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Weighted-Bit-Flipping-Based Sequential Scheduling decoding algorithms for LDPC Codes

MATHEMATICAL PROBLEMS IN ENGINEERING 2013年第1期2013卷 1-6页

作者： Zhu, Qing Wu, Le-nan Southeast Univ Sch Informat Sci & Engn Nanjing 210096 Jiangsu Peoples R China

Low-density parity-check (LDPC) codes can be applied in a lot of different scenarios such as video broadcasting and satellite communications. LDPC codes are commonly decoded by an iterative algorithm called belief propagation (BP) over the corresponding Tanner graph. The original BP updates all the variable-nodes simultaneously, followed by all the check-nodes simultaneously as well. We propose a sequential scheduling algorithm based on weighted bit-flipping (WBF) algorithm for the sake of improving the convergence speed. Notoriously, WBF is a low-complexity and simple algorithm. We combine it with BP to obtain advantages of these two algorithms. Flipping function used in WBF is borrowed to determine the priority of scheduling. Simulation results show that it can provide a good tradeoff between FER performance and computation complexity for short-length LDPC codes.

关键词： SEQUENTIAL scheduling decoding algorithms LOW density parity check codes THEORY of wave motion SIMULATION methods & models ARTIFICIAL satellites in telecommunication

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Method for correcting both errors and erasures of RS codes using error-only and erasure-only decoding algorithms

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ELECTRONICS LETTERS 2013年第15期49卷 940-U43页

作者： Lu, Erl-Huei Lu, Pen-Yao Chen, Tso-Cho Chang Gung Univ Dept Elect Engn Tao Yuan 333 Taiwan Univ Sci & Technol China Dept Avion Hengshan Township 31241 Hsinchu County Taiwan

A method for correcting both errors and erasures of Reed-Solomon (RS) codes using error-only and erasure-only decoding algorithms is proposed. First, the method removes the effect of erasures from syndromes, then it uses error-only and erasure-only correcting processes to correct errors and erasures, respectively;thus, the overall decoding complexity can be reduced substantially. Furthermore, with hardware implementation, the most time-consuming operations in these two processes can be calculated concurrently to obtain a significant reduction of decoding latency.

关键词： decoding algorithms REED-Solomon codes FINITE fields (Algebra) SIGNAL-to-noise ratio GAUSSIAN elimination

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Power error locating pairs

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DESIGNS CODES AND CRYPTOGRAPHY 2020年第8期88卷 1561-1593页

作者： Couvreur, Alain Panaccione, Isabella INRIA 1 Rue Honore Estienne OrvesCampus Ecole Polytech F-91120 Palaiseau France Ecole Polytech UMR 7161 CNRS LIX F-91128 Palaiseau France

We present a new decoding algorithm based on error locating pairs and correcting an amount of errors exceeding half the minimum distance. When applied to Reed-Solomon or algebraic geometry codes, the algorithm is a reformulation of the so-calledpower decodingalgorithm. Asymptotically, it corrects errors up to Sudan's radius. In addition, this new framework applies to any code benefiting from an error locating pair. Similarly to Pellikaan's and Kotter's approach for unique algebraic decoding, our algorithm provides a unified point of view for decoding codes with an algebraic structure beyond the half minimum distance. It permits to get an abstract description of decoding using only codes and linear algebra and without involving the arithmetic of polynomial and rational function algebras used for the definition of the codes themselves. Such algorithms can be valuable for instance for cryptanalysis to construct a decoding algorithm of a code without having access to the hidden algebraic structure of the code.

关键词： Error correcting codes Reed-Solomon codes Algebraic geometry codes decoding algorithms Power decoding Error correcting pairs Cyclic codes

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Min-Sum Algorithm Using Multi-Edge-Type Normalized Scheme for ATSC 3.0 LDPC Decoders

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IEEE TRANSACTIONS ON BROADCASTING 2020年第3期66卷 729-736页

作者： Gao, Na Xu, Yin He, Dazhi Park, Sung-Ik Hong, Hanjiang Ju, Hao Chen, Changwen Zhang, Wenjun Shanghai Jiao Tong Univ Sch Elect Engn Shanghai 200240 Peoples R China Elect & Telecommun Res Inst Broadcasting Syst Res Dept Daejeon 34129 South Korea SUNY Buffalo Dept Comp Sci & Engn Buffalo NY 14260 USA

To offer commercial LDPC decoders with better performance, in this paper, multi-edge-type (MET) normalized scheme is proposed to improve the performance of traditional min-sum algorithm (MSA) and its modified versions. With respect to sum-product algorithm (SPA), we firstly analyze and find out that the degradations of convergence in different edge types are distinct in MSA theoretically. To compensate the different degradations above, proposed MET-normalized scheme is used in normalized min-sum algorithm (MET-NMSA). In addition, MET-based density evolution (MET-DE) is also presented to search optimized MET-scaling factors for MET-NMSA. To further verify the validity of MET-normalized scheme, Advanced Television Systems Committee (ATSC) 3.0 LDPC codes are used to evaluate MET-NMSA in comparison with the conventional algorithms, i.e., normalized min-sum algorithm (NMSA), offset min-sum algorithm (OMSA) and variable-scaling normalized min-sum algorithm (VS-NMSA). Extensive simulation results show that MET-NMSA for ATSC 3.0 LDPC decoders has at most 1.53dB, 0.21dB and 0.35dB gain over NMSA, OMSA and VS-NMSA respectively when frame error rate (FER) is at 10(-4) level over additive white Gaussian noise (AWGN) channels using QPSK modulation.

关键词： decoding Phase change materials Manganese Iterative decoding Convergence Approximation algorithms ATSC 3 0 LDPC codes MET-normalized scheme decoding algorithms density evolution

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Multiple channel error-correction algorithms for LCC decoding of Reed-Solomon codes and its high-speed architecture design

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IET COMMUNICATIONS 2017年第9期11卷 1407-1415页

作者： Wang, Lingyu Zhang, Wei Wang, Yang Hu, Yan Liu, Yanyan Tianjin Univ Sch Elect Informat Engn Tianjin 300072 Peoples R China Nankai Univ Coll Elect Informat & Opt Engn Tianjin 300071 Peoples R China

Reed-Solomon (RS) code is one of the most widely used error control codes. The decoding algorithms of RS code can be briefly divided into hard-decision decoding (HDD) and algebraic soft-decision decoding (ASD). However, traditional RS decoding algorithms perform unsatisfactorily over bursty channel. Therefore, many modified RS decoding algorithms utilised in bursty channel decoding were proposed. However all of them are HDD and the computation is costly. In this study, the authors propose an ASD algorithm which can be utilised both in additive white Gaussian noise channel and bursty channel. In order to be utilised in multiple channel, the proposed algorithm combines original HDD-based low-complexity chase (HDD-LCC) and burst-error correcting (BC) together. What's more, BC is also modified by adding in the mechanism of pre-judgement to reduce the iterations of BC. The modified algorithm can give a coding gain reaching up to 0.1268 and 1.33dB compared with BC and HDD-LCC, respectively when symbol error rate (SER) is 10(-4) in bursty channel. The proposed RS decoder is implemented and synthesised with Semiconductor Manufacturing International Corporation 0.13-m CMOS technology library. The results show the proposed decoder can operate at 200MHz to achieve the throughput of 1.673Gbps.

关键词： Reed-Solomon codes error correction codes channel coding Gaussian channels multiple channel error correction algorithms LCC decoding Reed-Solomon codes high-speed architecture design RS code error control codes decoding algorithms hard-decision decoding HDD algebraic soft-decision decoding ASD RS decoding algorithms bursty channel bursty channel decoding additive white Gaussian noise channel Semiconductor Manufacturing International Corporation CMOS technology library

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LDPC Channel Coding in Ultraviolet Communication System 18

LDPC Channel Coding in Ultraviolet Communication System

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18th International Conference on Optical Communications and Networks (ICOCN)

作者： Wang, Weiwei Su, Ping Ma, Jianshe Tsinghua Univ Grad Sch Shenzhen Shenzhen 518055 Peoples R China Tsinghua Univ Dept Precis Instrument Beijing 100084 Peoples R China

ISBN: (纸本)9781728127644

Low-Density Parity-Check (LDPC) codes are applied into ultraviolet (UV) communication system. In this paper, LU decomposition algorithm is adopted as the channel coding method. Simulations are conducted to compare the performance of different LDPC decoding algorithms in UV communication system. The results show that the belief propagation (BP) based UV system has a better bit error ratio (BER) performance than the one with the bit flipping (BF) decoding algorithm. Moreover, communication system performance trade-offs among transmission distance, path loss, frame length and BER are studied.

关键词： LDPC codes UV communication LU decomposition decoding algorithms BER

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Sums of Key Functions Generating Cryptosystems 19th

Sums of Key Functions Generating Cryptosystems

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19th Annual International Conference on Computational Science (ICCS)

作者： Kalashnykova, Nataliya Avramenko, Viktor V. Kalashnikov, Viacheslav Univ Autonoma Nuevo Leon UANL Av Univ S-N San Nicolas De Los Garza 66455 Nuevo Leon Mexico Tecnol Monterrey ITESM Sur Av Eugenio Garza Sada 2501 Sur Monterrey 64849 NL Mexico Cent Econ & Math Inst CEMI Nakhimovsky Pr 47 Moscow 117418 Russia Sumy State Univ SumDU Rimsky Korsakov Str 2 UA-40007 Sumy Ukraine

ISBN: (纸本)9783030227500;9783030227494

The paper develops an algorithm based on derivative disproportion functions (DDF) for modeling a cryptosystem for transmitting and receiving devices. The transmitted symbols are encoded with the aid of sums of at least two of those functions weighted with random coefficients. Some important properties of the derivative disproportion functions are also discussed. Numerical experiments demonstrate that the algorithm is quite reliable and robust.

关键词： Cryptosystems Derivative disproportion functions (DDF) decoding algorithms

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decoding neuronal diversity in the developing cerebral cortex: from single cells to functional networks

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CURRENT OPINION IN NEUROBIOLOGY 2018年 53卷 146-155页

作者： Mancinelli, Sara Lodato, Simona IRCCS Humanitas Clin & Res Ctr Via Manzoni 56 I-20089 Rozzano Milan Italy Humanitas Univ Dept Biomed Sci Via Rita Levi Montalcini 4 I-20090 Pieve Emanuele Milan Italy

The neocortex is by far one of the most complex regions of the mammalian brain, characterized by an extraordinary diversity of neuronal and non-neuronal cell types, whose coordinated development and function guarantee the execution of high order cognitive, sensory, and motor behaviours. decoding its heterogeneity and understanding the molecular strategies upon which the cerebral cortex is built during development have been at the core of neuroscientists' work for decades. Here, we will focus on the current classification of neuronal types (both excitatory and inhibitory) of the neocortex in light of the insights provided by recent single-cell omit technologies, which have offered with unprecedented resolution an extended framework to interpret cortical diversity and its developmental origin. We will cover the impact of neuronal subtype identity on generating specific neuronal networks (neuron-to-neuron interaction), as well as their effect on the development of the non-neuronal populations in the cerebral cortex.

关键词： decoding algorithms BIODIVERSITY CEREBRAL cortex TRANSCRIPTOMES EXCITATORY amino acids

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Expander l₀-decoding

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APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS 2018年第3期45卷 642-667页

作者： Mendoza-Smith, Rodrigo Tanner, Jared Univ Oxford Math Inst Oxford OX2 6GG England

We introduce two new algorithms, Serial-l(0) and Parallel-l(0) for solving a large underdetermined linear system of equations y = Ax is an element of R-m when it is known that x is an element of R-n has at most k < m nonzero entries and that A is the adjacency matrix of an unbalanced left d-regular expander graph. The matrices in this class are sparse and allow a highly efficient implementation. A number of algorithms have been designed to work exclusively under this setting, composing the branch of combinatorial compressed-sensing (CCS). Serial-l(0) and Parallel-l(0) iteratively minimise parallel to y - A<(x)over cap>parallel to(0) by successfully combining two desirable features of previous CCS algorithms: the coordinate selection strategy of ER [1] for updating (x) over cap, and the parallel updating mechanism of SMP [2]. We are able to link these elements and guarantee convergence in O(dn log k) operations by introducing a randomised scaling of columns in A, with scaling chosen independent of the measured vector. We also empirically observe that the recovery properties of Serial-l(0) and Parallel-l(0) degrade gracefully as the signal is allowed to have its non-zero values chosen adversarially. Moreover, we observe Serial-l(0) and Parallel-l(0) to be able to solve large scale problems with a larger fraction of nonzeros than other algorithms when the number of measurements is substantially less than the signal length;in particular, they are able to reliably solve for a k-sparse vector x is an element of R-n from m expander measurements with n/m = 10(3) and k/m up to four times greater than what is achievable by l(1)-regularisation from dense Gaussian measurements. Additionally, due to their low computational complexity, Serial-l(0) and Parallel-l(0) are observed to be able to solve large problems sizes in substantially less time than other algorithms for compressed sensing. In particular, Parallel-l(0) is structured to take advantage of massively parallel architec

关键词： Compressed sensing Combinatorial compressed sensing decoding algorithms Dissociated signals Expander graphs

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Extracting multidimensional stimulus-response correlations using hybrid encoding-decoding of neural activity

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NEUROIMAGE 2018年第PartA期180卷 134-146页

作者： Dmochowski, Jacek P. Ki, Jason J. DeGuzman, Paul Sajda, Paul Parra, Lucas C. CUNY Dept Biomed Engn New York NY 10031 USA Neuromatters LLC New York NY 10038 USA Columbia Univ Dept Biomed Engn New York NY 10027 USA

In neuroscience, stimulus-response relationships have traditionally been analyzed using either encoding or decoding models. Here we propose a hybrid approach that decomposes neural activity into multiple components, each representing a portion of the stimulus. The technique is implemented via canonical correlation analysis (CCA) by temporally filtering the stimulus (encoding) and spatially filtering the neural responses (decoding) such that the resulting components are maximally correlated. In contrast to existing methods, this approach recovers multiple correlated stimulus-response pairs, and thus affords a richer, multidimensional analysis of neural representations. We first validated the technique's ability to recover multiple stimulus-driven components using electroencephalographic (EEG) data simulated with a finite element model of the head. We then applied the technique to real EEG responses to auditory and audiovisual narratives experienced identically across subjects, as well as uniquely experienced video game play. During narratives, both auditory and visual stimulus-response correlations (SRC) were modulated by attention and tracked inter-subject correlations. During video game play, SRC varied with game difficulty and the presence of a dual task. Interestingly, the strongest component extracted for visual and auditory features of film clips had nearly identical spatial distributions, suggesting that the predominant encephalographic response to naturalistic stimuli is supramodal. The diversity of these findings demonstrates the utility of measuring multidimensional SRC via hybrid encoding-decoding.

关键词： STIMULUS & response (Psychology) NEURAL physiology NEUROSCIENCES ELECTROENCEPHALOGRAPHY decoding algorithms

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