• Korean Journal of Mathematics
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• v.10 no.1
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• pp.89-95
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• 2002

We present a simple but new way of decoding the binary Golay code.

• Journal of the Korean Society for Nondestructive Testing
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• v.14 no.3
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• pp.185-193
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• 1994

Conventional ultrasonic flaw detection system uses a large amplitude narrow pulse to excite a transducer. However, these systems are limited in pulse energy. An excessively large amplitude causes a dielectric breakage of the transducer, and an excessively long pulse causes decrease of the resolution. Using the pulse compression, a long pulse of pseudorandom signal can be used without sacrificing resolution by signal correlation. In the present work, the pulse compression technique was implemented into an ultrasonic system. Golay code was used as a pseudorandom signal in this system, since pair sum of autocorrelations has no sidelobe. The equivalent input pulse of the Golay code was derived to analyze the pulse compression system. Throughout the experiment, the pulse compression technique has demonstrated for its improved SNR(signal to noise ratio) by reducing the system's white noise. And the experimental data also indicated that the SNR enhancement was propotional to the square root of the code length used. The technique seems to perform particularly well with highly energy-absorbent materials such as polymers, plastics and rubbers.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.25 no.3A
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• pp.391-398
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• 2000

In this paper, MRC(Maximum Ratio Combine) diversity, (23, 12) Golay code, (7, 5) Reed-Solomon code, and (3, 1) majority selection code are employed to improve the performance of DS/CDMA BRSK in Nakagami fading channel. and MRC diversity combined with other coding techniques is suggested, with which, the performance of DS/CDMA BRSK is compared and analyzed. Also, system required Eb/N0 to meet BER=10-5 for multi user data communication is obtained according to each techniques. From the results, when each techniques is employed to DS/CDMA BRSK system. coding employed system shows better performance than diversity employed system. Especially, Golay code shows better performance than oter codes. also MRC diversity is employed, the number of multiple access user to meet data communication requirement of BER=10-5 can accomodate up to 8 users. and when each code is employed, Golay code, majority selection code, and Reed-Solomon code shows the capacity of 14, 12, and 10 user respectively. But MRC diversity combined with coding techniques can reduce restriction of multiple access user. However, it is desirable these combined technique are employed according to service types and requirements provided.

• Proceedings of the KIEE Conference
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• 2001.11c
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• pp.187-190
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• 2001

A new ultrasound imaging technique based on simultaneous multiple transmit focusing using orthogonal modified Golay codes is presented. modified Golay codes are used to increase signal-to-noise-ratio(SNR) and maximize the transmit power efficiency(TPE). Conventional Golay codes consist of a pair of complementary codes with same length and can be compressed into a delta-like signal due to their complementary property. In the present work, two modified Golay codes focused at different depths are transmitted at the same time, which are mutually orthogonal. On receive, these orthogonal modified Golay codes are separately compressed into two short pulses and individually focused. These two focused beam are combined to form a frame of image with improved lateral resolution. Computer simulations are performed to verity the proposed method improves the lateral resolution of image compared with the conventional echo system.

• Journal of the Institute of Convergence Signal Processing
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• v.9 no.4
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• pp.304-312
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• 2008

Orthogonal codes like Walsh and Golay codes may have large correlation value when they are not synchronized, hence they are seldom used in asynchronous CDMA systems. Wysocki[1] showed that by multiplying the original Walsh-Hadamard matrix with an orthogonal transformation matrix the resultant matrix sustains orthogonality between row vectors and their cross-correlation can be reduced. Soberly and Wysocki[2] proposed similar scheme on Golay codes. This implies that using the proper orthogonal transformation cross-correlation of Walsh and Golay codes can be reduced, and the transformed codes can be used for user separation in the CDAM reverse link. In this paper we discuss cross-correlation related parameters which affect the performance of an asynchronous CDMA link, and we investigate the correlation properties of the transformed codes. When we designed orthogonal transformation matrices for Walsh and Golay codes, we minimized the maximum value of aperiodic cross-correlation of the codes ($ACC_{max}$) or the mean square value of the aperiodic cross-correlation($R_{cc}$) with preserving the orthogonality of the modified codes. We also evaluate the asynchronous CDMA system that uses the transformed Walsh and Golay codes.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.27 no.3A
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• pp.180-187
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• 2002

The decoding method using covering polynomials is an extended form of error-trapping decoding, and is a simple and effective means to implement decoders for cyclic codes. Covering polynomials can be used for soft-decision decoding as well as for decoding beyond the bounded distance of the code. The implementation complexity is proportional to the number of covering polynomials employed. In this paper, the soft-decision decoding procedure using covering polynomials is described, and the procedure is applied to the [23,12] Golay code. A new set of covering polynomials is derived for the procedure, which is presented as a generalized closed-form solution. The set can be efficiently utilized for decoding a class of cyclic codes including the Golay code. Computer simulation of the described procedure is performed to show the trade-offs between the decoder performance and complexity. It is demonstrated that soft-decision decoding of the Golay code using the derived set of covering polynomials has less than 0.2dB deviation from the optimal performance of maximum-likelihood decoding, with a reduced complexity when compared to the Chase Algorithm 2 combined with hard-decision decoding that has nearly identical performance.

• Journal of the Korean Mathematical Society
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• v.39 no.2
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• pp.289-317
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• 2002

We associate binary codes to polynomials over fields of characteristic two and show that the binary Golay codes are associated to the Mathieu group polynomials in characteristics two. We give two more polynomials whose Galois group in $M_{12}$ but different self-orthogonal binary codes are associated. Also, we find a family of $M_{24}$-coverings which includes previous ones.

• Journal of Satellite, Information and Communications
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• v.6 no.2
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• pp.125-130
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• 2011

In this paper, there was compared to the performance of the Auto Correlation Feature of each code using Spreading code for improving the data transmission technology in T-DMB disaster broadcasting. Generally, wireless mobile communication environment such as DMB occur the Inter Code Interference and the Multi-Path Interference in the process of the identification of the transmitter from the receiver. To solve this problem, spreading code technology was able to improve the security property. Also, it will be able to use in many fields of signal processing, because to control a period of the code can be variable. Therefore, in this paper, we studied to compare the performance of excellent orthogonal Golay code, Kasami code and ZCD(Zero Correlation Duration) code.

• Proceedings of the KOSOMBE Conference
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• v.1998 no.11
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• pp.115-116
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• 1998

Pulse echo techniques have been used for the conventional medical ultrasound imaging systems. However, their resolution is limited in the transmitted signal power. To overcome this limit, pulse compression method used in the radar systems was proposed. This system transmits a continuous coded signal and then compresses the received signal into the short and high resolution pulse by using correlator. The reflectors can be detected by cross-correlation between the transmitted signal and the received signal with the depth information. In this paper, we will present a comparative study of the performances of the most common sequences(pseudo-chirp, m-sequences, modified Golay code). The best result for improving resolution is obtained with the modified Golay Code.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.16 no.7 s.98
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• pp.690-696
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• 2005

It is very important to reduce the PAPR(Peak to Average Power Ratio) in the OFDM(Orthogonal Frequency Division Multiplexing) communication system. The proposed method in this paper is an effective PAPR reduction method using the Golay complementary codes without my side information. There are some PAPR reduction methods with the complementary code pairs or sequences. They are usually a type of the forward ewer correction codes so that they produce more redundancies and lower down the code rate. Because of this, the information rate may be cut down or more bandwidth must be required. In this paper, we propose a PAPR reduction method that uses the multi-phase complementary code f3r converting the 4-QAM into 16-QAM constellation. It does not change the code rate and does not require the side information.