soft-Aided Staircase Decoder Using Three-Level Channel Reliabilities

The soft-aided bit-marking (SABM) algorithm is based on the idea of marking bits as highly reliable bits (HRBs), highly unreliable bits (HUBs), and uncertain bits to improve the performance of hard-decision (HD) decoders. The HRBs and HUBs are used to assist the HD decoders to prevent miscorrections and to decode those originally uncorrectable cases via bit flipping (BF), respectively. In this paper, an improved SABM algorithm (called iSABM) is proposed for staircase codes (SCCs). Similar to the SABM, iSABM marks bits with the help of channel reliabilities, i.e., using the absolute values of the log-likelihood ratios. The improvements offered by iSABM include: (i) HUBs being classified using a reliability threshold, (ii) BF randomly selecting HUBs, and (iii) soft-aided decoding over multiple SCC blocks. The decoding complexity of iSABM is comparable of that of SABM. This is due to the fact that on the one hand no sorting is required (lower complexity) because of the use of a threshold for HUBs, while on the other hand multiple SCC blocks use soft information (higher complexity). Additional gains of up to 0.53 dB with respect to SABM and 0.91 dB with respect to standard SCC decoding at a bit error rate of $10^{-6}$ are reported. Furthermore, it is shown that using 1-bit reliability marking, i.e., only having HRBs and HUBs, only causes a gain penalty of up to 0.25 dB with a significantly reduced memory requirement.

Frequency Logarithmic Perturbation on the Group-Velocity Dispersion Parameter with Applications to Passive Optical Networks

Signal propagation in an optical fiber can be described by the nonlinear Schr\"odinger equation (NLSE). The NLSE has no known closed-form solution, mostly due to the interaction of dispersion and nonlinearities. In this paper, we present a novel closed-form approximate model for the nonlinear optical channel, with applications to passive optical networks. The proposed model is derived using logarithmic perturbation in the frequency domain on the group-velocity dispersion (GVD) parameter of the NLSE. The model can be seen as an improvement of the recently proposed regular perturbation (RP) on the GVD parameter. RP and logarithmic perturbation (LP) on the nonlinear coefficient have already been studied in the literature, and are hereby compared with RP on the GVD parameter and the proposed LP model. As an application of the model, we focus on passive optical networks. For a 20 km PON at 10 Gbaud, the proposed model improves upon LP on the nonlinear coefficient by 1.5 dB. For the same system, a detector based on the proposed LP model reduces the uncoded bit-error-rate by up to 5.4 times at the same input power or reduces the input power by 0.4 dB at the same information rate.

Temporal Energy Analysis of Symbol Sequences for Fiber Nonlinear Interference Modelling via Energy Dispersion Index

The stationary statistical properties of independent, identically distributed (i.i.d.) input symbols provide insights on the induced nonlinear interference (NLI) during fiber transmission. For example, kurtosis is known to predict the modulation format-dependent NLI. These statistical properties can be used in the design of probabilistic amplitude shaping (PAS), which is a popular scheme that relies on an amplitude shaper for increasing spectral efficiencies of fiber-optic systems. One property of certain shapers used in PAS -- including constant-composition distribution matchers -- that is often overlooked is that a time-dependency between amplitudes is introduced. This dependency results in symbols that are non-i.i.d., which have time-varying statistical properties. Somewhat surprisingly, the effective signal-to-noise ratio (SNR) in PAS has been shown to increase when the shaping blocklength decreases. This blocklength dependency of SNR has been attributed to time-varying statistical properties of the symbol sequences, in particular, to variation of the symbol energies. In this paper, we investigate the temporal energy behavior of symbol sequences, and introduce a new metric called energy dispersion index (EDI). EDI captures the time-varying statistical properties of symbol energies. Numerical results show strong correlations between EDI and effective SNR, with absolute correlation coefficients above 99% for different transmission distances.

Modeling of Nonlinear Interference Power for Dual-Polarization 4D Formats

We assess the accuracy of a recently introduced nonlinear interference model for general dual-polarization 4D formats.~ Unlike previous models for polarization-multiplexed 2D formats, an average gap from split-step Fourier simulations within 0.1 dB is demonstrated.

Model-Based Machine Learning for Joint Digital Backpropagation and PMD Compensation

In this paper, we propose a model-based machine-learning approach for dual-polarization systems by parameterizing the split-step Fourier method for the Manakov-PMD equation. The resulting method combines hardware-friendly time-domain nonlinearity mitigation via the recently proposed learned digital backpropagation (LDBP) with distributed compensation of polarization-mode dispersion (PMD). We refer to the resulting approach as LDBP-PMD. We train LDBP-PMD on multiple PMD realizations and show that it converges within 1% of its peak dB performance after 428 training iterations on average, yielding a peak effective signal-to-noise ratio of only 0.30 dB below the PMD-free case. Similar to state-of-the-art lumped PMD compensation algorithms in practical systems, our approach does not assume any knowledge about the particular PMD realization along the link, nor any knowledge about the total accumulated PMD. This is a significant improvement compared to prior work on distributed PMD compensation, where knowledge about the accumulated PMD is typically assumed. We also compare different parameterization choices in terms of performance, complexity, and convergence behavior. Lastly, we demonstrate that the learned models can be successfully retrained after an abrupt change of the PMD realization along the fiber.

End-to-End Learning of Geometrical Shaping Maximizing Generalized Mutual Information

GMI-based end-to-end learning is shown to be highly nonconvex. We apply gradient descent initialized with Gray-labeled APSK constellations directly to the constellation coordinates. State-of-the-art constellations in 2D and 4D are found providing reach increases up to 26\% w.r.t. to QAM.

Fiber Nonlinearity Mitigation via the Parzen Window Classifier for Dispersion Managed and Unmanaged Links

Machine learning techniques have recently received significant attention as promising approaches to deal with the optical channel impairments, and in particular, the nonlinear effects. In this work, a machine learning-based classification technique, known as the Parzen window (PW) classifier, is applied to mitigate the nonlinear effects in the optical channel. The PW classifier is used as a detector with improved nonlinear decision boundaries more adapted to the nonlinear fiber channel. Performance improvement is observed when applying the PW in the context of dispersion managed and dispersion unmanaged systems.