• Journal of the Korean Institute of Telematics and Electronics B
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• v.30B no.11
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• pp.17-26
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• 1993

In this paper, a VlSI architecture for Reed-Solomon (RS) decoder based on the Berlekamp algorithm is proposed. The proposed decoder provided both erasure and error correcting capability. In order to reduc the chip area, we reformulate the Berlekamp algorithm. The proposed algorithm possesses a recursive structure so that the number of cells for computing the errata locator polynomial can be reduced. Moreover, in our approach, only one finite field multiplication per clock cycle is required for implementation, provided an improvement in the decoding speed, and the overall architecture features parallel and pipelined structure, making a real time decoding possible. From the performance evaluation, it is concluded that the proposed VLSI architecture is more efficient in terms of VLSI implementation than the rcursive architecture based on the Euclid algorithm.

• Journal of the Korean Institute of Telematics and Electronics C
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• v.36C no.3
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• pp.8-16
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• 1999

This paper describes a VLSI design of Reed-Solomon(RS) decoder using the modified Euclid algorithm, with the main theme focused on the $\textit{GF}(2^8)$. To get area-efficient design, a number of new architectures have been devised with maximal register and Euclidean ALU unit sharing. One ALU is shared to replace 18 ALUs which computes an error locator polynomial and an error evaluation polynomial. Also, 18 registers are shared to replace 24 registers which stores coefficients of those polynomials. The validity and efficiency of the proposed architecture have been verified by simulation and by FLEX$^TM$ FPGA implementation in hardware description language VHDL. The proposed Reed-Solomon decoder, which has the capability of decoding RS(208,192,17) and RS(182,172,11) for Digital Versatile Disc(DVD), has been designed by using O.6$\mu\textrm{m}$ CMOS TLM Compass$^TM$ technology library, which contains totally 17k gates with a core area of 2.299$\times$2.284 (5.25$\textrm{mm}^2$). The chip can run at 20MHz while the DVD requirement is 3.74MHz.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.8 no.1
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• pp.170-178
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• 2004

In this work a high speed 8-error correcting Reed-Solomon decoder is designed using the modified Euclid algorithm. Decoding algorithm of Reed-Solomon codes consists of four steps, those are, compute syndromes, find error-location polynomials, decide error-locations, and determine error values. The decoding speed is increased and the latency is reduced by using the parallel architecture in the syndrome generator and a faster clock speed in the modified Euclid algorithm block. In addition. the error locator polynomial in Chien search block is separated into even and odd terms to increase the overall speed of the decoder. All the functionalities of the decoder are verified first through C++ programs. Verilog is used for hardware description, and then the decoder is synthesized with a $.25{\mu}m$ CMOS TML library. The functionalities of the chip is also verified through test vectors. The clock speed of the chip is 250MHz, and the maximum data rate is 1Gbps.

• 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.