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ON A RECURSIVE FORM OF welch-berlekamp algorithm

IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 1993年第1期E76A卷 132-138页

作者： ARAKI, K TAKADA, M MORII, M Saitama Univ Urawa-shi Japan

In this paper a recursive form of welch-berlekamp (W-B) algorithm is provided which is a novel and fast decoding algorithm.

关键词： INFORMATION THEORY AND CODING THEORY welch-berlekamp algorithm HALVING-DOUBLING STRATEGY RECURSIVE STRUCTURE

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Incomplete locator polynomials and redundant iterations reduction in the welch-berlekamp algorithm

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IEE PROCEEDINGS-COMMUNICATIONS 1998年第6期145卷 402-405页

作者： Xin, D Fudan Univ Shanghai 200433 Peoples R China

A concept named 'incomplete locator polynomial' is introduced as a replacement for the traditional approach. Theorems for finding the incomplete locators were established when the welch-berlekamp algorithm was employed for decoding Reed-Solomon codes, and an incomplete iteration strategy of decoding Reed-Solomon codes, based on finding incomplete locator polynomials is presented, by which the redundant iterations in the welch-berlekamp algorithm are reduced significantly.

关键词： error correcting codes Reed-Solomon codes welch-berlekamp algorithm

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Grobner basis view of welch-berlekamp algorithm for Reed-Solomon codes

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IEE PROCEEDINGS-COMMUNICATIONS 1995年第6期142卷 349-351页

作者： Jennings, SM S BANK UNIV SCH COMP INFORMAT SYST & MATHVLSILONDON SE1 0AAENGLAND

Grobner bases of modules have been used to provide a unifying theoretical approach to the various algorithms for solving the key equation Omega(x) = S(x)Lambda(x) (mod x(2t)) in decoding Reed-Solomon codes. The welch-berlekamp algorithm solves a different key equation based on rational interpolation. When the solution is viewed as a canonical element in a module M, the algorithm is developed by considering Grobner bases with respect to different term orders.

关键词： polynomials interpolation welch-berlekamp algorithm Interpolation and function approximation (numerical analysis) canonical element Grobner bases Codes Reed-Solomon codes key equation decoding rational interpolation

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On decoding byeyond BCH bound using Reed-Solomon decoder based on welch-berlekamp algorithm

On decoding byeyond BCH bound using Reed-Solomon decoder bas...

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9th World Multi-Conference on Systemics, Cybernetics and Informatics

作者： Mohri, Masami Morii, Masakatu Univ Tokushima Dept Informat Sci & Intelligent Syst Tokushima 7708506 Japan

ISBN: (纸本)9789806560567

It is known that the t-error-correcting Reed-Solomon (RS) code can detect more than t errors with high probability, and it is remarkable in case of t >= 5. In order to correct the (t + mu)-error, the histogram decoding algorithm and extended Euclidian decoding algorithm have been proposed. These methods use syndrome-type decoder such as BM algorithm or Euclidian algorithm. In this paper, we give the condition for detecting the (t + mu)-error by welch-berlekamp (WB) algorithm which is known as the non-syndrome decoder. Furthermore, we propose a hard-decision decoding method for correcting (t + 1)-error using histogram decoding and WB algorithm.

关键词： Reed-Solomon codes welch-berlekamp algorithm (t plus mu)-error histogram decoding algorithm

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ON THE PERFORMANCE AND COMPLEXITY OF A GENERALIZED MINIMUM DISTANCE REED-SOLOMON DECODING algorithm

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INTERNATIONAL JOURNAL OF SATELLITE COMMUNICATIONS 1994年第4期12卷 333-359页

作者： PEILE, RE Racal Research Ltd Worton Grange Reading Berkshire RG2 OSB U.K.

The article reports on the characteristics of an algorithm that implements generalized minimum distance (GMD) decoding of Reed-Solomon codes. The algorithm uses the novel welch-berlekamp (WB) algorithm, as modified by Tze-Hua, in order to minimize the complexity of the decoder. Both the WB algorithm and the GMD extension of the WB algorithm are described in outline. The performance of the GMD algorithm was simulated on AWGN channels and fading channels. Results are presented both for RS and concatenated RS codes. The gains over conventional decoding are larger for fading channels than for AWGN conditions but seem useful in all cases. The complexities of the GMD algorithm and the WB algorithm are analysed and compared to that of conventional RS decoding algorithms.

关键词： ERROR CORRECTION REED-SOLOMON CODES CONCATENATED CODES REED-MULLER CODES DECODING algorithmS GENERALIZED MINIMUM DISTANCE DECODING welch-berlekamp algorithm berlekamp-MASSEY algorithm

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Reliability-based forward recursive algorithms for algebraic soft-decision decoding of Reed-Solomon codes

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IEEE TRANSACTIONS ON COMMUNICATIONS 2007年第7期55卷 1273-1278页

作者： Xia, Haitao Cruz, J. R. Link A Media Devices Corp Santa Clara CA 95051 USA Univ Oklahoma Sch Elect & Comp Engn Norman OK 73019 USA

We propose efficient forward recursive algorithms for algebraic soft-decision list decoding of Reed-Solomon codes, which utilize channel reliability information, and outperform the Koetter-Vardy (KV) algorithm with lower decoding latency. We evaluate the performance of the proposed decoding algorithms on additive white Gaussian noise and partial response channels. Simulation results show that we can achieve better performance on a modified extended-extended partial response class 4 channel than on the best possible performance of the KV algorithm, as given by the asymptotic bound for high-rate codes.

关键词： generalized minimum distance algorithm Guruswami-Sudan (GS) algorithm Koetter-Vardy (KV) algorithm list decoding polynomial interpolation Reed-Solomon (RS) codes soft-decision decoding welch-berlekamp algorithm

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High-speed decoding algorithm for international standard code of user's data in optical disk

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PROGRESS IN NATURAL SCIENCE 1998年第2期8卷 208-213页

作者： Xin, DJ Fudan Univ Shanghai 200433 Peoples R China

A concept of incomplete error locator polynomial is introduced instead of the traditional error locator of indicating all errors included in a received word, and a new strategy based on finding incomplete error locators of error patterns is presented, with which the famous welch-berlekamp algorithm is reformed such that the number of iterations matches the weight of errors in decoding, and the decoding speed is thus increased to a great extent.

关键词： optical disk error correcting code welch-berlekamp algorithm international standard

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Simplified Procedure for Decoding Nonsystematic Reed-Solomon Codes over GF(2^m) Using Euclid's algorithm and the Fast Fourier Transform

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IEEE TRANSACTIONS ON COMMUNICATIONS 2009年第6期57卷 1588-1592页

作者： Lin, Tsung-Ching Chen, Pe-Din Truong, Trieu-Kien I Shou Univ Dept Informat Sci Dashu Township 84001 Kaohsiung Cty Taiwan

Gao's algorithm similar to Shiozaki's algorithm for decoding nonsystematic Reed-Solomon (RS) codes which is a subclass of the redundant residue polynomial codes is considered here. This algorithm computes the message polynomial directly without explicitly finding the error-locator polynomial and error-evaluator polynomial. In this letter, a simplified decoding algorithm to correct both errors and erasures is used in conjunction with Gao's algorithm for efficiently decoding RS codes. In addition, we show that the extended Gao algorithm similar to the Shiozaki-Truong-Cheung-Reed algorithm significantly reduces the decoding complexity.

关键词： Discrete Fourier transform erasure Euclidean algorithm Fermat number Reed-Solomon codes transform welch-berlekamp algorithm

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On the minimal interpolation problem and decoding RS codes

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IEEE TRANSACTIONS ON INFORMATION THEORY 2000年第4期46卷 1573-1580页

作者： Ma, X Wang, XM Xidian Univ Natl Key Lab ISN Xian 710071 Peoples R China

Some properties of the minimal interpolation problem are investigated, from which a simple proof of the validity of the welch-berlekamp algorithm is presented. A new keg equation is derived, which is closely related t... 详细信息

关键词： decoding Reed-Solomon codes Euclidean algorithm key equation minimal interpolation problem Reed-Solomon codes welch-berlekamp algorithm

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Analytic approach to coset-leader decoding leads to extension of the welch-berlekamp theorem

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JOURNAL OF STATISTICAL PLANNING AND INFERENCE 2001年第2期94卷 371-380页

作者： Xin, DJ Fudan Univ Shanghai 200433 Peoples R China

This paper provides a complete proof of the welch-berlekamp theorem on which the welch-berlekamp algorithm was founded. By introducing an analytic approach to coset-leader decoders for Reed-Solomon codes, the welch-berlekamp key-equation of error corrections is enlarged and a complete proof of the welch-berlekamp theorem is derived in a natural way, and the theorem is extended such that the BCH-bound constraint is moved. (C) 2001 Published by Elsevier Science B.V.

关键词： coset-leader decoding cyclic codes Reed-Solomon codes welch-berlekamp algorithm

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