On the Convergence Speed of Spatially Coupled LDPC Ensembles

Spatially coupled low-density parity-check codes show an outstanding performance under the low-complexity belief propagation (BP) decoding algorithm. They exhibit a peculiar convergence phenomenon above the BP threshold of the underlying non-coupled ensemble, with a wave-like convergence propagating through the spatial dimension of the graph, allowing to approach the MAP threshold. We focus on this particularly interesting regime in between the BP and MAP thresholds. On the binary erasure channel, it has been proved that the information propagates with a constant speed toward the successful decoding solution. We derive an upper bound on the propagation speed, only depending on the basic parameters of the spatially coupled code ensemble such as degree distribution and the coupling factor $w$. We illustrate the convergence speed of different code ensembles by simulation results, and show how optimizing degree profiles helps to speed up the convergence.Comment: 11 pages, 6 figure

Performance Prediction of Nonbinary Forward Error Correction in Optical Transmission Experiments

In this paper, we compare different metrics to predict the error rate of optical systems based on nonbinary forward error correction (FEC). It is shown that the correct metric to predict the performance of coded modulation based on nonbinary FEC is the mutual information. The accuracy of the prediction is verified in a detailed example with multiple constellation formats, FEC overheads in both simulations and optical transmission experiments over a recirculating loop. It is shown that the employed FEC codes must be universal if performance prediction based on thresholds is used. A tutorial introduction into the computation of the threshold from optical transmission measurements is also given.Comment: submitted to IEEE/OSA Journal of Lightwave Technolog

Probabilistic Eigenvalue Shaping for Nonlinear Fourier Transform Transmission

We consider a nonlinear Fourier transform (NFT)-based transmission scheme, where data is embedded into the imaginary part of the nonlinear discrete spectrum. Inspired by probabilistic amplitude shaping, we propose a probabilistic eigenvalue shaping (PES) scheme as a means to increase the data rate of the system. We exploit the fact that for an NFT-based transmission scheme the pulses in the time domain are of unequal duration by transmitting them with a dynamic symbol interval and find a capacity-achieving distribution. The PES scheme shapes the information symbols according to the capacity-achieving distribution and transmits them together with the parity symbols at the output of a low-density parity-check encoder, suitably modulated, via time-sharing. We furthermore derive an achievable rate for the proposed PES scheme. We verify our results with simulations of the discrete-time model as well as with split-step Fourier simulations.Comment: Published in IEEE/OSA Journal of Lightwave Technology, 201

Low-Complexity Near-Optimum Symbol Detection Based on Neural Enhancement of Factor Graphs

We consider the application of the factor graph framework for symbol detection on linear inter-symbol interference channels. Based on the Ungerboeck observation model, a detection algorithm with appealing complexity properties can be derived. However, since the underlying factor graph contains cycles, the sum-product algorithm (SPA) yields a suboptimal algorithm. In this paper, we develop and evaluate efficient strategies to improve the performance of the factor graph-based symbol detection by means of neural enhancement. In particular, we consider neural belief propagation and generalizations of the factor nodes as an effective way to mitigate the effect of cycles within the factor graph. By applying a generic preprocessor to the channel output, we propose a simple technique to vary the underlying factor graph in every SPA iteration. Using this dynamic factor graph transition, we intend to preserve the extrinsic nature of the SPA messages which is otherwise impaired due to cycles. Simulation results show that the proposed methods can massively improve the detection performance, even approaching the maximum a posteriori performance for various transmission scenarios, while preserving a complexity which is linear in both the block length and the channel memory.Comment: revised version. arXiv admin note: text overlap with arXiv:2203.0333

A Spatially Coupled LDPC Coding Scheme with Scalable Decoders for Space Division Multiplexing

In this paper, we study the application of spatially coupled LDPC codes with sub-block locality for space division multiplexing. We focus on the information exchange between the sub-blocks and compare decoding strategies with respect to the complexity, performance and the information flow.Comment: 3 pages plus comments, 3 figures, European Conference on Optical Communication (ECOC) 202