• Bulletin of the Korean Mathematical Society
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• v.36 no.2
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• pp.247-257
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• 1999

In this article, we give an example of local derivation, that is not derivation, on the algebra F(x1,…, xn) of rational functions in x1, …, xn over an infinite field F, and show that if X is a set of symbols and {x1,…, xn} is a finite subset of X, n$\geq$1, then each local derivation of F[x1,…, xn] into F[X] is a F-derivation and each local derivation of F[X] into itself is also a F-derivation.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.30A no.3
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• pp.16-33
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• 1993

New decoding algorithm of double-error-correction Reed-Solmon codes over GF(2$^{8}$) for optical compact disks is proposed and decoding algorithm of RS codes with triple-error-correcting capability is presented in this paper. First of all. efficient algorithms for estimating the number of errors in the received code words are presented. The most complex circuits in the RS decoder are parts for soving the error-location numbers from error-location polynomial, so the complexity of those circuits has a great influence on overall decoder complexity. One of the most known algorithm for searching the error-location number is Chien's method, in which all the elements of GF(2$^{m}$) are substituted into the error-location polynomial and the error-location number can be found as the elements satisfying the error-location polynomial. But Chien's scheme needs another 1 frame delay in the decoder, which reduces decoding speed as well as require more stroage circuits for the received ocode symbols. The ther is Polkinghorn method, in which the roots can be resolved directly by solving the error-location polynomial. Bur this method needs additional ROM (readonly memory) for storing tthe roots of the all possible coefficients of error-location polynomial or much more complex cicuit. Simple, efficient, and high speed method for solving the error-location number and decoding algorithm of double-error correction RS codes which reudce considerably the complexity of decoder are proposed by using Hilbert theorems in this paper. And the performance of the proposed decoding algorithm is compared with that of conventional decoding algorithms. As a result of comparison, the proposed decoding algorithm is superior to the conventional decoding algorithm with respect to decoding delay and decoder complexity. And decoding algorithm of RS codes with triple-error-correcting capability is presented, which is suitable for error-correction in digital audio tape, also.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.5C
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• pp.443-451
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• 2003

We propose an appropriate approach of defining the linear complexities (LC) of sequences over unknown symbol set. We are able to characterize those p-ary sequences whose R-tuple versions now eve. GF($p^{R}$ ) have the same characteristic polynomial as the original with respect to any basis. This leads to a construction of $p^{R}$ -ary sequences whose characteristic polynomial is essentially over GF(p). In addition, we can characterize those $p^{R}$ -ary sequences whose characteristic polynomials are uniquely determined when symbols are represented as R-tuples over GF(p) with respect to any basis.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.44 no.3 s.357
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• pp.61-67
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• 2007

In Reed Solomon decoder, when there are more than 4 error symbols, we usually use Chien search machine to find those error positions. In this case, classical method requires complex and relatively slow digital circuitry to implement it. In this paper we propose New fast and cost effective Chien search machine design method using Galois Subfield transformation. Example is given to show the method is working well. This new design can be applied to the case where there are more than 5 symbol errors in the Reed-Solomon code word.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.43 no.3 s.345
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• pp.49-58
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• 2006

In this paper, a curve-fitting channel estimation method is proposed for orthogonal frequency division multiplexing (OFDM) system in a time-varying frequency-selective fading channel. The method can greatly improve channel state information (CSI) estimation accuracy by performing smoothing and interpolation through consecutive curve-fitting processes in both time domain and frequency domain. It first evaluates least-squares (LS) estimates using pilot symbols and then the estimates are approximated to a polynomial with proper degree in the LS error sense, starting from one preferred domain in which pilots we densely distributed. Smoothing, interpolation, and prediction are performed subsequently to obtain CSI estimates for data transmission. The channel estimation processes are completed by smoothing and interpolating CSI estimates in the other domain once again using the channel estimates obtained in one domain. The performance of proposed method is influenced heavily on the time variation and frequency selectivity of channel and pilot arrangement. Hence, a proper degree of polynomial and an optimum approximation interval according to various system and channel conditions are required for curve-fitting. From extensive simulation results in various channel environments, we see that the proposed method performs better than the conventional methods including the optimal Wiener filtering method, in terms of the mean square error (MSE) and bit error rate (BER).

• The Journal of Korean Institute of Communications and Information Sciences
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• v.25 no.3B
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• pp.472-486
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• 2000

This paper analysis the performance of joint receiving structure consisting of the decorrelating multiuser detection and beamfromenr-RAKE receive for DS-CDMA communication systems. In asynchronous transmission as the number of simultaneous users increase. the capacity of CDMA system becomes severly reduced due to the nonideal orthogonality between user-assigned PN sequences and improper power control. Accordingly, the CDMA receiving system becomes vulnerable to the multiple access interferences and the near-far problem under multipath fading channel environment. To withstand these undesired performance degradations, this paper proposes the new type of multiuser detection which has a form of the hybrid structure of concatenating beamformer-RAKE receiver and decorrelating multiuser detection. the beam former-RAKE receiver performs temporal and spatial diversity combining with alleviating fading effect and suppressing undesired interferences, and the multiuser detection plays a role of making the receiver robust to the near-far problem. Regarding the individual merit on the usage of either multiuser detection or beamformer-RAKE receiver, the hybrid one is expected to produce the enhanced performance in multipath fading CDMA channel. However major drawback of using decorrelating multiuser detection for practical deployment is arised from its computational complexity , which is exponentially increased as more number of users and transmitted symbols involve. To diminish the computational complexity, this paper exploits an efficient block Toeplitz inversion technique using matrix Levinson polynomial will be introduced. And this paper provided the mathematical analysis to show the efficiency of the proposed joint structure under the multipath propagation environment. And results of a series of exhaustive computer simulations are presented in order to demonstrate the overall performance of the proposed hybrid structure in multipath fading CDMA channel.

• Current Optics and Photonics
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• v.2 no.5
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• pp.422-430
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• 2018

Rolling shutter operation of CMOS cameras can be utilized in optical camera communications in order to transmit data from an LED to mobile devices such as smart-phones. From temporally modulated light, a spatial flicker pattern is obtained in the captured image, and this is used for signal recovery. Due to the degradation of rolling shutter images caused by light smear, motion blur, and focus blur, the conventional decoding schemes for rolling shutter cameras based on the pattern width for 'OFF' and 'ON' cannot guarantee robust communications performance for practical uses. Aside from conventional techniques, such as polynomial fitting, histogram equalization can be used for blurry light mitigation, but it requires additional computation abilities resulting in burdens on mobile devices. This paper proposes a transition-based decoding scheme for rolling shutter cameras in order to offer simple and robust data decoding in the presence of image degradation. Based on the designed synchronization pulse and modulated data symbols according to the LED dimming level, the decoding process is conducted by observing the transition patterns of two sequential symbol pulses. For this, the extended symbol pulse caused by consecutive symbol pulses with the same level determines whether the second pulse should be included for the next bit decoding or not. The proposed method simply identifies the transition patterns of sequential symbol pulses other than the pattern width of 'OFF' and 'ON' for data decoding, and thus, it is simpler and more accurate. Experimental results ensured that the transition-based decoding scheme is robust even in the presence of blurry lights in the captured image at various dimming levels