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

A new approach to optimise Non-Binary LDPC codes for Coded Modulations

International audienceThis paper is dedicated to the optimisation of Non-Binary LDPC codes when associated to high-order modulations. To be specific, we propose to specify the values of the non-zero NB-LDPC parity matrix coefficients depending on the corresponding check node equation and the Euclidean distance of the coded modulation. In other words, we explore the joint optimisation of the modulation mapping and the non-binary matrix. The performance gains announced by a theoretical analysis based on the Union Bound are confirmed by simulations results. We obtain an 0.2-dB gain in the high SNR regime compared to other state-of-the-art matrices

Forward Error Correction for High Capacity Transmission Systems

Αυτή η μελέτη διερευνά την αλληλεπίδραση μεταξύ FEC διόρθωσης σφαλμάτων προώθησης και ψηφιακού αντιστάθμιση μη γραμμικότητας DBP σε ένα κανάλι ινών μεγάλων αποστάσεων. Πρώτον, α Η προσέγγιση που βασίζεται στην έρευνα χρησιμοποιείται για τον προσδιορισμό των τεχνολογιών αιχμής στο FEC για το κανάλι ινών και προσαρμόστε τα στο τελικό σχέδιο. Οι σχεδιαστικές επιλογές περιλαμβάνουν το χρήση τετριμμένων bit κωδικοποιημένης διαμόρφωσης αρχιτεκτονικής T-BICM με συνενωμένη σχήμα κώδικα που χρησιμοποιεί έναν επαναληπτικό soft αποκωδικοποιητή. Η απαίτηση για συνενωμένη Η εφαρμογή FEC οδήγησε σε μια άλλη έρευνα για έναν κώδικα καλής απόδοσης συνδυασμός. Το ακανόνιστο LDPC και το οιονεί κυκλικό QC-LDPC, που υιοθετήθηκαν από το DVB-S2 και Τα πρότυπα IEEE 802.11, αντίστοιχα, συνδυάστηκαν με τον κώδικα σκάλας και σύγκριση με βάση τις επιτευχθείσες επιδόσεις. Αποδεικνύουμε ότι αυξάνοντας τις ίνες απόσταση μετάδοσης κατά 1/3, από 300km έως 400km, διατηρώντας παράλληλα την η ίδια απόδοση και η χρήση των ίδιων γενικών εξόδων, δηλαδή 27,5% είναι εφικτό όταν υλοποίηση του DBP με 2 βήματα/περιοχή ή 3 βήματα/περιοχή, ανάλογα με το αν το Οι επαναλήψεις αποκωδικοποίησης είναι 10 ή 5. Αυτή η μελέτη καταλήγει με την εύνοια του LDPC από το DVB-S2 πάνω από το QC-LDPC του IEEE 802.11 για κανάλι ινών μεγάλων αποστάσεων. Το συμπέρασμα βγαίνει με βάση σχετικά με την καλύτερη απόδοση για το LDPC-DVB, λόγω των μεγάλων μηκών κωδικών του και του υποστήριξη για υψηλούς ρυθμούς κωδικοποίησης με αποτέλεσμα χαμηλές γενικές απαιτήσειςThis study investigates the interplay between forward error correction FEC and digital back-propagation DBP nonlinearity compensation on a long-haul fibre channel. First, a research-based approach is used to identify the state-of-the-art technologies in FEC for the fibre channel and adapt them to the final design. The design choices includes the usage of trivial bit interleaved coded modulation T-BICM architecture with a concatenated code scheme that uses an iterative soft decoder. The requirement for a concatenated FEC implementation motivated another investigation of a well-performing code combination. The Irregular LDPC and quasi-cyclic QC-LDPC, adopted from DVB-S2 and IEEE 802.11 standards, respectively, were each concatenated with staircase code and compared based on the attained performance. We prove that increasing the fibre transmission distance by a factor of 1/3, from 300km to 400km, while maintaining the same performance and using the same overhead, i.e. 27.5\% is achievable when implementing DBP with 2 steps/span or 3 steps/span, depending on whether the decoding iterations are 10 or 5. This study concludes with favouring LDPC from DVB-S2 over IEEE 802.11's QC-LDPC for long haul fibre channel. The conclusion is made based on the better attained performance for LDPC-DVB, due to its long code lengths, and its support for high coding rates resulting low overhead requirement

Low-Density Hybrid-Check Coded Superposition Mapping and its Application in OFDM and MIMO

Since Shannon’s landmark paper, many approaches have been proposed to achieve the channel capacity. In the low SNR regime, the problem has almost been solved by capacity achieving channel codes. The research on coded modulation in the high SNR regime is still under development. Among many methods in accomplishing this goal, superposition mapping is an elegant way as it does not require extra shaping to generate a Gaussian-like distributed signal. Superposition mapping has been shown to offer very close to capacity performance for the AWGN channel by combining with an irregular channel code. The aim of this thesis is to search for a code which provides stable performance for moderate sequence length and sufficient number of iterations, which is more suitable for implementation. Concerning channel coding for superposition mapping, a generalized code design has recently been proposed. The so-called low-density hybrid-check (LDHC) coding intends to contrive coding and modulation in a joint way. The LDHC coding is constructed by integrating modulation into the Tanner graph. Thus, the complete code can be obtained by taking the effects of all the components into account. In this thesis, the LDHC code design is extended to OFDM and MIMO. For OFDM, the bit loading can be realized in the graph. In case of MIMO with spatial multiplexing, the code is extended to the spatial domain. In both cases, a suitable system structure will be proposed in this thesis. It will also be shown how this novel code design improves the system performance

Optimization of a Coded-Modulation System with Shaped Constellation

Conventional communication systems transmit signals that are selected from a signal constellation with uniform probability. However, information-theoretic results suggest that performance may be improved by shaping the constellation such that lower-energy signals are selected more frequently than higher-energy signals. This dissertation presents an energy efficient approach for shaping the constellations used by coded-modulation systems. The focus is on designing shaping techniques for systems that use a combination of amplitude phase shift keying (APSK) and low-density parity check (LDPC) coding. Such a combination is typical of modern satellite communications, such as the system used by the DVB-S2 standard.;The system implementation requires that a subset of the bits at the output of the LDPC encoder are passed through a nonlinear shaping encoder whose output bits are more likely to be a zero than a one. The constellation is partitioned into a plurality of sub-constellations, each with a different average signal energy, and the shaping bits are used to select the sub-constellation. An iterative receiver exchanges soft information among the demodulator, LDPC decoder, and shaping decoder. Parameters associated with the modulation and shaping code are optimized with respect to information rate, while the design of the LDPC code is optimized for the shaped modulation with the assistance of extrinsic-information transfer (EXIT) charts. The rule for labeling the constellation with bits is optimized using a novel hybrid cost function and a binary switching algorithm.;Simulation results show that the combination of constellation shaping, LDPC code optimization, and optimized bit labeling can achieve a gain in excess of 1 dB in an additive white Gaussian noise (AWGN) channel at a rate of 3 bits/symbol compared with a system that adheres directly to the DVB-S2 standard

Design and Performance Analysis for LDPC Coded Modulation in Multiuser MIMO Systems

The channel capacity can be greatly increased by using multiple transmit and receive antennas, which is usually called multi-input multi-output (MIMO) systems. Iterative processing has achieved near-capacity on a single-antenna Gaussian or Rayleigh fading channel. How to use the iterative technique to exploit the capacity potential in single-user and/or multiuser MIMO systems is of great interest. We propose a low-density parity-check (LDPC) coded modulation scheme in multiuser MIMO systems. The receiver can be regarded as a serially concatenated iterative detection and decoding scheme, where the LDPC decoder performs the role of outer decoder and the multiuser demapper does that of the inner decoder. For the proposed scheme, appropriate selection of a bit-to-symbol mapping is crucial to achieve a good performance, so we investigate and find the best mapping under various cases.Analytical bound serves as a useful tool to assess system performance. The search for powerful codes has motivated the introduction of efficient bounding techniques tailored to some ensembles of codes. We then investigate combinatorial union bounding techniques for fast fading multiuser MIMO systems. The union upper bound on maximum likelihood (ML) decoding error probability provides a prediction for the system performance, with which the simulated system performance can be compared. Closed-form expression for the union bound is obtained, which can be evaluated efficiently by using a polynomial expansion. In addition, the constrained channel capacity and the threshold obtained from extrinsic information transfer (EXIT) chart can also serve as performance measures. Based on the analysis for fast fading case, we generalize the union upper bound to the block fading case