Alex Alvarado

Felipe Villenas, Yunus Can Gültekin, Alex Alvarado

We consider optical communications with intensity modulation and direct detection affected by laser relative intensity noise (RIN). Starting from a continuous-time waveform model, we derive an equivalent discrete-time channel model. As a result of RIN, the resulting channel model exhibits signal-dependent noise with memory. Unlike the commonly-assumed model in the literature, the conditional variance of this noise term has a polynomial dependence on the symbol of interest. Finally, we study achievable information rates for this channel under practically-relevant system parameters. We take a mismatched decoding approach and compute the generalized mutual information (GMI) using a memoryless decoding metric. Our numerical results show that when the memory in the channel is ignored by the receiver, GMI saturates as the constellation size increases, and thus, dense constellations do not offer gains. We also show that this saturation results from nonsymmetric nonvanishing contributions of the symbols to the GMI.

Hernan Cordova, Alexios Balatsoukas-Stimming, Yunus Can Gültekin et al.

Min-Sum (MS) decoding is a popular low-complexity alternative to belief propagation (BP), retaining only the minimum incoming message magnitude during check-node (CN) processing, at the cost of systematic message magnitude overestimation. The scaled MS (SMS) decoder compensates for this effect using a fixed scaling factor. We propose the syndrome adaptive gain Min-Sum (SAGMS) decoder for quantum low-density parity-check (QLDPC) codes, which adapts the message gain online based on the fraction of unsatisfied stabilizers, requiring no per-code or per-noise level optimization. We show that the scaling factor required for SMS to match belief propagation decreases with the CN degree, so any fixed scaling optimized for one degree incurs into a growing penalty as the CN degree varies. SAGMS avoids this limitation by adapting the gain during decoding. Simulations on generalized bicycle QLDPC codes demonstrate that SAGMS matches or outperforms the frame error rate (FER) of an offline optimized SMS decoder. Moreover, SAGMS approaches BP performance and, under certain conditions outperforms it while retaining MS-level complexity.

Chin-Hung Chen, Ivana Nikoloska, Wim van Houtum et al.

This paper presents a fully blind phase-aware expectation-maximization (EM) algorithm for OFDM systems with the phase-shift keying (PSK) modulation. We address the well-known local maximum problem of the EM algorithm for blind channel estimation. This is primarily caused by the unknown phase ambiguity in the channel estimates, which conventional blind EM estimators cannot resolve. To overcome this limitation, we propose to exploit the extrinsic information from the decoder as model evidence metrics. A finite set of candidate models is generated based on the inherent symmetries of PSK modulation, and the decoder selects the most likely candidate model. Simulation results demonstrate that, when combined with a simple convolutional code, the phase-aware EM algorithm reliably resolves phase ambiguity during the initialization stage and reduces the local convergence rate from 80% to nearly 0% in frequency-selective channels with a constant phase ambiguity. The algorithm is invoked only once after the EM initialization stage, resulting in negligible additional complexity during subsequent turbo iterations.

Chin-Hung Chen, Boris Karanov, Wim van Houtum et al.

Recently, a data-driven Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm tailored to channels with intersymbol interference has been introduced. This so-called BCJRNet algorithm utilizes neural networks to calculate channel likelihoods. BCJRNet has demonstrated resilience against inaccurate channel tap estimations when applied to a time-invariant channel with ideal exponential decay profiles. However, its generalization capabilities for practically-relevant time-varying channels, where the receiver can only access incorrect channel parameters, remain largely unexplored. The primary contribution of this paper is to expand upon the results from existing literature to encompass a variety of imperfect channel knowledge cases that appear in real-world transmissions. Our findings demonstrate that BCJRNet significantly outperforms the conventional BCJR algorithm for stationary transmission scenarios when learning from noisy channel data and with imperfect channel decay profiles. However, this advantage is shown to diminish when the operating channel is also rapidly time-varying. Our results also show the importance of memory assumptions for conventional BCJR and BCJRNet. An underestimation of the memory largely degrades the performance of both BCJR and BCJRNet, especially in a slow-decaying channel. To mimic a situation closer to a practical scenario, we also combined channel tap uncertainty with imperfect channel memory knowledge. Somewhat surprisingly, our results revealed improved performance when employing the conventional BCJR with an underestimated memory assumption. BCJRNet, on the other hand, showed a consistent performance improvement as the level of accurate memory knowledge increased.

Yuncheng Yuan, Péter Scheepers, Lydia Tasiou et al.

This paper analyzes the design and competitiveness of four neural network (NN) architectures recently proposed as decoders for forward error correction (FEC) codes. We first consider the so-called single-label neural network (SLNN) and the multi-label neural network (MLNN) decoders which have been reported to achieve near maximum likelihood (ML) performance. Here, we show analytically that SLNN and MLNN decoders can always achieve ML performance, regardless of the code dimensions -- although at the cost of computational complexity -- and no training is in fact required. We then turn our attention to two transformer-based decoders: the error correction code transformer (ECCT) and the cross-attention message passing transformer (CrossMPT). We compare their performance against traditional decoders, and show that ordered statistics decoding outperforms these transformer-based decoders. The results in this paper cast serious doubts on the application of NN-based FEC decoders in the short and medium block length regime.

Chin-Hung Chen, Boris Karanov, Wim van Houtom et al.

It has been recognized that the impulsive noise (IN) generated by power devices poses significant challenges to wireless receivers. In this paper, we comprehensively assess the achievable information rate (AIR) for the well-established Markov-Middleton IN model with a phase-shift keying (PSK) input sequence across various channel conditions, including matched and mismatched decoding scenarios. Upon determining information-theoretic bounds, we propose an optimal turbo-differentially encoded (DE)-PSK-IN receiver design based on a commonly used commercial transmission setup consisting of a convolutional encoder, bit-level interleaver, and a DE-PSK symbol mapper. We show that by incorporating the differential decoder into the maximum a-posteriori-based (MAP) IN detector, we can significantly enhance the receiver performance with a 4.5 dB gain compared to the conventional MAP-based turbo-PSK-IN receiver and a gap of around 1 dB to the theoretical bounds. We also propose a suboptimal separate receiver design that can be implemented with half the complexity of the joint design and near-optimal performance. We have evaluated the performance of the proposed receiver designs through extensive simulations, demonstrating their effectiveness in real-world scenarios with limited interleaver depth and mismatched state implementation.

Yunus Can Gültekin, Péter Scheepers, Yuncheng Yuan et al.

We investigate the design of two neural network (NN) architectures recently proposed as decoders for forward error correction: the so-called single-label NN (SLNN) and multi-label NN (MLNN) decoders. These decoders have been reported to achieve near-optimal codeword- and bit-wise performance, respectively. Results in the literature show near-optimality for a variety of short codes. In this paper, we analytically prove that certain SLNN and MLNN architectures can, in fact, always realize optimal decoding, regardless of the code. These optimal architectures and their binary weights are shown to be defined by the codebook, i.e., no training or network optimization is required. Our proposed architectures are in fact not NNs, but a different way of implementing the maximum likelihood decoding rule. Optimal performance is numerically demonstrated for Hamming $(7,4)$, Polar $(16,8)$, and BCH $(31,21)$ codes. The results show that our optimal architectures are less complex than the SLNN and MLNN architectures proposed in the literature, which in fact only achieve near-optimal performance. Extension to longer codes is still hindered by the curse of dimensionality. Therefore, even though SLNN and MLNN can perform maximum likelihood decoding, such architectures cannot be used for medium and long codes.

Chin-Hung Chen, Ivana Nikoloska, Wim van Houtum et al.

Impulsive noise (IN) commonly generated by power devices can severely degrade the performance of high sensitivity wireless receivers. Accurate channel state information (CSI) knowledge is essential for designing optimal maximum a posteriori detectors. This paper examines blind channel estimation methods based on the expectation-maximization (EM) algorithm tailored for scenarios impacted by bursty IN, which can be described by the Markov-Middleton model. We propose a constrained EM algorithm that exploits the trellis structure of the IN model and the transmitted binary phase shift keying (BPSK) symbols. By enforcing shared variance among specific trellis states and symmetry in the transition matrix, the proposed constrained EM algorithm adapted for the bursty IN channel has an almost two times faster convergence rate and better estimation performance than the standard EM approach. We comprehensively evaluate the robustness of both standard and constrained EM estimators under different types of CSI uncertainties. The results indicate that the final estimations of both EM estimators are robust enough to mismatch Markov-Middleton model parameters. However, as the level of CSI uncertainty increases, the convergence rate decreases.

Rick M. Bütler, Christian Häger, Henry D. Pfister et al.

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.

Christian Häger, Henry D. Pfister, Rick M. Bütler et al.

We propose a model-based machine-learning approach for polarization-multiplexed systems by parameterizing the split-step method for the Manakov-PMD equation. This approach performs hardware-friendly DBP and distributed PMD compensation with performance close to the PMD-free case.

Kadir Gümüs, Alex Alvarado, Bin Chen et al.

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.

Abdelkerim Amari, Xiang Lin, Octavia A. Dobre et al.

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.

Christian Häger, Henry D. Pfister, Rick M. Bütler et al.

For the efficient compensation of fiber nonlinearity, one of the guiding principles appears to be: fewer steps are better and more efficient. We challenge this assumption and show that carefully designed multi-step approaches can lead to better performance-complexity trade-offs than their few-step counterparts.

Abdelkerim Amari, Xiang Lin, Octavia A. Dobre et al.

We investigate the performance of a machine learning classification technique, called the Parzen window, to mitigate the fiber nonlinearity in the context of dispersion managed and dispersion unmanaged systems. The technique is applied for detection at the receiver side, and deals with the non-Gaussian nonlinear effects by designing improved decision boundaries. We also propose a two-stage mitigation technique using digital back propagation and Parzen window for dispersion unmanaged systems. In this case, digital back propagation compensates for the deterministic nonlinearity and the Parzen window deals with the stochastic nonlinear signal-noise interactions, which are not taken into account by digital back propagation. A performance improvement up to 0:4 dB in terms of Q factor is observed.