• Journal of KIISE:Computing Practices and Letters
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• v.6 no.4
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• pp.448-456
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• 2000

As the system complexity increases, it is important to develop high-level verification techniques for fast and efficient design verifications. In this research, fast verification techniques for hardware and software co-design systems have been developed by using logic emulation and algorithm-level simulation. For faster and superior functional verification, we partition the system being designed into hardware and software parts, and implement the divided parts by using interface modules. We also propose several hardware design techniques for efficient hardware emulation. Experimental results, obtained by using a Reed-Solomon decoder system, show that our new verification methodology is more than 12,000 times faster than a commercial simulation tool for the modified Euclid's algorithm block and the overall verification time is reduced by more than 50%.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.23 no.6
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• pp.1575-1582
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• 1998

Reed-Solomon(RS) code which is especially effective against burst error is studied as a forward error correction technique in this ppaer. The circuits of RS encoder and decoder for ASIC implementation are designed and presented employing modified Euclid's algorithm. The functionalities of the designed circuits are verified though C programs which simulates the circuits over the various errors and erasures. The pipelined circuits using systolic arrays are designed for ASIC realization in VHDL, and verified through the logic simulations. Finally the circuit synthesis of RS encoder and decoder can be achieved.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2001.10a
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• pp.648-651
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• 2001

This paper describes the 8-error-correction (204, 188) Reed-Solomon Decode. over GF(2$^{8}$ ) for a satellite communication. It is synthsized using a CMOS library. Decoding algorithm of Reed-Solomon codes consists of four steps which are to compute syndromes, to find error-location polynomial, to decide error-location, and to slove error-values. The decoder is designed using Modified Euclid algorithm in this paper. First of all, The functionalities of the circuit are verified through C++ programs, and then it is designed in Verilog HDL. It is verified through the logic simulations of each blocks. Finally, The Reed-Solomon Decoder is synthesized with Synopsys Tool.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.41 no.3
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• pp.187-187
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• 2004

In this paper, we present an efficient architecture of a versatile Reed-Solomon (RS) decoder which can be programmed to decode RS codes continuously with my message length k as well as any block length n. This unique feature eliminates the need of inserting zeros for decoding shortened RS codes. Also, the values of the parameters n and k, hence the error-correcting capability t can be altered at every codeword block. The decoder permits 3-step pipelined processing based on the modified Euclid's algorithm (MEA). Since each step can be driven by a separate clock, the decoder can operate just as 2-step pipeline processing by employing the faster clock in step 2 and/or step 3. Also, the decoder can be used even in the case that the input clock is different from the output clock. Each step is designed to have a structure suitable for decoding RS codes with varying block length. A new architecture for the MEA is designed for variable values of the t. The operating length of the shift registers in the MEA block is shortened by one, and it can be varied according to the different values of the t. To maintain the throughput rate with less circuitry, the MEA block uses both the recursive technique and the over-clocking technique. The decoder can decodes codeword received not only in a burst mode, but also in a continuous mode. It can be used in a wide range of applications because of its versatility. The adaptive RS decoder over GF($2^8$) having the error-correcting capability of upto 10 has been designed in VHDL, and successfully synthesized in an FPGA chip.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.41 no.3
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• pp.29-38
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• 2004

In this paper, we present an efficient architecture of a versatile Reed-Solomon (RS) decoder which can be programmed to decode RS codes continuously with my message length k as well as any block length n. This unique feature eliminates the need of inserting zeros for decoding shortened RS codes. Also, the values of the parameters n and k, hence the error-correcting capability t can be altered at every codeword block. The decoder permits 3-step pipelined processing based on the modified Euclid's algorithm (MEA). Since each step can be driven by a separate clock, the decoder can operate just as 2-step pipeline processing by employing the faster clock in step 2 and/or step 3. Also, the decoder can be used even in the case that the input clock is different from the output clock. Each step is designed to have a structure suitable for decoding RS codes with varying block length. A new architecture for the MEA is designed for variable values of the t. The operating length of the shift registers in the MEA block is shortened by one, and it can be varied according to the different values of the t. To maintain the throughput rate with less circuitry, the MEA block uses both the recursive technique and the over-clocking technique. The decoder can decodes codeword received not only in a burst mode, but also in a continuous mode. It can be used in a wide range of applications because of its versatility. The adaptive RS decoder over GF(2$^{8}$ ) having the error-correcting capability of upto 10 has been designed in VHDL, and successfully synthesized in an FPGA chip.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.43 no.4 s.346
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• pp.38-48
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• 2006

In this paper, we developed a hardware architecture of Reed-Solomon RS(255,239) decoder for the DMB mobile terminals. The DMB provides multimedia broadcasting service to mobile terminals, hence it should have small dimension for low power and short decoding delay for real-time processing. We modified Euclid algorithm to apply it to the key equation solving which is the most complicated part of the RS decoding. We also designed a small finite field divider to avoid the use of large Inverse-ROM table, and it consumed 17 clocks. After synthesis with Synopsis on Samsung STD130 $0.18{\mu}m$ Standard Cell library, the Euclid block had 30,228 gates and consumed 288 clocks, which gave the 25% reduced area compared to other existing designs. The size of the entire RS decoder was about 45,000 gates.

• 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.

• Proceedings of the IEEK Conference
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• 2001.09a
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• pp.245-248
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• 2001

본 논문에서는 연집 오류(burst error)에 우수한 정정 능력을 보이는 고속 RS(Reed-Solomon) 복호기를 제안한다. 제안된 RS 복호기는 RS(n, k, t); (37 < n ≤ 255, 21 < k ≤ 239, t = 8)의 사양을 지원하며 수정 유클리드 알고리즘(modified Euclid´s algorithm)을 이용한 시스톨릭 어레이(systolic array) 방식의 병렬처리 구조로 설계되었다. 고속 RS 복호기의 효율적인 VSLI 설계를 위하여 새로운 방식의 수정 유클리드 알고리즘 연간 회로를 제안한다. 제안된 수정 유클리드 알고리즘 회로는 2t + 1의 연산 지연 시간을 갖으며 기존 구조의 연산 지연 시간인 3t + 37에 비하여 t = 8 인 경우 약 72%의 연산 지연이 감소하였다. 제안된 구조를 VHDL을 이용하여 설계하였으며 SAMSUNG 0.5㎛(KG80) 라이브러리를 이용하여 논리 합성과 타이밍 검증을 수행하였다. 합성된 RS 복호기의 총 게이트 수는 약 77,000 개이며 최대 80MHz의 동작 속도를 나타내었다.

• Proceedings of the IEEK Conference
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• 2003.07b
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• pp.1027-1030
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• 2003

In this paper, we designed GF(2$^{m}$ ) inversion and division processor for Elliptic Curve Cryptographic system. The processor that has 191 by m value designed using Modified Euclid Algorithm. The processor is designed using 0.35 ${\mu}{\textrm}{m}$ CMOS technology and consists of about 14,000 gates and consumes 370 mW. From timing simulation results, it is verified that the processor can operate under 367 Mhz clock frequency due to 2.72 ns critical path delay. Therefore, the designed processor can be applied to Elliptic Curve Cryptographic system.

• Proceedings of the IEEK Conference
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• 2003.07a
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• pp.549-552
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• 2003

In this paper, an efficient architecture of a versatile Reed-Solomon (RS) decoder is designed, where the message length k as well as the block length n can be variable. The decoder permits 3-step pipelined processing based on the modified Euclid's algorithm(MEA). A new architecture for the MEA is designed for variable values of error correcting capability t. To maintain the throughput rate with less circuitry, the MEA block uses both the recursive and the overclocking technique. The decoder can decode a codeword received not only in a burst mode, but also in a continuous mode. It can be used in a wide range of applications due to its versatility. A versatile RS decoder over GF(2$^{8}$ ) having the error-correcting capability of up to 10 has been designed in VHDL, and successfully synthesized in an FPGA chip.