• Title/Summary/Keyword: Iterations

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Progressive Edge-Growth Algorithm for Low-Density MIMO Codes

  • Jiang, Xueqin;Yang, Yi;Lee, Moon Ho;Zhu, Minda
    • Journal of Communications and Networks
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    • v.16 no.6
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    • pp.639-644
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    • 2014
  • In low-density parity-check (LDPC) coded multiple-input multiple-output (MIMO) communication systems, probabilistic information are exchanged between an LDPC decoder and a MIMO detector. TheMIMO detector has to calculate probabilistic values for each bit which can be very complex. In [1], the authors presented a class of linear block codes named low-density MIMO codes (LDMC) which can reduce the complexity of MIMO detector. However, this code only supports the outer-iterations between the MIMO detector and decoder, but does not support the inner-iterations inside the LDPC decoder. In this paper, a new approach to construct LDMC codes is introduced. The new LDMC codes can be encoded efficiently at the transmitter side and support both of the inner-iterations and outer-iterations at the receiver side. Furthermore they can achieve the design rates and perform very well over MIMO channels.

Simple Stopping Criterion Algorithm using Variance Values of Noise in Turbo Code (터보부호에서 잡음 분산값을 사용한 간단한 반복중단 알고리즘)

  • Jeong Dae-Ho;Kim Hwan-Yong
    • 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.103-110
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    • 2006
  • Turbo code, a kind of error correction coding technique, has been used in the field of digital mobile communication system. As the number of iterations increases, it can achieves remarkable BER performance over AWGN channel environment. However, if the number of iterations Is increases in the several channel environments, any further iteration results in very little improvement, and requires much delay and computation in proportion to the number of iterations. To solve this problems, it is necessary to device an efficient criterion to stop the iteration process and prevent unnecessary delay and computation. In this paper, it proposes an efficient and simple criterion for stopping the iteration process in turbo decoding. By using variance values of noise derived from mean values of LLR in turbo decoder, the proposed algorithm can largely reduce the computation and average number of iterations without BER performance degradation. As a result of simulations, the computation of the proposed algorithm is reduced by about $66{\sim}80%$ compared to conventional algorithm. The average number of iterations is reduced by about $13.99%{\sim}15.74%$ compared to CE algorithm and about $17.88%{\sim}18.59%$ compared to SCR algorithm.

HIGHER ORDER ITERATIONS FOR MOORE-PENROSE INVERSES

  • Srivastava, Shwetabh;Gupta, D.K.
    • Journal of applied mathematics & informatics
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    • v.32 no.1_2
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    • pp.171-184
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    • 2014
  • A higher order iterative method to compute the Moore-Penrose inverses of arbitrary matrices using only the Penrose equation (ii) is developed by extending the iterative method described in [1]. Convergence properties as well as the error estimates of the method are studied. The efficacy of the method is demonstrated by working out four numerical examples, two involving a full rank matrix and an ill-conditioned Hilbert matrix, whereas, the other two involving randomly generated full rank and rank deficient matrices. The performance measures are the number of iterations and CPU time in seconds used by the method. It is observed that the number of iterations always decreases as expected and the CPU time first decreases gradually and then increases with the increase of the order of the method for all examples considered.

ACCELERATION OF MACHINE LEARNING ALGORITHMS BY TCHEBYCHEV ITERATION TECHNIQUE

  • LEVIN, MIKHAIL P.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.22 no.1
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    • pp.15-28
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    • 2018
  • Recently Machine Learning algorithms are widely used to process Big Data in various applications and a lot of these applications are executed in run time. Therefore the speed of Machine Learning algorithms is a critical issue in these applications. However the most of modern iteration Machine Learning algorithms use a successive iteration technique well-known in Numerical Linear Algebra. But this technique has a very low convergence, needs a lot of iterations to get solution of considering problems and therefore a lot of time for processing even on modern multi-core computers and clusters. Tchebychev iteration technique is well-known in Numerical Linear Algebra as an attractive candidate to decrease the number of iterations in Machine Learning iteration algorithms and also to decrease the running time of these algorithms those is very important especially in run time applications. In this paper we consider the usage of Tchebychev iterations for acceleration of well-known K-Means and SVM (Support Vector Machine) clustering algorithms in Machine Leaning. Some examples of usage of our approach on modern multi-core computers under Apache Spark framework will be considered and discussed.

A New Method of Finding Real Roots of Nonlinear System Using Extended Fixed Point Iterations (확장된 고정점이론을 이용한 비선형시스템의 근을 구하는 방법)

  • Kim, Sung-Soo;Kim, Ji-Soo
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.67 no.2
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    • pp.277-284
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    • 2018
  • In this paper, a new numerical method of finding the roots of a nonlinear system is proposed, which extends the conventional fixed point iterative method by relaxing the constraints on it. The proposed method determines the real valued roots and expands the convergence region by relaxing the constraints on the conventional fixed point iterative method, which transforms the diverging root searching iterations into the converging iterations by employing the metric induced by the geometrical characteristics of a polynomial. A metric is set to measure the distance between a point of a real-valued function and its corresponding image point of its inverse function. The proposed scheme provides the convenience in finding not only the real roots of polynomials but also the roots of the nonlinear systems in the various application areas of science and engineering.

ITERATES OF WEIGHTED BEREZIN TRANSFORM UNDER INVARIANT MEASURE IN THE UNIT BALL

  • Lee, Jaesung
    • Korean Journal of Mathematics
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    • v.28 no.3
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    • pp.449-457
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    • 2020
  • We focus on the interations of the weighted Berezin transform Tα on Lp(τ), where τ is the invariant measure on the complex unit ball Bn. Iterations of Tα on L1R(τ) the space of radial integrable functions played important roles in proving 𝓜-harmonicity of bounded functions with invariant mean value property. Here, we introduce more properties on iterations of Tα on L1R(τ) and observe differences between the iterations of Tα on L1(τ) and Lp(τ) for 1 < p < ∞.

LOCAL CONVERGENCE OF FUNCTIONAL ITERATIONS FOR SOLVING A QUADRATIC MATRIX EQUATION

  • Kim, Hyun-Min;Kim, Young-Jin;Seo, Jong-Hyeon
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.1
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    • pp.199-214
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    • 2017
  • We consider fixed-point iterations constructed by simple transforming from a quadratic matrix equation to equivalent fixed-point equations and assume that the iterations are well-defined at some solutions. In that case, we suggest real valued functions. These functions provide radii at the solution, which guarantee the local convergence and the uniqueness of the solutions. Moreover, these radii obtained by simple calculations of some constants. We get the constants by arbitrary matrix norm for coefficient matrices and solution. In numerical experiments, the examples show that the functions give suitable boundaries which guarantee the local convergence and the uniqueness of the solutions for the given equations.

Finding an initial solution and modifying search direction by the centering force in the primal-dual interior point method (원쌍대 내부점기법에서 초기해 선정과 중심화 힘을 이용한 개선 방향의 수정)

  • 성명기;박순달
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • 1996.04a
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    • pp.530-533
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    • 1996
  • This paper deals with finding an initial solution and modifying search direction by the centrering force in the predictor-corrector method which is a variant of the primal-dual barrier method. These methods were tested with NETLIB problems. Initial solutions which are located close to the center of the feasible set lower the number of iterations, as they enlarge the step length. Three heuristic methods to find such initial solution are suggested. The new methods reduce the average number of iterations by 52% to at most, compared with the old method assigning 1 to initial valurs. Solutions can move closer to the central path fast by enlarging the centering force in early steps. It enlarge the step length, so reduces the number of iterations. The more effective this method is the closer the initial solution is to the boundary of the feasible set.

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Implementation of a Band-Pass Filter with Diffusion Neural Network and the Operation of Difference (확산신경망과 차분연산에 의한 대역통과 필터의 구현)

  • 이재성;허만택;이종혁;남기곤;김재창;박의열
    • Journal of the Korean Institute of Telematics and Electronics B
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    • v.32B no.7
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    • pp.1036-1044
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    • 1995
  • In this paper, a band-pass filter is implemented with the diffusion and difference processes by using the diffusion neural network model. The center frequency of this band-pass filter can be varied by iterations of the diffusion and difference operations, and the selectivity can be determined by iterations of the difference operation. We propose an efficient algorithm that can generate various band-pass filters using arbitrary diffusion and difference iterations. This algorithm needs only simple operations of diffusion and difference.

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A study on constructing a good initial basis in the simplex method (단체법에서의 초기기저 구성에 관한 연구)

  • 서용원;김우제;박순달
    • Korean Management Science Review
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    • v.13 no.3
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    • pp.105-113
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    • 1996
  • Constructing an initial basis is an important process in the simplex method. An initial basis greatly affects the number of iterations of iterations and the execution time in the simplex method. The purpose of this paper is to construct a good initial basis. First, to avoid linear dependency among the chosen columns, an enhanced Gaussian elimination method and a method using non-duplicated nonzero elements are developed. Second, for an order to choose variables, the sparsity of the column is used. Experimenal results show that the proposed method can reduce the number of iterations and the execution time compared with Bixby's method by 12%.

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