• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.785-794
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• 2013

Soon after Lee and O'Sullivan proposed a new interpolation algorithm for algebraic soft-decision decoding of Reed-Solomon codes, there have been some attempts to apply a coordinate transformation technique to the new algorithm, with a remarkable complexity reducing effect. In this paper, a conceptually simple way of applying the transformation technique to the interpolation algorithm is proposed.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.24 no.8A
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• pp.1238-1244
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• 1999

In this paper, a new design of a triple-erroe-correcting (TEC) Reed-Solomon decoder is presented based on direct decoding method which is more efficient for the case of relatively small error correction capability. The proposed decoder requires only 9 GF(2m) multipliers in obtaining the error-locator polynomial and the error-evaluator polynomial, whereas other decoders needs 24 multipliers. Thus, the attractive feature of this decoder is its remarkable simplicity from the point of view of implementation. Futhermore, the proposed TEC Reed-Solomon decoder has very simple control circuit and short decoding delay. Therefore this decoder can be implemented by simple hardware and also save buffer memory which stores received sequence.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.30A no.11
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• pp.21-28
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• 1993

Decoding algorithm of noncyclic Reed-Solomon codes consists of four steps which are to compute syndromes, to find error-location polynomial, to decide error-location, and to solve error-values. There is a decoding method by which the computation of both error-location polynomial and error-evaluator polynimial can be avoided in conventional decoding methods using Euclid algorithm. The disadvantage of this method is that the same amount of computation is needed that is equivalent to solve the avoided polynomial. This paper considers the division method on polynomial on GF(2$^{m}$) systematically. And proposes a novel method to find error correcting polynomial by simple mathematical expression without the same amount of computation to find the two avoided polynomial. Especially. proposes the method which the amount of computation to find F (x) from the division M(x) by x, (x-1),....(x--${\alpha}^{n-2}$) respectively can be avoided. By applying the simple expression to decoding procedure on RS codes, propses a new decoding algorithm, and to show the validity of presented method, computer simulation is performed.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.36 no.4C
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• pp.191-196
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• 2011

In this paper, we propose a design method of Reed-Solomon (23, 17) decoder for UWB using direct decoding method. The direct decoding algorithm is more efficient for the case of relatively small error correction capability. The proposed decoder requires only 9 $GF(2^m)$ multipliers in obtaining the error-locator polynomial and the error-evaluator polynomial, whereas other decoders need about 20 multipliers. Thus, the attractive feature of this decoder is its remarkable simplicity from the point of view of hardware implementation. Futhermore, the proposed decoder has very simple control circuit and short decoding delay. Therefore this decoder can be implemented by simple hardware and also save buffer memory which stores received sequence.

• The Transactions of the Korea Information Processing Society
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• v.7 no.1
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• pp.306-312
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• 2000

In this paper, the efficient architecture of small Reed-solomon architecture is suggested. Here, 3-stage pipeline is adopted. In decoding, error-location polynomials are obtained by BMA using fast iteration method, and syndrome polynomials, where calculation complexity is required, are obtained by parallel calculation using ROM table, and the roots of error location polynomial are calculated by ROM table using Chein search algorithm. In the suggested decoder, it is confirmed that 3 symbol random errors can be corrected and 124Mbps decoding rate is obtained using 25 Mhz system clock.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.47 no.11
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• pp.54-64
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• 2010

Reed-Solomon (RS) codes are the most widely used error correcting codes in digital communications and data storage. Recently, Sudan found algorithm of list decoder for RS codes. List decoder has larger decoding radius than conventional hard-decision decoding algorithms and return more than one candidate polynomial. But, the algorithm includes interpolation and factorization step that demand massive computations. In this paper, an efficient architecture and processing schedule are proposed. The architecture consists of R-MAC, memories, and control unit. The R-MAC computes both of RC and PU steps that are main part of the factorization algorithm. The proposed architecture can achieve higher hardware utilization efficiency (HUE) and throughput by using efficient processing schedule and memory architecture. Also, the architecture can be designed flexibly with scalability for various applications. We design and synthesize our architecture using Dongbu-Anam $0.18{\mu}m$ standard cell library and the maximum clock frequency is 330MHz.

• Journal of the Korean Institute of Telematics and Electronics
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• v.26 no.2
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• pp.10-17
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• 1989

The Berlekamp-Massey algorithm, the method of using the Euclid algorithm, and Fourier transforms over a finite field can be used for the decoding of Reed-Solomon codes (called RS codes). RS codes can also be decoded by the algorithm that was developed by Peterson and refined by the Gorenstein and Zierler. However, the decoding of RS codes using the Peterson-Gorenstein-Zieler algorithm offers sometimes computational or implementation advantages. The decoding procedure of the double-error correcting (31,27) Rs code over the symbol field GF ($2^5$) will be analyized in this paper. The complete analysis, gate array design, and implementation for encoder/decoder pair of (31.27)RS code are performed with a strong theoretical justification.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.18 no.10
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• pp.1495-1507
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• 1993

In this paper, an implementation of RS (Reed-Solomon) code decoder for CDP (Compact Disc Player) using microprogramming method is presented. In this decoding strategy, the equations composed of Newton's identities are used for computing the coefficients of the error locator polynomial and for checking the number of erasures in C2(outer code). Also, in C2 decoding the values of erasures are computed from syndromes and the results of C1(inner code) decoding. We pulled up the error correctability by correcting 4 erasures or less. The decoder contains an arithmetic logic unit over GF(28) for error correcting and a decoding controller with programming ROM, and also microinstructions. Microinstructions are used for an implementation of a decoding algorithm for RS code. As a result, it can be easily modified for upgrade or other applications by changing the programming ROM only. The decoder is implemented by the Logic Level Modeling of Verilog HDL. In the decoder, each microinstruction has 14 bits( = 1 word), and the size of the programming ROM is 360 words. The number of the maximum clock-cycle for decoding both C1 and C2 is 424.

• Journal of the Semiconductor & Display Technology
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• v.13 no.4
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• pp.7-13
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• 2014

In this paper, an area-efficient degree-computationless modified Euclidean (DCME) algorithm is presented and implemented for high-speed Reed-Solomon (RS) decoder. The DCME algorithm can be used to solve the key equation in Reed-Solomon decoder to get the error location polynomial and the error value polynomial. A pipelined recursive structure is adopted for reducing the area of key equation solver (KES) block with sacrifice of an amount of decoding latency. For comparisons, KES block for RS(255,239,8) decoder with the proposed architecture is implemented using Verilog HDL and synthesized using Synopsys design tool and 65nm CMOS technology. The synthesis results show that the proposed architecture can be implemented with less gate counts than other existing DCME architectures.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.10 no.1
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• pp.3-11
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• 2000

AAL-1에서는 (128, 124) Reed-Solomon부호를 사용한 인터리버 및 디인터리버에 의해 ATM 셀에서 발생하는 오류를 정정하고 있다. Reed-Solomon부호의 복호법 중 직접복호법은 오류위치다항식의 계산없이 오류위치와 오류치를 알 수 있으며 유한체 GF(2m)의 표현에서 정규기저를 사용하면 곱셈과 나눗셈을 단순한게 비트 이동만으로 처리할 수 있다. 직접복호법과 정규기저를 사용하여 ATM 적응계층에 적용 가능한 (128, 124) Reed-Solomon부호의 복호기를 설계하고 VHDL로 시뮬레이션 하였으며 이 복호기는 동일한 복호회로에 의해 둘 또는 하나의 심벌에 발생한 오류를 정정할 수 있다.