• Proceedings of the Korean Institute of Communication Sciences Conference
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• 1984.10a
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• pp.15-18
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• 1984

The majority - logic decoding algorithm for Geometry code is more simply imlemented than the known decoding algorithm for BCH codes. Thus, the moderate code word, Geometry codes provide rather effective error control. The purpose of this paper is to investigate the Reed - Muller code and to design the encoder and decoder circuit and to find the performance for (15, 11) Reed - muller code. Experimental results show that the system has not only single error - correcting ability but also good performance.

• Asia-pacific Journal of Multimedia Services Convergent with Art, Humanities, and Sociology
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• v.4 no.2
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• pp.369-378
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• 2014

The Reed-Muller code is one of the efficient algorithms for multiple bit error correction, however, its high-computation requirement inherent in the decoding process prohibits its use in practical applications. To solve this problem, this paper proposes a graphics processing unit (GPU)-based parallel error control approach using Reed-Muller R(r, m) coding for real-time wireless communication systems. GPU offers a high-throughput parallel computing platform that can achieve the desired high-performance decoding by exploiting massive parallelism inherent in the algorithm. In addition, we compare the performance of the GPU-based approach with the equivalent sequential approach that runs on the traditional CPU. The experimental results indicate that the proposed GPU-based approach exceedingly outperforms the sequential approach in terms of execution time, yielding over 70× speedup.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2010.10a
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• pp.162-164
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• 2010

Terrestrial trunked radio (TETRA) standard specifies shortened Reed-Muller (RM) codes as forward error correction means for control signals. In this paper, we compare decoding algorithms for RM codes in TETRA, in terms of performance and complexity trade-off. Belief propagation and majority logic decoding algorithms are selected for comparison.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.10 no.5
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• pp.209-217
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• 1985

Using the Reed-Muller Codes, the encoder and decoder system has been designed and tested in this paper. The error correcting capability of this code is [J/2} or less and the error correcting procedure can be implemented easily by using simple logic circuitry. The encoding and decoding circuits are obtained by the cyclic property and for the O15, 11) Reed-Muller code majority-logic decoding is taken. The performance is measured in error probability and weight destribution. The encoder and decoder system has been designed, implemented and interfaced with the microcomputer by using the 8255 chip. Experimental results show that the system has single error-correcting capability and total execution time for a data is about 70usec. When the probability of channel error is $10^{-6}$~$10^{-4}$ the system using the (15, 11) Reed-Muller code works very good.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.37 no.1A
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• pp.43-50
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• 2012

The use of an error-correcting code is essential in digital communication systems where the channel is noisy. Unless a receiver has accurate channel coding parameters, it becomes difficult to decode the digitized encoding bits correctly. In this paper, estimation algorithm for RM(Reed-Muller) codes using FHT (Fast Hadamard algorithm) is proposed. The proposed algorithm estimates the channel coding parameters of RM codes and then decodes the codes using the characteristic of FHT. And we also verify the algorithm by performing intensive computer simulation in additive white gaussian noise (AWGN) channel.

• Journal of electromagnetic engineering and science
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• v.3 no.1
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• pp.50-56
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• 2003

This paper proposes a coding scheme of control channel for mobile packet communication to maximize the minimum Hamming distance, which is based on shifting of basis vectors of Reed Muller code with optimized dynamic puncturing and/or(partial) sequence repetition. Since the maximum likelihood decoding can be performed using the extremely simple FHT(Fast Hadamard Transformation), it is suitable for real time optimum decoding of control channel information with very little complexity. We show applications of the proposed coding method to TFCI(Transport Format Combination Indicator) code in split and normal modes of 3GPP W-CDMA system. We also discuss how this method can reduce rate indication error over AWGN(Additive White Gaussian Noise) as well as fading channels when the proposed coding scheme is applied to 1xEV-DV system of $3^{rd}$TEX> generation partnership project 2(3GPP2) to indicate the data rate transmitted on the reverse traffic channel by a Mobile Station(MS).

• The Journal of Korean Institute of Communications and Information Sciences
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• v.29 no.8C
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• pp.1069-1075
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• 2004

In this paper, we show the equivalence between complementary code keying (CCK) codeword and coset of the first order Reed-Muller (RM) code with variables of three. The CCK codewords are Golay sequences which have peak-to-average power ratio (PAPR) of two at most and can correct one error. We propose a CCK-orthogonal frequency division multiplexing (OFDM) modem to reduce PAPR. Also, we present the performance improvement techniques by increasing the variables of four to correct three errors and reduce PAPR at least 9㏈ with this system. Although, two Fast Hadamard Transform (FHT) blocks of size 8 64 are required at the receiver, we reduce the complexity by using FHT blocks of size 8 64 and 2 4 without deteriorating the performance. We generalize our results that we may increase the variables of RM code to enhance the error correcting and PAPR reduction capabilities without increasing receiver's complexity.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.38C no.1
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• pp.109-117
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• 2013

Polar codes are the first provable error correcting code achieving the symmetric channel capacity in a wide case of binary input discrete memoryless channel(BI-DMC). However, finite length polar codes have an error floor problem with successive-cancellation list(SCL) decoder. From previous works, we can solve this problem by concatenating CRC(Cyclic Redundancy Check) codes. In this paper we propose to make polar codes having extended-minimum distance from original polar codes without outer codes using correlation with generate matrix of polar codes and that of RM(Reed-Muller) codes. And we compare performance of proposed polar codes with that of polar codes concatenating CRC codes.

• Journal of the Korean Mathematical Society
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• v.47 no.6
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• pp.1167-1182
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• 2010

We study codes meeting a generalized version of the Singleton bound for higher weights. We show that some of the higher weight enumerators of these codes are uniquely determined. We give the higher weight enumerators for MDS codes, the Simplex codes, the Hamming codes, the first order Reed-Muller codes and their dual codes. For the putative [72, 36, 16] code we find the i-th higher weight enumerators for i = 12 to 36. Additionally, we give a version of the generalized Singleton bound for non-linear codes.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.30 no.9C
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• pp.860-870
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• 2005

In this paper we propose a new method to derive GRM(Generalized Reed-Muller) coefacients for each $2^{n}$ polarities using cell of karnaugh map(k-map). Generally, there are the serial and parallel method to derive GRM coefficients. As a serial method, Green method generates GRM coefncients using transform matrix. And as a parallel method, Besslich algorithm produces GRM coefficients of each polarity using the generated anteriorly. Green's method generates GRM coefficients for n-variable by calculating transform matrix for one-variable and n-times kronecker product this matrix. And Besslich's method generates GRM coefficients of each polarity in order of Grey-code. But those methods have disadvantages that the number of variable exceeding four makes transform matrix large and there are so many operation steps. In this paper, GRM coefficients is generated by producing cell [$f_{i}$] minimizing variable on k-map and operating this cell [$f_{i}$] and transform matrix for one-variable. So, we can generate GRM coefficients of all polarities easily by using the proposed method.