• 대한수학회보
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• 제36권2호
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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.

• 전자공학회논문지A
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• 제30A권3호
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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.

• 한국통신학회논문지
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• 제28권5C호
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• pp.443-451
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• 2003

본 논문에서는 임의의 심볼 집합 상의 수열의 선형복잡도를 정의한다. 또한 본 논문에서는 기저의 선택과 상관없이 자신의 GF($p^{k}$ ) 상의 R-tuple 수열이 자신과 같은 특성다항식을 갖는 $p^{R}$-ary 수열의 특성을 밝히며 이는 결과적으로 GF(p) 상의 특성다항식을 갖는 $p^{+}$ -ary 수열의 생성을 가능하게 한다. 마지막으로 심볼이 GF(p) 상의 R-tuple로 표현될 때 기저의 선택과 무관하게 유일한 특성다항식을 갖는 $p^{R}$-ary 수열의 특성을 밝힌다.

• 대한전자공학회논문지TC
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• 제44권3호
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• pp.61-67
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• 2007

리드솔로몬 복호기에서 4중 오류 이상의 오류치와 위치를 발견해 정정시는 보통 치엔탐색기를 사용한다. 이때 기존의 방법은 회로량이 많고 지연시간이 길어 비효율적이었다. 본 논문에서는 갈로이스 부분장을 이용 이 탐색기를 속도도 빠르고 회로량도 대폭 줄인 새로운 효율적 탐색기회로 설계법을 제시한다. 본 논문에서는 4중 오류위치를 정확히 추출함을 보였으나, 이새 설계된 탐색기회로는 5중이상의 오류위치도 정확히 찾을 수 있는 설계이다. 새로운 회로는 정확히 오류위치를 발견할 수 있음이 예를 통해 검증되었다.

• 대한전자공학회논문지TC
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• 제43권3호
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• pp.49-58
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• 2006

본 논문에서는 시변 주파수 선택적 페이딩 채널에서 OFDM (orthogonal frequency division multiplexing) 시스템을 위한 curve-fitting 채널추정 방법을 제안한다. 제안된 방법은 시간영역 및 주파수영역에서 1차원 curve-fitting을 통하여 smoothing과 interpolation을 순차적으로 수행함으로써 채널추정 정확도를 크게 개선할 수 있다. 먼저, 파일럿 심벌들을 사용하여 LS(least-Square) 추정치를 구하고, 이를 바탕으로 파일럿 밀도가 상대적으로 높은 영역을 선택하여 최소자승오차 기준에 따라 적절한 차수의 다항식으로 1차원 curve-fitting을 수행한다. 다음으로, 이 다항식을 이용하여 주어진 범위 내에 존재하는 LS 추정치들을 smoothing하고, interpolation 또는 prediction을 통하여 데이터 전송을 위하여 필요한 채널추정치들을 구한다. 이어서, 선택된 영역에서 얻어진 채널추정치들을 나머지 영역에서 또 다른 다항식을 사용하여 동일한 과정으로 1차원 curve-fitting을 통하여 smoothing과 interpolation을 수행함으로써 시간영역 및 주파수영역에서의 채널추정을 완료한다. 모의실험을 통하여 다양한 채널환경에서 MSE (mean square error) 및 BER (bit error rate) 성능을 분석한 결과, 제안된 방법이 기존의 채널추정 방법들에 비하여 월등히 우수하며, 최적의 Wiener 필터링 방법보다도 우수함을 보였다.

• 한국통신학회논문지
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• 제25권3B호
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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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• 제2권5호
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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