• Proceedings of the KIEE Conference
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• 1998.11b
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• pp.575-578
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• 1998

In this paper, we propose a VLSI architecture of Reed-Solomon decoder. Our goal is the development of an architecture featuring parallel and pipelined processing to improve the speed and low power design. To achieve the this goal, we analyze the RS decoding algorithm to be used parallel and pipelined processing efficiently, and modified the Euclid's algorithm arithmetic part to apply the parallel structure in RS decoder. The overall RS decoder are compared to Shao's, and we show the 10% area efficiency than Shao's time domain decoder and three times faster, in addition, we approve the proposed RS decoders with Altera FPGA Flex 10K-50, and Implemeted with LG 0.6{\mu}$ processing.

• Journal of Integrative Natural Science
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• v.1 no.2
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• pp.149-159
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• 2008

We develop two algorithms that nd a minimal polynomial of a finite sequence. One uses Euclid's algorithm, and the other is in essence a minimal polynomial version of the Berlekamp-Massey algorithm. They are formulated naturally and proved algebraically using polynomial arithmetic. They connects up seamlessly with decoding procedure of alternant codes.

• 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.31 no.8C
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• pp.763-770
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• 2006

In this paper, a variable Reed-Solomon(RS) decoder with erasure decoding functionality is designed based on the modified Euclid's algorithm(MEA). The variability of the decoder is implemented through shortening and puncturing based on the RS(124, 108, 8) code, other than the primitive RS(255, 239, 8) code. This leads to shortening the decoding latency. The decoder performs 4-step pipelined operation, where each step is designed to be clocked by an independent clock. Thus by using a faster clock for the MEA block, the complexity and the decoding latency can be reduced. It can support both continuous- and burst-mode decoding. It has been designed in VHDL and synthesized in an FPGA chip, consuming 3,717 logic cells and 2,048-bit memories. The maximum decoding throughput is 33 MByte/sec.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.11 no.5
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• pp.17-30
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• 2001

In this paper, we implemented a scalar multiplier needed at an elliptic curve cryptosystem over standard basis in $GF(2^{163})$. The scalar multiplier consists of a radix-16 finite field serial multiplier and a finite field inverter with some control logics. The main contribution is to develop a new fast finite field inverter, which made it possible to avoid time consuming iterations of finite field multiplication. We used an algorithmic transformation technique to obtain a data-independent computational structure of the Extended Euclid GCD algorithm. The finite field multiplier and inverter shown in this paper have regular structure so that they can be easily extended to larger word size. Moreover they can achieve 100% throughput using the pipelining. Our new scalar multiplier is synthesized using Hyundai Electronics 0.6$\mu\textrm{m}$ CMOS library, and maximum operating frequency is estimated about 140MHz. The resulting data processing performance is 64Kbps, that is it takes 2.53ms to process a 163-bit data frame. We assure that this performance is enough to be used for digital signature, encryption & decryption and key exchange in real time embedded-processor environments.

• Proceedings of the IEEK Conference
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• 2000.06b
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• pp.262-265
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• 2000

This paper describes design of a (32, 28) Reed Solomon decoder for optical compact disk provides double error detecting and correcting capability. The most complex circuit in the RS decoder is part for solving the error location numbers from error location polynomial, and the circuit has great influence on overall decoder complexity. We use RAM based architecture with Euclid algorithm, Chien search algorithm and Forney algorithm. We have developed VHDL model and Performed logic synthesis using the SYNOPSYS CAD tool. Then, the RS decoder has been implemented with FPGA. The total umber of gate is about 11,000 gates and it operates at 20MHz.

• 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 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.