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Laurent Schmalen

Publications and source records attributed to Laurent Schmalen.

At least 73 records · Page 4Linked to original sources
arXiv2024

A Joint Code and Belief Propagation Decoder Design for Quantum LDPC Codes

Quantum low-density parity-check (QLDPC) codes are among the most promising candidates for future quantum error correction schemes. However, a limited number of short to moderate-length QLDPC codes have been designed and their decoding performance is sub-optimal with a quaternary belief propagation (BP) decoder due to unavoidable short cycles in their Tanner graphs. In this paper, we propose a novel joint code and decoder design for QLDPC codes. The constructed codes have a minimum distance of about the square root of the block length. In addition, it is, to the best of our knowledge, the first QLDPC code family where BP decoding is not impaired by short cycles of length 4. This is achieved by using an ensemble BP decoder mitigating the influence of assembled short cycles. We outline two code construction methods based on classical quasi-cyclic codes and finite geometry codes. Numerical results demonstrate outstanding decoding performance over depolarizing channels.

cs.IT↗
arXiv2024

Performance Analysis of Generalized Product Codes with Irregular Degree Distribution

This paper investigates the theoretical analysis of intrinsic message passing decoding for generalized product codes (GPCs) with irregular degree distributions, a generalization of product codes that allows every code bit to be protected by a minimum of two and potentially more component codes. We derive a random hypergraph-based asymptotic performance analysis for GPCs, extending previous work that considered the case where every bit is protected by exactly two component codes. The analysis offers a new tool to guide the code design of GPCs by providing insights into the influence of degree distributions on the performance of GPCs.

cs.IT↗
arXiv2024

Optimized Soft-Aided Decoding of OFEC and Staircase Codes

We propose a novel soft-aided hard-decision decoding algorithm for general product-like codes. It achieves error correcting performance similar to that of a soft-decision turbo decoder for staircase and OFEC codes, while maintaining a low complexity.

cs.IT↗
arXiv2024

CNN-Based Equalization for Communications: Achieving Gigabit Throughput with a Flexible FPGA Hardware Architecture

To satisfy the growing throughput demand of data-intensive applications, the performance of optical communication systems increased dramatically in recent years. With higher throughput, more advanced equalizers are crucial, to compensate for impairments caused by inter-symbol interference (ISI). The latest research shows that artificial neural network (ANN)-based equalizers are promising candidates to replace traditional algorithms for high-throughput communications. On the other hand, not only throughput but also flexibility is a main objective of beyond-5G and 6G communication systems. A platform that is able to satisfy the strict throughput and flexibility requirements of modern communication systems are field programmable gate arrays (FPGAs). Thus, in this work, we present a high-performance FPGA implementation of an ANN-based equalizer, which meets the throughput requirements of modern optical communication systems. Further, our architecture is highly flexible since it includes a variable degree of parallelism (DOP) and therefore can also be applied to low-cost or low-power applications which is demonstrated for a magnetic recording channel. The implementation is based on a cross-layer design approach featuring optimizations from the algorithm down to the hardware architecture, including a detailed quantization analysis. Moreover, we present a framework to reduce the latency of the ANN-based equalizer under given throughput constraints. As a result, the bit error ratio (BER) of our equalizer for the optical fiber channel is around four times lower than that of a conventional one, while the corresponding FPGA implementation achieves a throughput of more than 40 GBd, outperforming a high-performance graphics processing unit (GPU) by three orders of magnitude for a similar batch size.

cs.AR↗
arXiv2024

Endomorphisms of Linear Block Codes

The automorphism groups of various linear codes are extensively studied yielding insights into the respective code structure. This knowledge is used in, e.g., theoretical analysis and in improving decoding performance, motivating the analyses of endomorphisms of linear codes. In this work, we discuss the structure of the set of transformation matrices of code endomorphisms, defined as a generalization of code automorphisms, and provide an explicit construction of a bijective mapping between the image of an endomorphism and its canonical quotient space. Furthermore, we introduce a one-to-one mapping between the set of transformation matrices of endomorphisms and a larger linear block code enabling the use of well-known algorithms for the search for suitable endomorphisms. Additionally, we propose an approach to obtain unknown code endomorphisms based on automorphisms of the code. Furthermore, we consider ensemble decoding as a possible use case for endomorphisms by introducing endomorphism ensemble decoding. Interestingly, EED can improve decoding performance when other ensemble decoding schemes are not applicable.

cs.IT↗
arXiv2024

Loss Design for Single-carrier Joint Communication and Neural Network-based Sensing

We evaluate the influence of multi-snapshot sensing and varying signal-to-noise ratio (SNR) on the overall performance of neural network (NN)-based joint communication and sensing (JCAS) systems. To enhance the training behavior, we decouple the loss functions from the respective SNR values and the number of sensing snapshots, using bounds of the sensing performance. Pre-processing is done through conventional sensing signal processing steps on the inputs to the sensing NN. The proposed method outperforms classical algorithms, such as a Neyman-Pearson-based power detector for object detection and ESPRIT for angle of arrival (AoA) estimation for quadrature amplitude modulation (QAM) at low SNRs.

eess.SP↗
arXiv2024

Introducing RSESS: An Open Source Enumerative Sphere Shaping Implementation Coded in Rust

In this work, we present an open-source implementation of the enumerative sphere shaping (ESS) algorithm used for probabilistic constellation shaping (PCS). PCS aims at closing the shaping gap caused by using uniformly distributed modulation symbols in channels for which information theory shows non-uniformly distributed signaling to be optimal. ESS is one such PCS algorithm that sets itself apart as it operates on a trellis representation of a subset of the possible symbol sequences. ESS leads to an empirical distribution of the symbols that closely approximates the optimal distribution for the additive white Gaussian noise (AWGN) channel. We provide an open-source implementation of this algorithm in the compiled language Rust, as well as Python bindings with which our Rust code can be called in a regular Python script. We also compare simulation results on the AWGN channel using our implementation with previous works on this topic.

cs.IT↗
arXiv2024

Log-Log Domain Sum-Product Algorithm for Information Reconciliation in Continuous-Variable Quantum Key Distribution

In this paper, we present a novel log-log domain sum-product algorithm (SPA) for decoding low-density parity-check (LDPC) codes in continuous-variable quantum key distribution (CV-QKD) systems. This algorithm reduces the fractional bit width of decoder messages, leading to a smaller memory footprint and a lower resource consumption in hardware implementation. We also provide practical insights for fixed-point arithmetic and compare our algorithm with the conventional SPA in terms of performance and complexity. Our results show that our algorithm achieves comparable or better decoding accuracy than the conventional SPA while saving at least $25\%$ of the fractional bit width.

cs.IT↗
arXiv2023

Fractional Chirp-Slope-Shift-Keying for SDR-based Search and Rescue Applications

The use of modern software-defined radio (SDR) devices enables the implementation of efficient communication systems in numerous scenarios. Such technology comes especially handy in the context of search and rescue (SAR) systems, enabling the incorporation of additional communication data transmission into the otherwise sub-optimally used SAR bands at 121.5 and 243~MHz. In this work, we propose a novel low-complexity, energy-efficient modulation scheme that allows transmission of additional data within chirped homing signals, while still meeting the standards of international SAR systems such as COSPAS-SARSAT. The proposed method modulates information onto small deviations of the chirp slope with respect to the required unmodulated chirp, which can be easily detected at the receiver side using digital signal processing.

eess.SP↗
arXiv2023

Unsupervised ANN-Based Equalizer and Its Trainable FPGA Implementation

In recent years, communication engineers put strong emphasis on artificial neural network (ANN)-based algorithms with the aim of increasing the flexibility and autonomy of the system and its components. In this context, unsupervised training is of special interest as it enables adaptation without the overhead of transmitting pilot symbols. In this work, we present a novel ANN-based, unsupervised equalizer and its trainable field programmable gate array (FPGA) implementation. We demonstrate that our custom loss function allows the ANN to adapt for varying channel conditions, approaching the performance of a supervised baseline. Furthermore, as a first step towards a practical communication system, we design an efficient FPGA implementation of our proposed algorithm, which achieves a throughput in the order of Gbit/s, outperforming a high-performance GPU by a large margin.

eess.SP↗