• Journal of the Institute of Electronics Engineers of Korea TC
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• v.49 no.5
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• pp.15-20
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• 2012

In this paper, we show new method to find the error locations of received Reed-Solomon code word. New design is much faster and has much simpler logic circuit than the former design method. This optimization was possible by very simplified square/$X^4$ calculating circuit, parallel processing and not using the very complex Divider. The Reed Solomon decoder using this new Chien Machine can be applicated for data protection of almost all digital communication and consumer electronic devices.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.25 no.5B
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• pp.966-973
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• 2000

In this paper, we propose a novel RS decoder design yielding smallr circuit size shorter coding latency. The proposed architecture of RS decoder has the following two features. First, circuit size reduced by using Euclid algorithm with mutual operation between cells. Second, coding latency is reduced by using higher frequency than syndrome and error value calculation block. We performed simulation with C language and MATLAB in order to verify the decoding algorithm and implemented using FPGA chips in VHDL.

• 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.

• 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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.10 no.3
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• pp.147-152
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• 1985

The error-trapping decoder is constructed for the (7, 3) Reed-Solomon code. The syndrome resister is constructed with the encoder and the substanial test logic circuits. The element of GF(8) is represented by the triple D-flip-floops. The hardware is constructed. And it is controlled by the micro computer(Apple II). The time for the encoding and the decoding were $350\musecs and 910u secs respectively. The experimental results show that the two symbol errors were corrected and 4-bit-binary-burst errors were also corrected.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.46 no.4
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• pp.40-45
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• 2009

In This Paper, New Efficient Arithmatic Logic Unit Design for Calculating Error Values of Reed Solomon Decoder is described. Error Values are solved by solving Linear system of Equations, So called Newtonian set of identity equations. Here We Need Galois Multiplier, Adder, Divider on GF($2^8$) field. We prove how the Hardware circuits are improved better than the classical circuits. The method to find error location is not covered here, since many other researchers have already deeply studied it.

• 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.

• Journal of Navigation and Port Research
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• v.28 no.1
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• pp.23-29
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• 2004

This paper deals with Reed-Solomon Coding for EUROFIX system EUROFIX is an integrated navigation and communication system, which combines Differential GNSS and Loran-C EUROFIX transmits DGNSS(Differential Global Navigation Satellite Systems) (data by pulse position modulation of Loran-C pulses. Loran-C system is regarded as a satellite backup system in recent. And now, it is important to detect and correct much errors in communication systems. Error corrections or correction algorithm is actively studied nowadays because of this. In this paper, we study and design encoder and decoder of Reed Solomon Code using Finite Galois Field Fourier Transformation for error corrections in EUROFIX data transmission. Through extensive simulation, the designed Reed Solomon code is shown to be effective for error correction in EUROFIX data transmission.

• Proceedings of the Korea Electromagnetic Engineering Society Conference
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• 2005.11a
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• pp.131-136
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• 2005

UWB is the most spotlighted wireless technology that transmits data at very high rates using low power over a wide spectrum of frequency band. UWB technology makes it possible to transmit data at rate over 100Mbps within 10 meters. To preserve important header information, MB-OFDM UWB adopts Reed-Solomon(23,17) code. In receiver, RS decoder needs high speed and low latency using efficient hardware. In this paper, we suggest the architecture of RS decoder for MB-OFDM UWB. We adopts Modified-Euclidean algorithm for key equation solver block which is most complex in area. We suggest pipelined processing cell for this block and show the detailed architecture of syndrome, Chien search and Forney algorithm block. At last, we show the hardware implementation results of RS decoder for ASIC implementation.