• Journal of the Korea Institute of Information and Communication Engineering
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• v.9 no.1
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• pp.188-198
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• 2005

The Goldschmidt iterative algorithm for finding a floating point square root calculated it by performing a fixed number of multiplications. In this paper, a variable latency Goldschmidt's square root algorithm is proposed, that performs multiplications a variable number of times until the error becomes smaller than a given value. To find the square root of a floating point number F, the algorithm repeats the following operations: $R_i=\frac{3-e_r-X_i}{2},\;X_{i+1}=X_i{\times}R^2_i,\;Y_{i+1}=Y_i{\times}R_i,\;i{\in}\{{0,1,2,{\ldots},n-1} }}'$with the initial value is $'\;X_0=Y_0=T^2{\times}F,\;T=\frac{1}{\sqrt {F}}+e_t\;'$. The bits to the right of p fractional bits in intermediate multiplication results are truncated, and this truncation error is less than $'e_r=2^{-p}'$. The value of p is 28 for the single precision floating point, and 58 for the doubel precision floating point. Let $'X_i=1{\pm}e_i'$, there is $'\;X_{i+1}=1-e_{i+1},\;where\;'\;e_{i+1}<\frac{3e^2_i}{4}{\mp}\frac{e^3_i}{4}+4e_{r}'$. If '|X_i-1|<2^{\frac{-p+2}{2}}\;'$ is true, $'\;e_{i+1}<8e_r\;'$ is less than the smallest number which is representable by floating point number. So, $\sqrt{F}$ is approximate to $'\;\frac{Y_{i+1}}{T}\;'$. Since the number of multiplications performed by the proposed algorithm is dependent on the input values, the average number of multiplications per an operation is derived from many reciprocal square root tables ($T=\frac{1}{\sqrt{F}}+e_i$) with varying sizes. The superiority of this algorithm is proved by comparing this average number with the fixed number of multiplications of the conventional algorithm. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a square root unit. Also, it can be used to construct optimized approximate reciprocal square root tables. The results of this paper can be applied to many areas that utilize floating point numbers, such as digital signal processing, computer graphics, multimedia, scientific computing, etc.

• Investigative Magnetic Resonance Imaging
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• v.8 no.1
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• pp.42-49
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• 2004

Purpose : The quantization noise in magnetic resonance imaging (MRI) systems is analyzed. The signal-to-quantization noise ratio (SQNR) in the reconstructed image is derived from the level of quantization in the signal in spatial frequency domain. Based on the derived formula, the SQNRs in various main magnetic fields with different receiver systems are evaluated. From the evaluation, the quantization noise could be a major noise source determining overall system signal-to-noise ratio (SNR) in high field MRI system. A few methods to reduce the quantization noise are suggested. Materials and methods : In Fourier imaging methods, spin density distribution is encoded by phase and frequency encoding gradients in such a way that it becomes a distribution in the spatial frequency domain. Thus the quantization noise in the spatial frequency domain is expressed in terms of the SQNR in the reconstructed image. The validity of the derived formula is confirmed by experiments and computer simulation. Results : Using the derived formula, the SQNRs in various main magnetic fields with various receiver systems are evaluated. Since the quantization noise is proportional to the signal amplitude, yet it cannot be reduced by simple signal averaging, it could be a serious problem in high field imaging. In many receiver systems employing analog-to-digital converters (ADC) of 16 bits/sample, the quantization noise could be a major noise source limiting overall system SNR, especially in a high field imaging. Conclusion : The field strength of MRI system keeps going higher for functional imaging and spectroscopy. In high field MRI system, signal amplitude becomes larger with more susceptibility effect and wider spectral separation. Since the quantization noise is proportional to the signal amplitude, if the conversion bits of the ADCs in the receiver system are not large enough, the increase of signal amplitude may not be fully utilized for the SNR enhancement due to the increase of the quantization noise. Evaluation of the SQNR for various systems using the formula shows that the quantization noise could be a major noise source limiting overall system SNR, especially in three dimensional imaging in a high field imaging. Oversampling and off-center sampling would be an alternative solution to reduce the quantization noise without replacement of the receiver system.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.9 no.2
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• pp.380-389
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• 2005

The Goldschmidt iterative algorithm for a floating point divide calculates it by performing a fixed number of multiplications. In this paper, a variable latency Goldschmidt's divide algorithm is proposed, that performs multiplications a variable number of times until the error becomes smaller than a given value. To calculate a floating point divide '$\frac{N}{F}$', multifly '$T=\frac{1}{F}+e_t$' to the denominator and the nominator, then it becomes ’$\frac{TN}{TF}=\frac{N_0}{F_0}$'. And the algorithm repeats the following operations: ’$R_i=(2-e_r-F_i),\;N_{i+1}=N_i{\ast}R_i,\;F_{i+1}=F_i{\ast}R_i$, i$\in${0,1,...n-1}'. The bits to the right of p fractional bits in intermediate multiplication results are truncated, and this truncation error is less than ‘$e_r=2^{-p}$'. The value of p is 29 for the single precision floating point, and 59 for the double precision floating point. Let ’$F_i=1+e_i$', there is $F_{i+1}=1-e_{i+1},\;e_{i+1}',\;where\;e_{i+1}, If '$[F_i-1]<2^{\frac{-p+3}{2}}$ is true, ’$e_{i+1}<16e_r$' is less than the smallest number which is representable by floating point number. So, ‘$N_{i+1}$ is approximate to ‘$\frac{N}{F}$'. Since the number of multiplications performed by the proposed algorithm is dependent on the input values, the average number of multiplications per an operation is derived from many reciprocal tables ($T=\frac{1}{F}+e_t$) with varying sizes. 1'he superiority of this algorithm is proved by comparing this average number with the fixed number of multiplications of the conventional algorithm. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a divider. Also, it can be used to construct optimized approximate reciprocal tables. The results of this paper can be applied to many areas that utilize floating point numbers, such as digital signal processing, computer graphics, multimedia, scientific computing, etc

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.43 no.3 s.345
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• pp.21-32
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• 2006

A new SRAM circuit with row-by-row activation and low-swing write schemes is proposed to reduce switching power of active cells as well as leakage one of sleep cells in this paper. By driving source line of sleep cells by $V_{SSH}$ which is higher than $V_{SS}$, the leakage current can be reduced to 1/100 due to the cooperation of the reverse body-bias. Drain Induced Barrier Lowering (DIBL), and negative $V_{GS}$ effects. Moreover, the bit line leakage which may introduce a fault during the read operation can be eliminated in this new SRAM. Swing voltage on highly capacitive bit lines is reduced to $V_{DD}-to-V_{SSH}$ from the conventional $V_{DD}-to-V_{SS}$ during the write operation, greatly saving the bit line switching power. Combining the row-by-row activation scheme with the low-swing write does not require the additional area penalty. By the SPICE simulation with the Berkeley Predictive Technology Modes, 93% of leakage power and 43% of switching one are estimated to be saved in future leakage-dominant 70-un process. A test chip has been fabricated using $0.35-{\mu}m$ CMOS process to verify the effectiveness and feasibility of the new SRAM, where the switching power is measured to be 30% less than the conventional SRAM when the I/O bit width is only 8. The stored data is confirmed to be retained without loss until the retention voltage is reduced to 1.1V which is mainly due to the metal shield. The switching power will be expected to be more significant with increasing the I/O bit width.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.44 no.8
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• pp.52-59
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• 2007

In this paper, we analyzed and measured implant isolation characteristics for a 1.25 Gbps monolithic integrated hi-directional (M-BiDi) optoelectronic system-on-a-chip, which is a key component to constitute gigabit passive optical networks (PONs) for a fiber-to-the-home (FTTH). Also, we derived an equivalent circuit of the implant structure under various DC bias conditions. The 1.25 Gbps M-BiDi transmit-receive SoC consists of a laser diode with a monitor photodiode as a transmitter and a digital photodiode as a digital data receiver on the same InP wafer According to IEEE 802.3ah and ITU-T G.983.3 standards, a receiver sensitivity of the digital receiver has to satisfy under -24 dBm @ BER=10-12. Therefore, the electrical crosstalk levels have to maintain less than -86 dB from DC to 3 GHz. From analysed and measured results of the implant structure, the M-BiDi SoC with the implant area of 20 mm width and more than 200 mm distance between the laser diode and monitor photodiode, and between the monitor photodiode and digital photodiode, satisfies the electrical crosstalk level. These implant characteristics can be used for the design and fabrication of an optoelectronic SoC design, and expended to a mixed-mode SoC field.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.46 no.12
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• pp.108-116
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• 2009

In this paper, we propose a Ethernet based audio distribution system with a new L1/L2 hybrid switching scheme, and evaluate its performance. The proposed scheme not only offers guaranteed low latency and jitter characteristics that are essentially required for the distribution of high-quality uncompressed audio traffic, and but also provide an efficient transmission of data traffic on the Ethernet environment. The audio distribution system with a proposed scheme consists of a master node and a number of relay nodes, and all nodes are mutually connected as a daisy-chain topology through up and downlinks. The master node generates an audio frame for each cycle of 125us, and the audio frame has 24 time slotted audio channels for carrying stereo 24 channels of 16-bit PCM sampled audio. On receiving the audio frame from its upstream node via the downlink, each intermediate node inserts its audio traffic to the reserved time slot for itself, then relays again to next node through its physical layer(L1) transmission - repeating. After reaching the end node, the audio frame is loopbacked through the uplink. On repeating through the uplink, each node makes a copy of audio slot that node has to receive, then play the audio. When the audio transmission is completed, each node works as a normal L2 switch, thus data frames are switched during the remaining period. For supporting this L1/L2 hybrid switching capability, we insert a glue logic for parsing and multiplexing audio and data frames at MII(Media Independent Interlace) between the physical and data link layers. The proposed scheme can provide a good delay performance and transmission efficiency than legacy Ethernet based audio distribution systems. For verifying the feasibility of the proposed L1/L2 hybrid switching scheme, we use OMNeT++ as a simulation tool with various parameters. From the simulation results, one can find that the proposed scheme can provides outstanding characteristics in terms of both jitter characteristic for audio traffic and transmission efficiency of data traffics.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.8 no.1
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• pp.123-136
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• 2004

In this paper, complexity and regularity of polynomial multiplication over $GF({2^n})$ are defined by using Hamming weight of rows and columns of the matrix ever GF(2) which represents polynomial multiplication. It is shown experimentally that in order to construct the block cipher robust against differential cryptanalysis, polynomial multiplication of substitution layer and the permutation layer should have high complexity and high regularity. With result of the experiment, a way of constituting S box and G function is suggested in the block cipher whose structure is similar to SEED, which is KOREA standard of 128-bit block cipher. S box can be formed with a nonlinear function and an affine transform. Nonlinear function must be strong with differential attack and linear attack, and it consists of an inverse number over $GF({2^8})$ which has neither a fixed pout, whose input and output are the same except 0 and 1, nor an opposite fixed number, whose output is one`s complement of the input. Affine transform can be constituted so that the input/output correlation can be the lowest and there can be no fixed point or opposite fixed point. G function undergoes linear transform with 4 S-box outputs using the matrix of 4${\times}$4 over $GF({2^8})$. The components in the matrix of linear transformation have high complexity and high regularity. Furthermore, G function can be constituted so that MDS(Maximum Distance Separable) code can be formed, SAC(Strict Avalanche Criterion) can be met, and there can be no weak input where a fixed point an opposite fixed point, and output can be two`s complement of input. The primitive polynomials of nonlinear function affine transform and linear transformation are different each other. The S box and G function suggested in this paper can be used as a constituent of the block cipher with high security, in that they are strong with differential attack and linear attack with no weak input and they are excellent at diffusion.

• The KIPS Transactions:PartA
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• v.12A no.5 s.95
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• pp.413-420
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• 2005

The Newton-Raphson iterative algorithm for finding a floating point reciprocal square mot calculates it by performing a fixed number of multiplications. In this paper, a variable latency Newton-Raphson's reciprocal square root algorithm is proposed that performs multiplications a variable number of times until the error becomes smaller than a given value. To find the rediprocal square root of a floating point number F, the algorithm repeats the following operations: '$X_{i+1}=\frac{{X_i}(3-e_r-{FX_i}^2)}{2}$, $i\in{0,1,2,{\ldots}n-1}$' with the initial value is '$X_0=\frac{1}{\sqrt{F}}{\pm}e_0$'. The bits to the right of p fractional bits in intermediate multiplication results are truncated and this truncation error is less than '$e_r=2^{-p}$'. The value of p is 28 for the single precision floating point, and 58 for the double precision floating point. Let '$X_i=\frac{1}{\sqrt{F}}{\pm}e_i$, there is '$X_{i+1}=\frac{1}{\sqrt{F}}-e_{i+1}$, where '$e_{i+1}{<}\frac{3{\sqrt{F}}{{e_i}^2}}{2}{\mp}\frac{{Fe_i}^3}{2}+2e_r$'. If '$|\frac{\sqrt{3-e_r-{FX_i}^2}}{2}-1|<2^{\frac{\sqrt{-p}{2}}}$' is true, '$e_{i+1}<8e_r$' is less than the smallest number which is representable by floating point number. So, $X_{i+1}$ is approximate to '$\frac{1}{\sqrt{F}}$. Since the number of multiplications performed by the proposed algorithm is dependent on the input values, the average number of multiplications Per an operation is derived from many reciprocal square root tables ($X_0=\frac{1}{\sqrt{F}}{\pm}e_0$) with varying sizes. The superiority of this algorithm is proved by comparing this average number with the fixed number of multiplications of the conventional algorithm. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a reciprocal square root unit. Also, it can be used to construct optimized approximate reciprocal square root tables. The results of this paper can be applied to many areas that utilize floating point numbers, such as digital signal processing, computer graphics, multimedia, scientific computing, etc.

• Journal of the Korea Organic Resources Recycling Association
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• v.9 no.1
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• pp.65-72
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• 2001

Four newly isolated bacteria from soil were used to manufacture microbial inoculum to compost food waste. The bacteria, GM103, V25, V31, and V35, were identified as Bacillus licheniformis, B. subtilis, B. stearothermophilius, and B, subtilis, respectively. The bacterial strains were efficient to degrade protein and starch and also able to inhibit the growth of plant pathogenic fungus Rhizopus stronifer. The GM103 showed distinct capability in degrading starch, but grow only aerobically. The other three bacterial strains. V25, V31, and V35, could grow both aerobically as well as anaerobically, in 10%(w/v) salt, at $50^{\circ}C$, and had good viability and survival rate in soil. These characteristics of the bacterial strains are very adquate in Korean food composting containing high concentration of salt, especially at home. By mixing the 4 bacterial culture broth with molasses, beet pulp, zeolite, The bacterial inoculum for food waste composting-BIOTOP-CLEAN-was made. The performance of food waste composting by the BIOTOP-CLEAN was compared with that by control(not treated) and HS(other demestic company's inoculum product for food waste composting). The maximum temperature of the food waste during the composting with the BIOTOP-CLEAN was $50^{\circ}C$, while those of the control and HS were $30^{\circ}C$ and $35^{\circ}C$, respectively. The BIOTOP-CLEAN gave the good smell and showed dark brown color, while the control gave bad smell and HS gave less bad smell. These indicates that the food waste composting by the BIOTOP-CLEAN had been well accomplished. The culture broth of V25, V31, V35 were sparyed to the plants of tomato, chinese cabbage, raddish, red pepper every month and the spraying the culture broth to these plant significantly improved the production yield of the crops, due to the control effect of the bacterial strains against the plant pathogens.

• Journal of Mushroom
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• v.18 no.1
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• pp.120-124
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• 2020

This study was conducted to provide basic data for setting a standard medium for winter mushroom cultivation. Investigation of medium composition in winter mushroom farms in Korea revealed that the types of medium used for each farm were slightly different and that the mixing ratio of the medium also varied. All farmers used corncob, rice bran, and beet pulp as the main media, and calcium carbonate and ground oyster shells were used at 1.0~3.8% to adjust the pH of the medium. Analysis of the physicochemical properties of the mixed media showed nitrogen content of 1.28~1.52%, carbon content of 45.7~48.5%, and C/N ratio of 30.7~37.9. The content of inorganic components was significantly different in each farm, depending on the type and amount of minerals in the mixed medium. Mycelial growth was the fastest at Farm 2, reaching 6.5 cm within 34 days of culture, followed by Farm 4 at 5.7 cm, whereas Farm 1, 3, and 5 showed similar growth. Mycelial density was high without any significant difference between farms. Survey of yield according to medium composition in each farm showed the highest yield in Farm 2 at 173.4 g/bottle, followed by Farm 1 at 168.4 g/bottle, whereas Farm 3 and 4 showed similar yield. However, Farm 4 had the lowest yield at 145.4 g/bottle. Therefore, mushroom yield was different depending on the medium composition in the farm, and thus selection of a medium that can be used universally in multiple mushroom farms was considered possible.