• Title/Summary/Keyword: Legendre sequences

Search Result 8, Processing Time 0.023 seconds

Extended sequences of sequences generated by GMW sequences and No sequences (GMW 수열과 No 수열에 의해서 생성된 수열의 확장수열)

  • Cho, Sung-Jin;Yim, Ji-Mi;Kim, Jin-Gyoung;Kim, Seok-Tae
    • The Journal of the Korea institute of electronic communication sciences
    • /
    • v.7 no.2
    • /
    • pp.271-277
    • /
    • 2012
  • In this paper, we introduce the extended sequences of sequences generated by GMW sequences and No sequences. And we analyze cross-correlatons of the extended sequences. Also we give extended sequences which are constructed from Legendre sequences. This is helpful to a cryptosystem and a communication system. Particularly this study is useful to the CDMA system signal design.

Hall's Sextic Residue 시퀀스 및 기타 시퀀스의 Trace 함수에 의한 표현

  • 이환근;노종선;정하봉;양경철;송홍엽
    • The Journal of Korean Institute of Communications and Information Sciences
    • /
    • v.22 no.6
    • /
    • pp.1273-1278
    • /
    • 1997
  • Pseudonoise sequences of period 2$^{m}$ -1 with idel autocorrelation have been researched such as m-sequences, GMW sequences, Legendre sequences, and extended sequences. The m-sequences, the GMW sequences, the Legendre sequences, and the extended sequences are best described in terms of the trace function by previous works. Besides, there are Hall's sextic residue sequences and miscellaneous sequences with ideal autocorrelation, whose general constructions are not known so far. However, are are no explicit descripton of the Hall's sextic residue sequences and the miscellaneous sequences in terms of the trace function. In this paper, the Hall's sextic residue sequences and the miscellaneous sequences of period 2$^{m}$ -1 are expressed as a sum of trace functions. The miscellaneous sequences with ideal autocorrelation, which are newly found by computer search, are also expressed as a sum of trace functions.

  • PDF

Design of Binary Sequences with Optimal Cross-correlation Values (최적의 상호상관관계를 갖는 이진 수열의 설계)

  • Choi, Un-Sook;Cho, Sung-Jin
    • The Journal of the Korea institute of electronic communication sciences
    • /
    • v.6 no.4
    • /
    • pp.539-544
    • /
    • 2011
  • Balanced binary sequences of period $2^n-1(n{\geq}1)$ having the two-valued autocorrelation function have many applications in spread-spectrum communications system. In this paper we propose new nonlinear binary sequences which are constructed from Legendre sequences with the same cross-correlation as the sequences proposed by Cho. These sequences include the m-sequences, GMW sequences, Kasami sequences and No sequences which are described in terms of the trace function over a finite field. Also the proposed sequences have more low cross-correlation distribution than the quadratic form sequences proposed by Klapper.

On Lengthening the Period of Known Binary Sequences Preserving the Ideal Autocorrelation

  • No, Jong-Seon;Yang, Kyeong-Cheol;Chung, Ha-Bong;Song, Hong-Yeop
    • Journal of Electrical Engineering and information Science
    • /
    • v.2 no.6
    • /
    • pp.217-222
    • /
    • 1997
  • Recently, No et al. presented a new construction of binary sequences with ideal autocorrelation property. In this paper, we applied this method into some of the well-known binary sequences with ideal autocorrelation, and the results are described in detail. First, the GMW sequences are shown to be a natural extension of m-sequences with respect to this method. Second, new binary sequences with ideal autocorrelation property are explicitly constructed from Legendre sequences, Hall's sextic residue sequences, and other known sequences of miscellaneous type.

  • PDF

A FAST ALGORITHM FOR REGION-ORIENTED TEXTURE CODING

  • Bae, Cheol-Soo;Kim, Hyun-yul
    • The Journal of Korea Institute of Information, Electronics, and Communication Technology
    • /
    • v.7 no.4
    • /
    • pp.205-211
    • /
    • 2014
  • This paper addresses the framework of object-oriented image coding, describing a new algorithm, based on monodimensional Legendre polynomials, for texture approximation. Through the use of 1D orthogonal basis functions, the computational complexity which usually makes prohibitive most of 2D region-oriented approaches is significantly reduced, while only a slight increment of distortion is introduced. In the aim of preserving the bidimensional intersample correlation of the texture information as much as possible, suitable pseudo-bidimensional basis functions have been used, yielding significant improvements with respect to the straightforward 1D approach. The algorithm has been experimented for coding still images as well as motion compensated sequences, showing interesting possibilities of application for very low bitrate video coding.

A Fast Algorithm for Region-Oriented Texture Coding

  • Choi, Young-Gyu;Choi, Chong-Hwan;Cheong, Ha-Young
    • The Journal of Korea Institute of Information, Electronics, and Communication Technology
    • /
    • v.9 no.6
    • /
    • pp.519-525
    • /
    • 2016
  • This paper addresses the framework of object-oriented image coding, describing a new algorithm, based on monodimensional Legendre polynomials, for texture approximation. Through the use of 1D orthogonal basis functions, the computational complexity which usually makes prohibitive most of 2D region-oriented approaches is significantly reduced, while only a slight increment of distortion is introduced. In the aim of preserving the bidimensional intersample correlation of the texture information as much as possible, suitable pseudo-bidimensional basis functions have been used, yielding significant improvements with respect to the straightforward 1D approach. The algorithm has been experimented for coding still images as well as motion compensated sequences, showing interesting possibilities of application for very low bitrate video coding.

p-Adaptive Mesh Refinement of Plate Bending Problem by Modified SPR Technique (수정 SPR 기법에 의한 휨을 받는 평판문제의 적응적 p-체눈 세분화)

  • Jo, Jun-Hyung;Lee, Hee-Jung;Woo, Kwang-Sung
    • Proceedings of the Computational Structural Engineering Institute Conference
    • /
    • 2007.04a
    • /
    • pp.481-486
    • /
    • 2007
  • The Zienkiewicz-Zhu(Z/Z) error estimate is slightly modified for the hierarchical p-refinement, and is then applied to L-shaped plates subjected to bending to demonstrate its effectiveness. An adaptive procedure in finite element analysis is presented by p-refinement of meshes in conjunction with a posteriori error estimator that is based on the superconvergent patch recovery(SPR) technique. The modified Z/Z error estimate p-refinement is different from the conventional approach because the high order shape functions based on integrals of Legendre polynomials are used to interpolate displacements within an element, on the other hand, the same order of basis function based on Pascal's triangle tree is also used to interpolate recovered stresses. The least-square method is used to fit a polynomial to the stresses computed at the sampling points. The strategy of finding a nearly optimal distribution of polynomial degrees on a fixed finite element mesh is discussed such that a particular element has to be refined automatically to obtain an acceptable level of accuracy by increasing p-levels non-uniformly or selectively. It is noted that the error decreases rapidly with an increase in the number of degrees of freedom and the sequences of p-distributions obtained by the proposed error indicator closely follow the optimal trajectory.

  • PDF

The Selective p-Distribution for Adaptive Refinement of L-Shaped Plates Subiected to Bending (휨을 받는 L-형 평판의 적응적 세분화를 위한 선택적 p-분배)

  • Woo, Kwang-Sung;Jo, Jun-Hyung;Lee, Seung-Joon
    • Journal of the Computational Structural Engineering Institute of Korea
    • /
    • v.20 no.5
    • /
    • pp.533-541
    • /
    • 2007
  • The Zienkiewicz-Zhu(Z/Z) error estimate is slightly modified for the hierarchical p-refinement, and is then applied to L-shaped plates subjected to bending to demonstrate its effectiveness. An adaptive procedure in finite element analysis is presented by p-refinement of meshes in conjunction with a posteriori error estimator that is based on the superconvergent patch recovery(SPR) technique. The modified Z/Z error estimate p-refinement is different from the conventional approach because the high order shape functions based on integrals of Legendre polynomials are used to interpolate displacements within an element, on the other hand, the same order of basis function based on Pascal's triangle tree is also used to interpolate recovered stresses. The least-square method is used to fit a polynomial to the stresses computed at the sampling points. The strategy of finding a nearly optimal distribution of polynomial degrees on a fixed finite element mesh is discussed such that a particular element has to be refined automatically to obtain an acceptable level of accuracy by increasing p-levels non-uniformly or selectively. It is noted that the error decreases rapidly with an increase in the number of degrees of freedom and the sequences of p-distributions obtained by the proposed error indicator closely follow the optimal trajectory.