• Journal of Communications and Networks
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• v.10 no.1
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• pp.5-9
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• 2008

Researchers have investigated many upper bound techniques applicable to error probabilities on the maximum likelihood (ML) decoding performance of turbo-like codes and low density parity check (LDPC) codes in recent years for a long codeword block size. This is because it is trivial for a short codeword block size. Previous research efforts, such as the simple bound technique [20] recently proposed, developed upper bounds for LDPC codes and turbo-like codes using ensemble codes or the uniformly interleaved assumption. This assumption bounds the performance averaged over all ensemble codes or all interleavers. Another previous research effort [21] obtained the upper bound of turbo-like code with a particular interleaver using a truncated union bound which requires information of the minimum Hamming distance and the number of codewords with the minimum Hamming distance. However, it gives the reliable bound only in the region of the error floor where the minimum Hamming distance is dominant, i.e., in the region of high signal-to-noise ratios. Therefore, currently an upper bound on ML decoding performance for turbo-like code with a particular interleaver and LDPC code with a particular parity check matrix cannot be calculated because of heavy complexity so that only average bounds for ensemble codes can be obtained using a uniform interleaver assumption. In this paper, we propose a new bound technique on ML decoding performance for turbo-like code with a particular interleaver and LDPC code with a particular parity check matrix using ML estimated weight distributions and we also show that the practical iterative decoding performance is approximately suboptimal in ML sense because the simulation performance of iterative decoding is worse than the proposed upper bound and no wonder, even worse than ML decoding performance. In order to show this point, we compare the simulation results with the proposed upper bound and previous bounds. The proposed bound technique is based on the simple bound with an approximate weight distribution including several exact smallest distance terms, not with the ensemble distribution or the uniform interleaver assumption. This technique also shows a tighter upper bound than any other previous bound techniques for turbo-like code with a particular interleaver and LDPC code with a particular parity check matrix.

• Journal of Institute of Control, Robotics and Systems
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• v.12 no.2
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• pp.93-100
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• 2006

In this paper, a new-type Extended Kalman Filter (EKF) is proposed as a robust nonlinear filter for a stochastic nonlinear system. The original EKF is widely used for various nonlinear system applications. But it is fragile to its estimation errors because they give rise to linearization errors that affect the system mode1 as the modeling errors. The linearization errors are nonlinear functions of the estimation errors therefore it is very difficult to obtain the accurate error covariance of the EKF using the linear form. The inaccurately estimated error covariance hinders the EKF from being a sub-optimal estimator. The proposed filter tries to obtain the upper bound of the error covariance tolerating the uncertainty of the error covariance instead of trying to obtain the accurate one. It treats the linearization errors as uncertain modeling errors that can be handled by the robust linear filtering. In order to be more robust to the estimation errors than the original EKF, the proposed filter minimizes the upper bound like the robust linear filter that is applied to the linear model with uncertainty. The in-flight alignment problem of the inertial navigation system with GPS position measurements is a good example that the proposed robust filter is applicable to. The simulation results show the efficiency of the proposed filter in the robustness to initial estimation errors of the filter.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.11 no.3
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• pp.352-357
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• 2000

The symbol error probability for the coherent detection of MPSK signals in additive white Gaussian noise(AWGN) can be evaluated exactly for M=2 and M=4. The MPSK symbol error probability bounds obtained in the past are simple to calculate, but not accurate. More recently, very tight bounds have been proposed, but they are complex to calculate. In this paper to obtain a simple and accurate lower bound for coherent MPSK symbol error probability in AWGN, we consider the symbol error probability for MPSK in Nakagami fading case first. Then as the Nakagami fading index m approaches to infinity, we obtain the symbol error probability for the MPSK in AWGN.

• Ocean and Polar Research
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• v.30 no.2
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• pp.149-158
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• 2008

The characteristic analysis of the estimated population parameters, i.e., standard deviation and error bound of coastal pollutant concentrations (hereafter PC, i.e., COD, TN, and TP concentrations), was carried out by using environmental data with different sampling frequency in Lake Shihwa and Incheon coastal zone. The results clearly show that standard deviation of the PC increases as its mean value increases. The error bounds of the annual mean values based on seasonally measured DO concentrations and PC data in Incheon coastal zone were estimated as ranges 2.26 mg/l, $0.68{\sim}0.86\;mg/l$, $0.62{\sim}0.80\;mg/l$, and $0.074{\sim}0.082\;mg/l$, respectively. In terms of annual mean of the DO concentration and PC in Lake Shihwa, the error bounds based on monthly measured data from 1997 to 2003 were also estimated as ranges 4.0 mg/l, 3.0 mg/l, $0.5{\sim}1.0\;mg/l$, and 0.05 mg/l, respectively. The error bound on the basis of real-time monitoring data is $7{\sim}13%$ only as compared to that of monthly measured data.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.16 no.1
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• pp.1-13
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• 2012

In this paper we present an a posteriori error estimator for the stabilized P1 nonconforming finite element method of the linear elasticity problem based on a nonsymmetric H(div)-conforming approximation of the stress tensor in the first-order Raviart-Thomas space. By combining the equilibrated residual method and the hypercircle method, it is shown that the error estimator gives a fully computable upper bound on the actual error. Numerical results are provided to confirm the theory and illustrate the effectiveness of our error estimator.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.27 no.1A
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• pp.18-25
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• 2002

In this paper, the performance of three types of serial concatenated convolutional codes (SCCC) in AWGN (additive white Gaussian noise) channel is compared and analyzed. As results of simulations, it can be observed that Type I shows the best error performance at lower signal-to-noise ratio (SNR) region. However, Type III shows the best error performance at higher SNR region. It can be also observed the error floor that the performance cannot be improved even though increasing of the number of iterations and SNR at Type I. However, the performance of Type II and Type III are still improved over the five iterations at higher SNR without error floor. And BER performance of three types can be closed to upper bound of three types with increase of SNR. It can be also observed that the upper bound of Type III shows the best performance among the three types due to the greatest free distance.

• Industrial Engineering and Management Systems
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• v.16 no.1
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• pp.92-102
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• 2017

In this paper, we consider a typical health care system via the help of Wireless Sensor Network (WSN) for wireless patient tracking. The wireless patient tracking module of this system performs localization out of samples of Received Signal Strength (RSS) variations and tracking through a Particle Filter (PF) for WSN assisted by multiple transmit-power information. We propose a modified PF, Kullback-Leibler Distance (KLD)-resampling PF, to ameliorate the effect of RSS variations by generating a sample set near the high-likelihood region for improving the wireless patient tracking. The key idea of this method is to approximate a discrete distribution with an upper bound error on the KLD for reducing both location error and the number of particles used. To determine this bound error, an optimal algorithm is proposed based on the maximum gap error between the proposal and Sampling Important Resampling (SIR) algorithms. By setting up these values, a number of simulations using the health care system's data sets which contains the real RSSI measurements to evaluate the location error in term of various power levels and density nodes for all methods. Finally, we point out the effect of different power levels vs. different density nodes for the wireless patient tracking.

• Communications of the Korean Mathematical Society
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• v.8 no.3
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• pp.545-554
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• 1993

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.245-259
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• 2007

This paper studies some properties of the value functions and gives some sufficient and necessary conditions about the presented global error and local error. And it leads to one kind of relationship between iterative points and optimal solution or K-T point.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.2
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• pp.49-56
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• 1998

In this paper, by the use of an Ostrowski type integral inequality for double integrals, we establish an upper bound for the estimation error variance of a continuous stream with stationary variogram.