• Journal of the Institute of Electronics Engineers of Korea SD
• /
• v.47 no.11
• /
• pp.54-64
• /
• 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 Korea Institute of Information and Communication Engineering
• /
• v.8 no.1
• /
• pp.170-178
• /
• 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.

• Journal of the Korean Institute of Telematics and Electronics C
• /
• v.36C no.6
• /
• pp.37-43
• /
• 1999

Two-way addressing method has been proposed for efficient VLSI implementation of Euclidean calculation circuit for pipelined Reed-Solomon decoder. This new circuit is operating with single clock while exploiting maximum parallelism, and uses register addressing instead of register shifting to minimize the switching power. Logic synthesis shows the circuit with the new scheme takes 3,000 logic gates, which is about 40% reduction from the previous 5,000 gate implementation. Computer simulation also shows the power consumption is about 3mW. The previous implementation with multiple clock consumed about 5mW.

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

• Journal of Advanced Navigation Technology
• /
• v.16 no.2
• /
• pp.190-196
• /
• 2012

In this paper, we propose an improved error correction code in order to improve the performance of digital modems for HF data communications and verify the performance of the proposed scheme. The proposed scheme employs outer Reed-Solomon codes concatenated with inner convolutional codes. Numerical results show that the proposed system significantly improves the bit error rate performance compared to the conventional PACTOR-III modems. Hence, the proposed system can improve the bandwidth efficiency of digital modems for HF data communications.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.28 no.6A
• /
• pp.405-413
• /
• 2003

This paper presents new DSP (Digital Signal Processor) instructions and their hardware architecture to efficiently implement RS (Reed-Solomon) codecs, which is one of the most widely used FEC (Forward Error Control) algorithms. The proposed DSP architecture can implement various primitive polynomials by program, and thus, hardwired codecs can be replaced. The new instructions and their hardware architecture perform GF (Galois Field) operations using the proposed GF multiplier and adder. Therefore, the proposed DSP architecture can significantly reduce the number of clock cycles compared with existing DSP chips. It can perform RS decoding rate of up to 228.1 Mbps on 130MHz DSP chips.

• Journal of the Institute of Electronics Engineers of Korea SD
• /
• v.42 no.7 s.337
• /
• pp.27-36
• /
• 2005

This paper presents an area-efficient architecture to implement the high-speed Reed-Solomon(RS) decoder, which is used in a variety of communication systems such as wireless and very high-speed optical communications. We present the new pipelined-recursive Modified Euclidean(PrME) architecture to achieve high-throughput rate and reducing hardware-complexity using folding technique. The proposed pipelined recursive architecture can reduce the hardware complexity about 80$\%$ compared to the conventional systolic-array and fully-parallel architecture. The proposed RS decoder has been designed and implemented with the 0.13um CMOS technology in a supply voltage of 1.2 V. The result show that total number of gate is 393 K and it has a data processing rate of S Gbits/s at clock frequency of 625 MHz. The proposed area-efficient architecture can be readily applied to the next generation FEC devices for high-speed optical communications as well as wireless communications.

• Journal of the Institute of Electronics Engineers of Korea SD
• /
• v.46 no.11
• /
• pp.48-55
• /
• 2009

This paper presents a high-speed Forward Error Correction (FEC) architecture based on three-parallel Reed-Solomon (RS) decoder for next-generation 100-Gb/s optical communication systems. A high-speed three-parallel RS(255,239) decoder has been designed and the derived structure can also be applied to implement the 100-Gb/s RS-FEC architecture. The proposed 100-Gb/s RS-FEC has been implemented with 0.13-${\mu}m$ CMOS standard cell technology in a supply voltage of 1.2V. The implementation results show that 16-Ch. RS-FEC architecture can operate at a clock frequency of 300MHz and has a throughput of 115-Gb/s for 0.13-${\mu}m$ CMOS technology. As a result, the proposed three-parallel RS-FEC architecture has a much higher data processing rate and low hardware complexity compared with the conventional two-parallel, three-parallel and serial RS-FEC architectures.

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

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.32 no.8A
• /
• pp.820-826
• /
• 2007

This paper proposes an enhanced degree computationless modified Euclid's(E-DCME) algorithm and its architecture for Reed-Solomon decoders. The proposed E-DCME algorithm has shorter critical path delay that is $T_{mult}+T_{add}+T_{mux}$ compared with the existing modified Euclid's algorithm and the degree computationless modified Euclid's(DCME) algorithm since it uses new initial conditions. The proposed E-DCME architecture employing a systolic array requires only 2t-1 clock cycles to solve the key equation without initial latency. In addition, the E-DCME architecture consisting of 3t basic cells has regularity and scalability since it uses only one processing element. The E-DCME architecture using the $0.18{\mu}m$ Samsung standard cell library consists of 18,000 gates.