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GENERALIZED KEY-EQUATION OF REMAINDER decoding algorithm FOR REED SOLOMON CODES

IEEE TRANSACTIONS ON INFORMATION THEORY 1992年第6期38卷 1801-1807页

作者： MORII, M KASAHARA, M KYOTO INST TECHNOL DEPT ELECTR & INFORMAT SCIKYOTO 606JAPAN

A new key-equation of the remainder decoding algorithm is presented. It is noted that the key-equation presents a general relationship between the errors on the received codeword and the coefficients of the remainder polynomial. It is shown that we can derive several key-equations proposed by Welch-Berlekamp and others from our new key-equation. Furthermore useful properties of the key-equations in fast decoding of Reed-Solomon codes are given.

关键词： CODING THEORY decoding algorithm REED SOLOMON CODES REMAINDER decoding WELCH BERLEKAMP algorithm

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Step-by-step decoding algorithm for Reed-Solomon codes

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IEE PROCEEDINGS-COMMUNICATIONS 2000年第1期147卷 8-12页

作者： Chen, TC Wei, CH Wei, SW Natl Chiao Tung Univ Dept Elect Engn Hsinchu 30050 Taiwan Chung Hua Univ Dept Elect Engn Hsinchu 30067 Taiwan

A new step-by-step decoding algorithm for decoding Reed-Solomon codes over GF(2(m)) is presented. Based on several properties of the syndrome matrices, the new step-by-step decoding algorithm can directly determine whether every received symbol is an error locator, The detection of error location is based only on the determinant of a v x v syndrome matrix, where v is the number of errors. When an error location is found, its corresponding error value can also be determined by performing a determinant division operation between two syndrome matrices. The new decoding algorithm can significantly reduce computation complexity and improve the decoding speed compared with the conventional step-by-step decoding algorithm.

关键词： matrices decoding algorithms Reed-Solomon codes Determinants decoding algorithm Syndromes

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Dynamics of the finite Toda molecule over finite fields and a decoding algorithm

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PHYSICS LETTERS A 1998年第4期249卷 295-302页

作者： Nakamura, Y Mukaihira, A Osaka Univ Grad Sch Engn Sci Dept Informat & Math Sci Toyonaka Osaka 5608531 Japan

The finite Toda molecule over finite fields is introduced whose dynamics are completely classified by conserved quantities. The trajectories blow up in a finite time or are periodic. A BCH-Goppa decoding algorithm is designed. The number of Toda particles is congruent with the maximal number of errors to be decoded. (C) 1998 Elsevier Science B.V.

关键词： Qd algorithm Lattice Galois fields Congruent Finite dynamics molecules crystal lattices decoding algorithm

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An optimal decoding algorithm for Molecular Communications systems with noise, memory, and pulse width

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NANO COMMUNICATION NETWORKS 2016年 9卷 7-16页

作者： Wang, Xiayang Lu, Yi Higgins, Matthew D. Leeson, Mark S. Univ Warwick Sch Engn Coventry CV4 7AL W Midlands England Univ Warwick WMG Coventry CV4 7AL W Midlands England

Molecular Communications (MC) is a promising paradigm to achieve message exchange between nano-machines. Due to the specific characteristics of MC systems, the channel noise and memory significantly influence the MC system performance. Aiming to mitigate the impact of these two factors, an adaptive decoding algorithm is proposed by optimising the symbol determination threshold. In this paper, this novel decoding scheme is deployed onto a concentration-based MC system with the transmitter emission process considered. To evaluate the performance, an information theoretical approach is developed to derive the Bit Error Rate (BER) and the channel capacity. Simulations are also carried out to verify the accuracy of these formulations, to compare the performance difference against other decoding schemes, and to illustrate the performance deviation caused by different designing of relevant parameters. Furthermore, the performance of MC systems with the distance unknown is also analysed. Comparisons between distance-pre-known and distance-unknown systems are provided. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Molecular Communications Molecule concentration decoding algorithm Bit Error Rate Capacity

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A Hardware decoding algorithm for Long-distance Transmission for Well Logging

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JOURNAL OF ENVIRONMENTAL AND ENGINEERING GEOPHYSICS 2012年第1期17卷 39-47页

作者： Cao, Ping Song, Ke-Zhu Yang, Jun-Feng Univ Sci & Technol China State Key Lab Particle Detect & Elect Hefei 230026 Peoples R China

Long-distance data transmission plays an important role in geophysical applications. This paper introduces a chip-encoded version of the Manchester-II decoding algorithm that can be used for long-distance transmission for well logging. It can be realized easily in a field programmable gate array (FPGA) hardware chip. We designed a wave tracking technique to optimize the algorithm's real-time decoding, adaptive capacity, and robust decoding. The algorithm could be divided into two modules, a data pre-processing module and a data decoding module, which is comprised of AMI code extraction and Manchester-II decoding. With the help of this algorithm, Manchester-II data transmitted via a 7,000 meter armored cable can be decoded in real time. Measurements in the lab and in situ show that communication systems based on this algorithm decoded correctly and achieved good bit error rate specifications. Compared to traditional methods using some specified encoding chips or digital signal processors, transmissions realized with this algorithm are less expensive and showed better adaptability and real-time performance. In addition to borehole geophysical applications, this algorithm can be used in environmental and engineering geophysical applications where data transmission over long distances is needed, whether on the surface or deep into the Earth.

关键词： decoding COMMUNICATION SYSTEMS decoding algorithm long distance transmission Remote WELLS Well logging adaptive capacity algorithms data transmission Field programmable gate arrays Computer hardware Real time

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Correcting capabilities of binary irregular LDPC code under low-complexity iterative decoding algorithm

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JOURNAL OF COMMUNICATIONS TECHNOLOGY AND ELECTRONICS 2016年第12期61卷 1432-1439页

作者： Rybin, P. S. Russian Acad Sci Kharkevich Inst Informat Transmiss Problems Moscow 127051 Russia

This paper deals with the irregular binary low-density parity-check (LDPC) codes and two iterative low-complexity decoding algorithms. The first one is the majority error-correcting decoding algorithm, and the second one is iterative erasure-correcting decoding algorithm. The lower bounds on correcting capabilities (the guaranteed corrected error and erasure fraction respectively) of irregular LDPC code under decoding (error and erasure correcting respectively) algorithms with low-complexity were represented. These lower bounds were obtained as a result of analysis of Tanner graph representation of irregular LDPC code. The numerical results, obtained at the end of the paper for proposed lower-bounds achieved similar results for the previously known best lower-bounds for regular LDPC codes and were represented for the first time for the irregular LDPC codes.

关键词： LDPC code irregular binary decoding algorithm iterative low-complexity errors erasures

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Low-complexity low-density parity check decoding algorithm for high-speed very large scale integration implementation

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IET COMMUNICATIONS 2012年第16期6卷 2575-2581页

作者： Angarita, F. Marin-Roig, J. Almenar, V. Valls, J. Univ Politecn Valencia Inst Telecomunicac & Aplicac Multimedia Gandia 46730 Spain

This study proposes a new low-complexity decoding algorithm for low-density parity check codes, which is a variation of the offset min-sum algorithm and achieves a similar performance with lower hardware cost. A finite precision study is presented and the hardware cost of the implementation of three very large scale integration architectures is evaluated. As a conclusion, the proposed algorithm achieves similar performance with an area saving of around 18, 10 and 14% for the memory-based partially parallel, fully parallel and sliced message passing implementations, respectively.

关键词： character parity check decoding algorithm Parity check Very large scale integration parity check codes valid parity check low density parity check codes

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Investigation into decoding algorithm for turbo codes

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ELECTRONICS LETTERS 2000年第9期36卷 809-810页

作者： Raphaeli, D Gurevitz, A Tel Aviv Univ Fac Engn Dept Elect Engn Syst IL-69978 Tel Aviv Israel

An investigation into the turbo decoder is presented. It was carried out to determine whether the decoded bit sequence constitutes a (at least) local maximum in the likelihood between possible codewords in the composite code trellis. The answer was obtained experimentally using a modified iterative turbo decoder. Results show that the turbo decoder does not necessarily lead to a maximum likelihood sequence estimator being realised for the composite code. Moreover, finding a closer code in a Euclidean distance sense only degrades the bit error rate of the system.

关键词： bit error rate BER modified iterative turbo decoder Euclidean distance probability composite code trellis error statistics maximum likelihood sequence estimation decoded bit sequence maximum likelihood sequence estimator decoding local maximum decoding algorithm turbo codes

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An Improved Low Complex Offset Min-Sum Based decoding algorithm for LDPC Codes

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MOBILE NETWORKS & APPLICATIONS 2019年第6期24卷 1848-1852页

作者： Roberts, Michaelraj Kingston Mohanram, S. Sudha Shanmugasundaram, N. Sri Eshwar Coll Engn Dept Elect & Commun Engn Coimbatore 641202 Tamil Nadu India

In recent times, many advanced wireless communication systems have adopted channel coding schemes to ease secure transmission and reception of wireless data over noisy perturbed channel conditions. Channel coding approaches using low-density parity-check (LDPC) codes are most interesting and fastest growing research areas in the domain of wireless communications. Due to its widespread popularity, adaptability and parallelism for cost-effective hardware implementations, LDPC codes are widely endorsed in a number of wireless communication standards. Over the years, many low complex decoding algorithms using LDPC codes were introduced to improve the data reliability of many wireless applications. This work introduces an efficient and robust offset min-sum decoding scheme for optimal decoding of LDPC codes. This improved approach introduces a new offset correction factor to suppress the error propagation during the approximation of high precision soft values within the given range boundary of signal strength-to-background noise ratio (SNR). The experimental results illustrate the competitive advantage of the proposed algorithm over several popular algorithms in terms of error rate performance, complexity reductions and convergence speed.

关键词： LDPC codes Wireless communication decoding algorithm Channel coding Computational complexity

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Modified UMP-BP decoding algorithm based on mean square error

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ELECTRONICS LETTERS 2004年第13期40卷 816-817页

作者： Kim, N Park, H ICU Sch Engn Taejon 305600 South Korea

The modified uniformly most powerful belief-propagation (UMP-BP) decoding algorithm is proposed. This utilises a new normalisation factor to diminish the error introduced by approximation of the soft values. The proposed algorithm shows better performance than the normalisation UMP-BP algorithm, and has the same complexity of implementation.

关键词： .LDPC codes decoding algorithm mean square error normalisation factor

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