Searcharxiv⌕ Search

arXiv subjects

Laurent Schmalen

Publications and source records attributed to Laurent Schmalen.

At least 37 records · Page 2Linked to original sources
arXiv2026

On the Error Rate of Binary BCH Codes under Error-and-erasure Decoding

Determining the exact decoding error probability of linear block codes is an interesting problem. For binary BCH codes, McEliece derived methods to estimate the error probability of a simple bounded distance decoding (BDD) for BCH codes. However, BDD falls short in many applications. In this work, we consider error-and-erasure decoding and its improved variants. We derive closed-form expressions for their error probabilities and validate them through simulations. Then, we illustrate their use in assessing concatenated coding schemes.

cs.IT↗
arXiv2026

Quantum CSS LDPC Codes based on Dyadic Matrices for Belief Propagation-based Decoding

Quantum low-density parity-check (QLDPC) codes provide a practical balance between error-correction capability and implementation complexity in quantum error correction (QEC). In this paper, we propose an algebraic construction based on dyadic matrices for designing both classical and quantum LDPC codes. The method first generates classical binary quasi-dyadic LDPC codes whose Tanner graphs have girth 6. It is then extended to the Calderbank-Shor-Steane (CSS) framework, where the two component parity-check matrices are built to satisfy the compatibility condition required by the recently introduced CAMEL-ensemble quaternary belief propagation decoder. This compatibility condition ensures that all unavoidable cycles of length 4 are assembled in a single variable node, allowing the mitigation of their detrimental effects by decimating that variable node.

cs.IT↗
arXiv2025

An Extension of Enumerative Sphere Shaping for Arbitrary Channel Input Distributions

A non-uniform channel input distribution is key for achieving the capacity of arbitrary channels. However, message bits are generally assumed to follow a uniform distribution which must first be transformed to a non-uniform distribution by using a distribution matching algorithm. One such algorithm is enumerative sphere shaping (ESS). Compared to algorithms such as constant composition distribution matching (CCDM), ESS can utilize more channel input symbol sequences, allowing it to achieve a comparably low rate loss. However, the distribution of channel input symbols produced by ESS is fixed, restricting the utility of ESS to channels with Gaussian-like capacity-achieving input distributions. In this paper, we generalize ESS to produce arbitrary discrete channel input distributions, making it usable on most channels. Crucially, our generalization replaces fixed weights used internally by ESS with weights depending on the desired channel input distribution. We present numerical simulations using generalized ESS with probabilistic amplitude shaping (PAS) to transmit sequences of 256 symbols over a simplified model of an unamplified coherent optical link, a channel with a distinctly non-Gaussian capacity-achieving input distribution. In these simulations, we found that generalized ESS improves the maximum transmission rate by 0.0425 bit/symbol at a frame error rate below 10^{-4} compared to CCDM.

cs.IT↗
arXiv2025

Neural Network-Based Single-Carrier Joint Communication and Sensing: Loss Design, Constellation Shaping and Precoding

We investigate the impact of higher-order modulation formats on the sensing performance of single-carrier joint communication and sensing (JCAS) systems. Several separate components such as a beamformer, a modulator, a target detector, an angle of arrival (AoA) estimator and a communication demapper are implemented as trainable neural networks (NNs). We compare geometrically shaped modulation formats to a classical quadrature amplitude modulation (QAM) scheme. We assess the influence of multi-snapshot sensing and varying signal-to-noise ratio (SNR) on the overall performance of the autoencoder-based system. To improve the training behavior of the system, we decouple the loss functions from the respective SNR values and the number of sensing snapshots, using upper bounds of the sensing and communication performance, namely the Cramér-Rao bound for AoA estimation and the mutual information for communication. The NN-based sensing outperforms classical algorithms, such as a Neyman-Pearson based power detector for object detection and ESPRIT for AoA estimation for both the trained constellations and QAM at low SNRs. We show that the gap in sensing performance between classical and shaped modulation formats can be significantly reduced through multi-snapshot sensing. Lastly, we demonstrate system extension to multi-user multiple-input multiple-output to address the improvement of spatial efficiency when servicing multiple user equipments. Our contribution emphasizes the importance of estimation bounds for training neural networks, especially when the trained solutions are deployed in varying SNR conditions.

eess.SP↗
arXiv2025

Interference Mitigation for OFDM-based Integrated Sensing and Communications with Arbitrary Modulation Formats

Integrated sensing and communication will be a key feature of future mobile networks, enabling highly efficient systems and numerous new applications by leveraging communication signals for sensing. In this paper, we analyze the impact of arbitrary modulation alphabets on the sensing performance of communication-centric OFDM systems as expected in the next-generation 6G networks. We evaluate existing interference mitigation techniques, such as coherent successive target cancellation, and propose an enhanced version of this algorithm. A systematic performance evaluation in multi-target scenarios, including the effects of scattering, demonstrates that our proposed interference mitigation methods achieve performance comparable to sensing-optimal constant modulus signals while utilizing higher order constellations for more efficient communications.

eess.SP↗
arXiv2025

Integrated Radio Sensing Capabilities for 6G Networks: AI/ML Perspective

The sixth-generation wireless communications (6G) is often labeled as "connected intelligence". Radio sensing, aligned with machine learning (ML) and artificial intelligence (AI), promises, among other benefits, breakthroughs in the system's ability to perceive the environment and effectively utilize this awareness. This article offers a tutorial-style survey of AI and ML approaches to enhance the sensing capabilities of next-generation wireless networks. To this end, while staying in the framework of integrated sensing and communication (ISAC), we expand the term "sensing" from radar, via spectrum sensing, to miscellaneous applications of radio sensing like non-cooperative transmitter localization. We formulate the problems, explain the state-of-the-art approaches, and detail AI-based techniques to tackle various objectives in the context of wireless sensing. We discuss the advantages, enablers, and challenges of integrating various sensing capabilities into an envisioned AI-powered multimodal multi-task network. In addition to the tutorial-style core of this work based on direct authors' involvement in 6G research problems, we review the related literature, and provide both a good start for those entering this field of research, and a topical overview for a general reader with a background in wireless communications

eess.SP↗
arXiv2025

High Girth Spatially-Coupled LDPC Codes with Hierarchical Structure

Quasi-cyclic (QC) low-density parity-check (LDPC) codes are a class of LDPC codes with a simple construction facilitating hardware implementation while achieving excellent performance. In this paper, we introduce an algorithm that constructs QC spatially-coupled (SC) LDPC codes with large girth while keeping the constraint length small. The algorithm offers a "protograph to basegraph" construction, focusing on finding small lifting sizes of QC codes while avoiding short cycles. This work extends the hierarchical quasi-cyclic (HQC) construction for block LDPC codes proposed by Wang et al. to the spatially coupled case. The construction is based on the cycle relevant matrix (CRM) derived from the periodic structure of time-invariant SC-LDPC codes. Numerical results show that the proposed algorithm effectively achieves the target girth with a small lifting factor, enabling low-complexity SC code construction.

cs.IT↗
arXiv2025

A Temporal Gaussian Noise Model for Equalization-enhanced Phase Noise

Equalization-enhanced Phase Noise causes burst-like distortions in high symbol-rate transmission systems. We propose a temporal Gaussian noise model that captures these distortions by introducing a time-varying distortion power. Validated through simulations and experiments, it enables accurate and simple performance prediction for high symbol-rate transmission systems.

eess.SP↗
arXiv2025

End-to-End Learning of Probabilistic Constellation Shaping through Importance Sampling

Probabilistic constellation shaping enables easy rate adaption and has been proven to reduce the gap to Shannon capacity. Constellation point probabilities are optimized to maximize either the mutual information or the bit-wise mutual information. The optimization problem is however challenging even for simple channel models. While autoencoder-based machine learning has been applied successfully to solve this problem [1], it requires manual computation of additional terms for the gradient which is an error-prone task. In this work, we present novel loss functions for autoencoder-based learning of probabilistic constellation shaping for coded modulation systems using automatic differentiation and importance sampling. We show analytically that our proposed approach also uses exact gradients of the constellation point probabilities for the optimization. In simulations, our results closely match the results from [1] for the additive white Gaussian noise channel and a simplified model of the intensity-modulation direct-detection channel.

cs.IT↗
arXiv2025

Uncertainty Propagation in the Fast Fourier Transform

We address the problem of uncertainty propagation in the discrete Fourier transform by modeling the fast Fourier transform as a factor graph. Building on this representation, we propose an efficient framework for approximate Bayesian inference using belief propagation (BP) and expectation propagation, extending its applicability beyond Gaussian assumptions. By leveraging an appropriate BP message representation and a suitable schedule, our method achieves stable convergence with accurate mean and variance estimates. Numerical experiments in representative scenarios from communications demonstrate the practical potential of the proposed framework for uncertainty-aware inference in probabilistic systems operating across both time and frequency domain.

cs.LG↗
arXiv2025

Protograph-Based LDPC Codes with Local Irregularity

Forward error correcting (FEC) codes are used in many communication standards with a wide range of re quirements. FEC codes should work close to capacity, achieve low error floors, and have low decoding complexity. In this paper, we propose a novel category of low-density parity-check (LDPC) codes, based on protograph codes with local irregularity. This new code family generalizes conventional protograph-based LDPC codes and is capable of reducing the iterative decoding threshold of the conventional counterpart. We introduce an adapted version of the protograph extrinsic information transfer (PEXIT) algorithm to estimate decoding thresholds on the binary input additive white Gaussian noise channel, perform optimiza tions on the local irregularity, and simulate the performance of some constructed codes.

cs.IT↗
arXiv2025

Subcode Ensemble Decoding of Polar Codes

In the short block length regime, pre-transformed polar codes together with successive cancellation list (SCL) decoding possess excellent error correction capabilities. However, in practice, the list size is limited due to the suboptimal scaling of the required area in hardware implementations. Automorphism ensemble decoding (AED) can improve performance for a fixed list size by running multiple parallel SCL decodings on permuted received words, yielding a list of estimates from which the final estimate is selected. Yet, AED is limited to appropriately designed polar codes. Subcode ensemble decoding (ScED) was recently proposed for low-density parity-check codes and does not impose such design constraints. It uses multiple decodings in different subcodes, ensuring that the selected subcodes jointly cover the original code. We extend ScED to polar codes by expressing polar subcodes through suitable pre-transformations (PTs). To this end, we describe a framework classifying pre-transformations for pre-transformed polar codes based on their role in encoding and decoding. Within this framework, we propose a new type of PT enabling ScED for polar codes, analyze its properties, and discuss how to construct an efficient ensemble.

cs.IT↗
arXiv2025

Removal of Small Weight Stopping Sets for Asynchronous Unsourced Multiple Access

In this paper, we analyze the formation of small stopping sets in joint factor graphs describing a frame-asynchronous two-user transmission. Furthermore, we propose an algorithm to completely avoid small stopping sets in the joint factor graph over the entire range of symbol delays. The error floor caused by these stopping sets is completely mitigated. Our key observation is that, while the order of bits in the codeword is irrelevant in a single-user environment, it turns out to be crucial in an asynchronous, unsourced two-user system. Subsequently, our algorithm finds a reordering of variable nodes which avoids the smallest stopping set in the joint graph. We show that further improvements can be achieved when girth optimization of the single-user graphs by progressive edge growth (PEG) is used in combination with our proposed algorithm. Starting with a randomized code construction with optimized degree distribution, our simulation results show that PEG followed by the proposed algorithm can improve the average per user probability of error in a noiseless channel by almost two orders of magnitude for a broad range of frame delays.

cs.IT↗
arXiv2025

On the Sensing Performance of FMCW-based Integrated Sensing and Communications with Arbitrary Constellations

Integrated sensing and communications (ISAC) is expected to play a major role in numerous future applications, e.g., smart cities. Leveraging native radar signals like the frequency modulated continuous wave (FMCW) waveform additionally for data transmission offers a highly efficient use of valuable physical radio frequency (RF) resources allocated for automotive radar applications. In this paper, we propose the adoption of higher-order modulation formats for data modulation onto an FMCW waveform and provide a comprehensive overview of the entire signal processing chain. We evaluate the impact of each component on the overall sensing performance. While alignment algorithms are essential for removing the information signal at the sensing receiver, they also introduce significant dispersion to the received signal. We analyze this effect in detail. Notably, we demonstrate that the impact of non-constant amplitude modulation on sensing performance is statistically negligible when the complete signal processing chain is considered. This finding highlights the potential for achieving high data rates in FMCW-ISAC systems without compromising the sensing capabilities.

eess.SP↗
arXiv2025

Improved Estimation Accuracy in OFDM-based Joint Communication and Sensing through Kalman Tracking and Interpolation

We investigate a monostatic orthogonal frequency-division multiplexing (OFDM)-based joint communication and sensing (JCAS) system for object tracking. Our setup consists of a transmitter and receiver equipped with an antenna array for fully digital beamforming. The native resolution of range and velocity in all radar-like sensing, including OFDM radar sensing, is limited by the observation time and bandwidth. In this work, we improve the parameter estimates (estimates of range) through interpolation methods and tracking algorithms. We verify our method by comparing the root mean squared error (RMSE) of the estimated range, velocity and angle and by comparing the mean Euclidean distance between the estimated and true position. We demonstrate how both a Kalman filter for tracking, and interpolation methods using zero-padding and the chirp Z-transform (CZT) improve the estimation error. We discuss the computational complexity of the different methods. We propose the KalmanCZT approach that combines tracking via Kalman filtering and interpolation via the CZT, resulting in a solution with flexible resolution that significantly improves the range RMSE.

eess.SP↗
arXiv2025

Quaternary Neural Belief Propagation Decoding of Quantum LDPC Codes with Overcomplete Check Matrices

Quantum low-density parity-check (QLDPC) codes are promising candidates for error correction in quantum computers. One of the major challenges in implementing QLDPC codes in quantum computers is the lack of a universal decoder. In this work, we first propose to decode QLDPC codes with a belief propagation (BP) decoder operating on overcomplete check matrices. Then, we extend the neural BP (NBP) decoder, which was originally studied for suboptimal binary BP decoding of QLPDC codes, to quaternary BP decoders. Numerical simulation results demonstrate that both approaches as well as their combination yield a low-latency, high-performance decoder for several short to moderate length QLDPC codes.

quant-ph↗