On Taylor Series, Mahmoud Ahmadian-attari, Hamid Saeedi · 2016
A new approach for the approximation of the channel log-likelihood ratio (LLR) for wireless channels based on Taylor series is proposed. The approximation is applied to the uncorrelated flat Rayleigh fading channel with unknown channel state information at the receiver. It is shown that the proposed approximation greatly simplifies the calculation of channel LLRs, and yet provides results almost identical to those based on the exact calculation of channel LLRs. The results are obtained in the context of bit-interleaved coded modulation (BICM) schemes with low-density parity-check (LDPC) codes, and include threshold calculations and error rate performance of finite-length codes. Compared to the existing approximations, the proposed method is either significantly less complex, or considerably more accurate.
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2007
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Hrouza, Ondřej · Brno University of Technology Digital Library (Brno University of Technology) · 2012
Práce se zabývá problematikou LDPC kódů. Jsou zde popsány metody vytváření paritní matice, kde je kladen důraz především na strukturované vytváření této matice za použití konečné geometrie: Euklidovské geometrie a projektivní geometrie. Další oblastí, které se práce věnuje je dekódování LDPC kódů. Práce porovnává čtyři dekódovací metody: Hard-Decision algoritmus, Bit-Flipping algoritmus, The Sum-Product algoritmus a Log Likelihood algoritmus, při kterých je kladen důraz především na iterativní dekódovací metody. Praktickým výstupem práce je program LDPC kódy, který vznik v prostředí Matlab. Tento program je rozdělen na dvě části -- Výuka LDPC kódů a Simulace LDPC kódů. Na základě výsledků získaných z programu Simulace LDPC kódů je vytvořeno porovnání vytvářecích a dekódovacích metod LDPC kódů. Pro porovnávání dekódovacích metod LDPC kódů byly využity BER charakteristiky a časová závislost jednotlivých metod na různých parametrech LDPC kódu (počet iterací nebo velikost paritní matice).
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Αχμέντ Μάχντι · 2015
Στα ψηφιακά συστήματα, η πληροφορία κωδικοποιείται σε ακολουθίες από 0και 1, που αντιστοιχούν στις δύο δυνατές καταστάσεις των τρανζίστορ, on - off, τα οποία λειτουργούν ως διακόπτες. Το πλεονέκτημα αυτό έχει επιφέρει σημαντικέςαλλαγές στον τρόπο επεξεργασίας της πληροφορίας. Η πληροφορία στη φύση παρουσιάζεται αποκλειατικά σε αναλογική μορφή, καθώς ο άνθρωπος μόνο αναλογικάσήματα μπορεί να αντιληφθεί. ´Ετσι λοιπόν, τα αναλογικά δεδομένα πρέπει να ψη-φιοποιηθούν, να μετατραπούν δηλαδή σε ακολουθίες από 0 και 1, ώστε ο δέκτης ναμην είναι υποχρεωμένος να κάνει μία εκτίμηση των άπειρων τιμών ενός αναλογικούσήματος, αλλά απλά να πάρει μία απόφαση μεταξύ των δύο διακριτών τιμών γιακάθε σήμα, 0 ή 1. Η διαδικασία αυτή καθιστά τα ψηφιακά σήματα πιο αξιόπισταγια τη μετάδοση πληροφορίας σε ένα ενθόρυβο περιβάλλον, καθώς μπορούν να ανι-χνεύονται σχεδόν τέλεια, όταν το επίπεδο του ϑορύβου δεν είναι ιδιαίτερα υψηλό,πράγμα που επιτρέπει την ανάκτηση των ψηφιακών στοιχείων, και μέσω των τεχνι-κών διόρθωσης λαθών είναι δυνατή η διόρθωση σφαλμάτων που συμβαίνουν κατά τημετάδοση.Η διατριβή επικεντρώνεται στην κατασκευή αποδοτικών κωδίκων LDPC και στη μελέτη της κωδικοποίησης για κώδικες LDPC. Συγκεκριμένα, στην παρούσα διατριβήακολουθείται μια σχεδιαστική μεθοδολογία βασισμένη στην από κοινού κατασκευήκαι υλοποίηση σε υλικό των κωδίκων LDPC και των κωδικοποιητών, αντίστοιχα.Στόχος είναι να αναπτυχθούν μεθοδολογίες κατασκευής κωδίκων LDPC με μεγάληικανότητα διόρθωσης λαθών, ιδιαίτερα σε χαμηλό BER , οι οποίοι ικανοποιούν προδιαγραφές συγκεκριμένων εφαρμογών, αλλά και να είναι κατάλληλοι για χρήση και σε άλλες εφαρμογές με παρόμοιες απαιτήσεις σε διορθωτική ικανότητα. Ταυτοχρόνως, υλοποιούνται σε υλικό διάφορες αρχιτεκτονικές κωδικοποιητών, οι οποίες επίσης ικανοποιούν ένα αρκετά μέγαλο εύρος από προδιαγραφές αρχιτεκτονικών, όπως υψηλό ρυθμό επεξεργασίας και μετάδοσης δεδομένων (Throughput rate), της τάξεως των πολλών Gbps, χαμηλή χρονική πολυπλοκότητα με μικρή επιφάνεια των κυκλωμάτων VLSI, χρήση μικρών μνημών και χαμηλή κατανάλωση ισχύος, αλλά και υποστήριξη κωδικοποίησης κωδίκων με πολλαπλούς ρυθμούς χρησιμοποιώντας είτε ένα μόνο κώδικα από τον οποίο παράγονται και άλλοι κώδικες με διαφορετικούς ρυθμούς, είτε χρησιμοποιώντας πολλούς κώδικες, ο καθένας από τους οποίουςυποστηρίζει ένα συγκεκριμένο ρυθμό. Στα πλαίσια της διατριβής, μελετούνται τα προβλήματα και η πολυπλοκότητα κωδικοποίησης κωδίκων LDPC μαζί με την διορθωτική ικανότητά τους. ´Εμφαση δίνεται στη κατασκευή και υλοποίηση των κωδίκων που ανήκουν στη κατηγορίατων QC-LDPC.
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Ondrej Hrouza · Digital Repository (National Repository of Grey Literature) · 2012
The aim of this thesis are problematics about LDPC codes. There are described metods to create parity check matrix, where are important structured metods using finite geometry: Euclidean geometry and projectice geometry. Next area in this thesis is decoding LDPC codes. There are presented four metods: Hard-Decision algorithm, Bit-Flipping algorithm, The Sum-Product algorithm and Log Likelihood algorithm, where is mainly focused on iterative decoding methods. Practical output of this work is program LDPC codes created in environment Matlab. The program is divided to two parts -- Practise LDPC codes and Simulation LDPC codes. The result reached by program Simulation LDPC codes is used to create a comparison of creating and decoding methods LDPC codes. For comparison of decoding methods LDPC codes were used BER characteristics and time dependence each method on various parameters LDPC code (number of iteration or size of parity matrix).
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Ondrej Hrouza · Digital Repository (National Repository of Grey Literature) · 2012
The aim of this thesis are problematics about LDPC codes. There are described metods to create parity check matrix, where are important structured metods using finite geometry: Euclidean geometry and projectice geometry. Next area in this thesis is decoding LDPC codes. There are presented four metods: Hard-Decision algorithm, Bit-Flipping algorithm, The Sum-Product algorithm and Log Likelihood algorithm, where is mainly focused on iterative decoding methods. Practical output of this work is program LDPC codes created in environment Matlab. The program is divided to two parts -- Practise LDPC codes and Simulation LDPC codes. The result reached by program Simulation LDPC codes is used to create a comparison of creating and decoding methods LDPC codes. For comparison of decoding methods LDPC codes were used BER characteristics and time dependence each method on various parameters LDPC code (number of iteration or size of parity matrix).
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Alí Emre Pusane, Roxana Smarandache, Pascal O. Vontobel et al. · IEEE Transactions on Information Theory · 2011
Low-density parity-check (LDPC) convolutional codes are capable of achieving excellent performance with low encoding and decoding complexity. In this paper, we discuss several graph-cover-based methods for deriving families of time-invariant and time-varying LDPC convolutional codes from LDPC block codes and show how earlier proposed LDPC convolutional code constructions can be presented within this framework. Some of the constructed convolutional codes significantly outperform the underlying LDPC block codes. We investigate some possible reasons for this “convolutional gain,” and we also discuss the-mostly moderate-decoder cost increase that is incurred by going from LDPC block to LDPC convolutional codes.
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Qi Zhang, Ng Chun Sum · 2004
Low-density parity-check (LDPC) codes are well known for their abilities to achieve near Shannon channel capacity limit and low decoding complexity compared with the turbo decoder. However, their encoding complexities grow with the square of the code length. In this paper, we proposed a type of LDPC product codes, which can significantly lower the encoding complexity at the expense of slight degradation in error-rate performance as well as slight increase in decoding complexity
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W.E. Ryan, Shu Lin · Cambridge University Press eBooks · 2009
Although a great deal of research effort has been expended on the design, construction, encoding, decoding, performance analysis, and applications of binary LDPC codes in communication and storage systems, very little has been done on nonbinary LDPC codes in these respects. The first study of nonbinary LDPC codes was conducted by Davey and MacKay in 1998. In their paper, they generalized the SPA for decoding binary LDPC codes to decode q-ary LDPC codes, called QSPA. Later, in 2000, MacKay and Davey introduced a fast-Fourier-transform (FFT)-based QSPA to reduce the decoding computational complexity of QSPA. This decoding algorithm is referred to as FFT-QSPA. MacKay and Davey's work on FFT-QSPA was further improved by Barnault and Declercq in 2003 and Declercq and Fossorier in 2007. Significant works on the design, construction and analysis of nonbinary LDPC codes didn't appear until the middle of 2000. Results in these works are very encouraging. They show that nonbinary LDPC codes have a great potential to replace widely used RS codes in some applications in communication and storage systems. This chapter is devoted to nonbinary LDPC codes.
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Qi, Z., Sum, N.C. · National University of Singapore · 2014
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Giovanni Cancellieri · Signals and communication technology · 2014
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William E. Ryan, Shu Lin, Stephen G. Wilson · Cambridge University Press eBooks · 2024
Channel coding lies at the heart of digital communication and data storage. Fully updated, including a new chapter on polar codes, this detailed introduction describes the core theory of channel coding, decoding algorithms, implementation details, and performance analyses. This new edition includes over 50 new end-of-chapter problems and new figures and worked examples throughout. The authors emphasize the practical approach and present clear information on modern channel codes, including turbo and low-density parity-check (LDPC) codes, detailed coverage of BCH codes, Reed-Solomon codes, convolutional codes, finite geometry codes, product codes as well as polar codes for error correction and detection, providing a one-stop resource for classical and modern coding techniques. Assuming no prior knowledge in the field of channel coding, the opening chapters begin with basic theory to introduce newcomers to the subject. Later chapters then extend to advanced topics such as code ensemble performance analyses and algebraic code design.
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Hyuntae Ahn, Inki Kim, Hee-Youl Kwak et al. · arXiv (Cornell University) · 2026
This paper studies the diversity of protographbased quasi-cyclic low-density parity-check (QC-LDPC) codes over nonergodic block-fading channels under iterative beliefpropagation decoding. We introduce diversity evolution (DivE), a Boolean-function-based analysis method that tracks how the fading dependence of belief-propagation messages evolves across decoding iterations. Under a Boolean approximation of block fading, DivE derives a Boolean fading function for each variable node (VN) output (i.e., the a-posteriori reliability after iterative decoding), from which the VN diversity order can be directly determined. Building on this insight, we develop a greedy blockmapping search that assigns protograph VNs to fading blocks so that all information VNs achieve full diversity, while including the minimum additional parity VNs when full diversity is infeasible at the nominal rate. Numerical results on the 5G New Radio LDPC codes show that the proposed search finds block mappings that guarantee full diversity for all information bits without modifying the base-graph structure, yielding a markedly steeper high-SNR slope and lower BLER than random mappings.
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Hyuntae Ahn, Inki Kim, Hee-Youl Kwak et al. · ArXiv.org · 2026
This paper studies the diversity of protographbased quasi-cyclic low-density parity-check (QC-LDPC) codes over nonergodic block-fading channels under iterative beliefpropagation decoding. We introduce diversity evolution (DivE), a Boolean-function-based analysis method that tracks how the fading dependence of belief-propagation messages evolves across decoding iterations. Under a Boolean approximation of block fading, DivE derives a Boolean fading function for each variable node (VN) output (i.e., the a-posteriori reliability after iterative decoding), from which the VN diversity order can be directly determined. Building on this insight, we develop a greedy blockmapping search that assigns protograph VNs to fading blocks so that all information VNs achieve full diversity, while including the minimum additional parity VNs when full diversity is infeasible at the nominal rate. Numerical results on the 5G New Radio LDPC codes show that the proposed search finds block mappings that guarantee full diversity for all information bits without modifying the base-graph structure, yielding a markedly steeper high-SNR slope and lower BLER than random mappings.
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Jaewha Kim, Jae-Won Kim, Jong‐Seon No · 2023
In this paper, we propose a new code design technique for GLDPC codes which we call partial doping. The proposed partial doping technique enables higher degrees of freedom in constructing protograph-based GLDPC codes. We optimize the partially-doped generalized LDPC codes over the binary erasure channels and the finite length analysis shows that it outperforms the regular LDPC codes for both code rates 1/2 and 1/4.
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Vibha Kulkarni, K. Jaya Sankar · 2015
Irregular Low-Density Parity-Check (LDPC) codes exhibit a performance extremely close to the Shannon capacity formula. In this paper, we presented a method of developing structured irregular LDPC codes from structured regular LDPC codes. The design is based on the expansion of the column-weight two LDPC codes. We used our proposed technique of developing a column-weight two structured regular LDPC codes based on Gray code representations and adapted the expansion method proposed in literature to convert regular codes into irregular ones, and it is noticed that there is an improvement in obtained code rates using the proposed technique. It is also found that encoding process is simpler and requires less memory.
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Yinchu Wang, Xiao Ma · SSRN Electronic Journal · 2023
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Juane Li, Shu Lin, Khaled Abdel-Ghaffar et al. · Cambridge University Press eBooks · 2016
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Juane Li, Shu Lin, Khaled Abdel-Ghaffar et al. · 2016
This paper presents a special type of LDPC codes with a structure related to but different from that of the spatially coupled LDPC codes. For an LDPC code of this type, its Tanner graph is composed of a set of small disjoint Tanner graphs which are connected together by a group of overall check-nodes, called global check-nodes. Codes of this type are called globally coupled LDPC codes and they perform well over both the additive Gaussian white noise and the binary-erasure channels. Furthermore, they are very effective at correcting erasures clustered in bursts. Two algebraic methods are presented for constructing these codes. A two-phase local/global iterative scheme for decoding these codes is presented. This decoding scheme allows correction of local random and global errors and/or erasures in two phases.
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Farzane Amirzade, Daniel Panario, Mohammad‐Reza Sadeghi · 2022 IEEE International Symposium on Information Theory (ISIT) · 2022
LDPC codes based on multi-edge protographs potentially have larger minimum distances compared to their counterparts, single-edge protographs. However, considering different features of their Tanner graph, such as short cycles, girth and other graphical structures, is harder than for Tanner graphs from single-edge protographs. Here, we provide a novel approach to construct the parity-check matrix of an LDPC code which is based on trades obtained from block designs. We employ our method to construct multi-edge quasi-cyclic (QC) LDPC codes.We use those trade-based matrices to define base matrices of multi-edge protographs. The construction of exponent matrices corresponding to these base matrices has less complexity than the ones proposed in the literature. We prove that these base matrices result in QC-LDPC codes with smaller lower bounds on the lifting degree than existing ones.
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