• Journal of the Korean Society for Precision Engineering
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• v.20 no.10
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• pp.169-176
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• 2003

Genetic algorithm (GA), which has a powerful searching ability and is comparatively easy to use and also to apply, is in the spotlight in the field of the optimization for mechanical systems these days. However, it also contains some problems of slow convergence and low efficiency caused by a huge amount of repetitive computation. To improve the processing efficiency of repetitive computation, some papers have proposed paralleled GA these days. There are some cases that mention the use of gray code or suggest using gray code partially in GA to raise its slow convergence. Gray code is an encoding of numbers so that adjacent numbers have a single digit differing by 1. A binary gray code with n digits corresponds to a hamiltonian path on an n-dimensional hypercube (including direction reversals). The term gray code is open used to refer to a reflected code, or more specifically still, the binary reflected gray code. However, according to proposed reports, gray code GA has lower convergence about 10-20% comparing with binary code GA without presenting any results. This study proposes new Full gray code GA (FGGA) applying a gray code throughout all basic operation fields of GA, which has a good data processing ability to improve the slow convergence of binary code GA.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.17 no.5
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• pp.51-59
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• 2017

In this paper, we propose a gray code order of antenna index permutations for differential spatial modulation (DSM). To facilitate the implementation, the well-known Trotter-Johnson ranking and unranking algorithms are adopted, which result in similar computational complexity to the existing DSM that uses the lexicographic order. The signal-to-noise ratio gain achieved by the proposed gray code order over the lexicographic order is also analyzed and verified via simulations. Based on the gray coding framework, we further propose a diversity-enhancing scheme named intersected gray (I-gray) code order, where the permutations of active antenna indices are selected directly from the odd (or even) positions of the full permutations in the gray code order. From analysis and simulations, it is shown that the I-gray code order can harvest an additional transmit diversity order with respect to the gray code order.

• Journal of KIISE:Software and Applications
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• v.32 no.3
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• pp.141-152
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• 2005

A new emotion-based image retrieval method is proposed in this paper. Query emotion descriptors called query color code and query gray code are designed based on the human evaluation on 13 emotions('like', 'beautiful', 'natural', 'dynamic', 'warm', 'gay', 'cheerful', 'unstable', 'light' 'strong', 'gaudy' 'hard', 'heavy') when 30 random patterns with different color, intensity, and dot sizes are presented. For emotion image retrieval, once a query emotion is selected, associated query color code and query gray code are selected. Next, DB color code and DB gray code that capture color and, intensify and dot size are extracted in each database image and a matching process between two color codes and between two gray codes are peformed to retrieve relevant emotion images. Also, a new relevance feedback method is proposed. The method incorporates human intention in the retrieval process by dynamically updating weights of the query and DB color codes and weights of an intra query color code. For the experiments over 450 images, the number of positive images was higher than that of negative images at the initial query and increased according to the relevance feedback.

• Journal of Electrical Engineering and Technology
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• v.13 no.2
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• pp.943-952
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• 2018

This paper presents a new type of absolute rotary encoder system based on the affine n-digit N-ary gray code. A brief comparison of the existing encoder systems is carried out in terms of resolution, encoding and decoding principles and number of sensor heads needed. Using the proposed method, two different types of encoder disks are designed, namely, color-coded disk and grayscale coded disk. The designed coded disk pattern is used to manufacture 3 digit 3 ary and 2 digit 5 ary grayscale coded disks respectively. The manufactured disk is used with the light emitter and photodetector assembly to design the entire encode system. Experimental analysis is done on the designed prototype with LabVIEW platform for data acquisition. A comparison of the designed system is done with the traditional binary gray code encoder system in terms of resolution, disk diameter, number of tracks and data acquisition system. The resolution of the manufactured system is 3 times higher than the conventional system. Also, for a 5 digit 5 ary coded encoder system, a resolution approximately 100 times better than the conventional binary system can be achieved. In general, the proposed encoder system gives $(N/2)^n$ times better resolution compared with the traditional gray coded disk. The miniaturization in diameter of the coded disk can be achieved compared to the conventional binary systems.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.647-655
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• 2016

Let H be a graph, and $k{\geq}{\chi}(H)$ an integer. We say that H has a cyclic Gray code of k-colourings if and only if it is possible to list all its k-colourings in such a way that consecutive colourings, including the last and the first, agree on all vertices of H except one. The Gray code number of H is the least integer $k_0(H)$ such that H has a cyclic Gray code of its k-colourings for all $k{\geq}k_0(H)$. For complete bipartite graphs, we prove that $k_0(K_{\ell},r)=3$ when both ${\ell}$ and r are odd, and $k_0(K_{\ell},r)=4$ otherwise.

• Korean Journal of Optics and Photonics
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• v.19 no.1
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• pp.60-67
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• 2008

An all-optical 4-bit Gray code to binary coded decimal (BCD) converter by means of commercially available numerical analysis tool (VPI) was demonstrated, for the first time to our knowledge. Circuit design approach was modified appropriately in order to fit the electrical method on an all-optical logic circuit based on a cross gain modulation (XGM) process so that signal degradation due to the non-ideal optical logic gates can be minimized. Without regenerations, Q-factor of around 4 was obtained for the most severely degraded output bit (least significant bit-LSB) with 2.5 Gbps clean input signals having 20 dB extinction ratio. While modifying the two-level simplification method and Karnaugh map method to design a Gray code to BCD converter, a general design concept was also founded (one-level simplification) in this research, not only for the Gray code to BCD converter but also for any general applications.

• ETRI Journal
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• v.28 no.3
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• pp.291-300
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• 2006

A simple and general bit log-likelihood ratio (LLR) expression is provided for Gray-coded rectangular quadrature amplitude modulation (R-QAM) signals. The characteristics of Gray code mapping such as symmetries and repeated formats of the bit assignment in a symbol among bit groups are applied effectively for the simplification of the LLR expression. In order to reduce the complexity of the max-log-MAP algorithm for LLR calculation, we replace the mathematical max or min function of the conventional LLR expression with simple arithmetic functions. In addition, we propose an implementation algorithm of this expression. Because the proposed expression is very simple and constructive with some parameters reflecting the characteristic of the Gray code mapping result, it can easily be implemented, providing an efficient symbol de-mapping structure for various wireless applications.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.12 no.3
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• pp.216-223
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• 1987

This paper presents an analysis of the effects of statistically independent channel errors on the mean-squared error performance of image transform coding systems. The analysis is discussed for several different stochasic statistics of the quantizer input valuse. The stochastic distributions under consideration here are Laplacian, Gaussian and uniform. For each case of the distributions, we evaluate the MSE performance when NBC, FBC, MDC and Gray code respectively is employed for encoding the quantized values of the transformed coeffecients into the corresponding code words. The result of this study shows that what code is desired to be chosen to minimize the MSE for the given stochastic distributions of the quantizer input values.

• Journal of Broadcast Engineering
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• v.17 no.5
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• pp.876-890
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• 2012

In this paper, we investigated the performances of the distributed video codec with adaptive Gray code to apply for frame-difference signal. That is, the best cases and the worst cases were analyzed and compared by considering the statistical characteristics of the frame difference signal in view of the Gray code allocation. Through computer simulations, if 9-bit data for frame difference signal is generated for luminance signal with 8-bit definition and so n-bit is allocated to the quantized coefficient, we were able to find the best method to reduce the virtual channel noise by adding $256+2^{9-n-1}$ to the frame difference signal. Through computer simulation with test video sequences, it was shown that the performance difference between the best cases and the worst cases is larger than about 1.5dB at same rate. It is expected that the results in this paper are applicable for the transform-domain scheme as well as the pixel-domain scheme.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.158.1-158
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• 2001

An algorithmic gray code analog-to-digital converter (ADC), which is based on gray coding, is proposed in this article. The realization method makes use of a MOS triangular function circuit to provide a high-speed operation and low accumulated error. The proposed ADC is simple, small in size and suitable for fabrication using a standard CMOS process. Simulation results showing the performances of the proposed circuit are also included.