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Volumn 56, Issue 3, 2010, Pages 1015-1022

Linear-time nearest point algorithms for Coxeter lattices

Author keywords

Channel coding; Lattice theory; Nearest point algorithm; Quantization

Indexed keywords

ARITHMETIC COMPLEXITY; LATTICE THEORIES; NEAREST POINT; NEAREST POINT ALGORITHM; WORST CASE; WORST-CASE COMPLEXITY;

EID: 77949498407     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2009.2039090     Document Type: Article
Times cited : (18)

References (38)
  • 1
    • 84957688279 scopus 로고    scopus 로고
    • An algorithm to compute a nearest point in the lattice a*n
    • M. Fossorier, H. Imai, S. Lin, and A. Poli, Eds. Karlsruhe, Germany: Springer Lecture Notes in Computer Science
    • I. V. L. Clarkson, "An algorithm to compute a nearest point in the lattice A*n," in Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, M. Fossorier, H. Imai, S. Lin, and A. Poli, Eds. Karlsruhe, Germany: Springer, 1999, vol.1719, Lecture Notes in Computer Science, pp. 104-120.
    • (1999) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes , vol.1719 , pp. 104-120
    • Clarkson, I.V.L.1
  • 3
    • 0029719917 scopus 로고    scopus 로고
    • Generating hard instances of lattice problems
    • May
    • M. Ajtai, "Generating hard instances of lattice problems," in Proc. 28th ACM Symp. Theory Computing, May 1996, pp. 99-108.
    • (1996) Proc. 28th ACM Symp. Theory Computing , pp. 99-108
    • Ajtai, M.1
  • 4
    • 0030679849 scopus 로고    scopus 로고
    • A public-key cryptosystem with worst-case/ average-case equivalence
    • May
    • M. Ajtai and C. Dwork, "A public-key cryptosystem with worst-case/ average-case equivalence," in Proc. 29th ACM Symp. Theory of Computing, May 1997, pp. 284-293.
    • (1997) Proc. 29th ACM Symp. Theory of Computing , pp. 284-293
    • Ajtai, M.1    Dwork, C.2
  • 5
    • 0037399394 scopus 로고    scopus 로고
    • Lattice decoding for joint detection in direct-sequence CDMA systems
    • L. Brunel and J. J. Boutros, "Lattice decoding for joint detection in direct-sequence CDMA systems," IEEE Trans. Inf. Theory, vol.49, pp. 1030-1037, 2003.
    • (2003) IEEE Trans. Inf. Theory , vol.49 , pp. 1030-1037
    • Brunel, L.1    Boutros, J.J.2
  • 7
    • 70350501698 scopus 로고    scopus 로고
    • Identifiability and aliasing in polynomial-phase signals, accepted for
    • R. G. McKilliam and I. V. L. Clarkson, "Identifiability and aliasing in polynomial-phase signals, accepted for," IEEE Trans. Signal Process., 2009.
    • (2009) IEEE Trans. Signal Process.
    • McKilliam, R.G.1    Clarkson, I.V.L.2
  • 9
    • 51349168627 scopus 로고    scopus 로고
    • Approximate maximum-likelihood period estimation from sparse, noisy timing data
    • May
    • I. V. L. Clarkson, "Approximate maximum-likelihood period estimation from sparse, noisy timing data," IEEE Trans. Signal Process., vol.56, no.5, pp. 1779-1787, May 2008.
    • (2008) IEEE Trans. Signal Process. , vol.56 , Issue.5 , pp. 1779-1787
    • Clarkson, I.V.L.1
  • 12
    • 0020102220 scopus 로고
    • Fast quantizing and decoding and algorithms for lattice quantizers and codes
    • Mar.
    • J. H. Conway and N. J. A. Sloane, "Fast quantizing and decoding and algorithms for lattice quantizers and codes," IEEE Trans. Inf. Theory, vol.28, pp. 227-232, Mar. 1982.
    • (1982) IEEE Trans. Inf. Theory , vol.28 , pp. 227-232
    • Conway, J.H.1    Sloane, N.J.A.2
  • 13
    • 0035271103 scopus 로고    scopus 로고
    • The hardness of the closest vector problem with preprocessing
    • D. Micciancio, "The hardness of the closest vector problem with preprocessing," IEEE Trans. Inf. Theory, vol.47, pp. 1212-1215, 2001.
    • (2001) IEEE Trans. Inf. Theory , vol.47 , pp. 1212-1215
    • Micciancio, D.1
  • 14
    • 0011039877 scopus 로고
    • Another np-complete partition problem and the complexity of computing short vectors in a lattice mathematisch instituut
    • Amsterdam The Netherlands
    • P. van Emde Boas, Another NP-Complete Partition Problem and the Complexity of Computing Short Vectors in a Lattice Mathematisch Instituut, Amsterdam, The Netherlands, 1981, Tech. Rep..
    • (1981) Tech. Rep.
    • Boas Emde P.Van1
  • 16
    • 0032636505 scopus 로고    scopus 로고
    • A universal lattice code decoder for fading channels
    • Jul.
    • E. Viterbo and J. Boutros, "A universal lattice code decoder for fading channels," IEEE Trans. Inf. Theory, vol.45, pp. 1639-1642, Jul. 1999.
    • (1999) IEEE Trans. Inf. Theory , vol.45 , pp. 1639-1642
    • Viterbo, E.1    Boutros, J.2
  • 17
    • 0002586419 scopus 로고
    • On the computation of lattice vectors of minimal length, successive minima and reduced bases with applications
    • M. Pohst, "On the computation of lattice vectors of minimal length, successive minima and reduced bases with applications," SIGSAM Bull., vol.15, no.1, pp. 37-44, 1981.
    • (1981) SIGSAM Bull. , vol.15 , Issue.1 , pp. 37-44
    • Pohst, M.1
  • 18
    • 0000126406 scopus 로고
    • Minkowski's convex body theorem and integer programming
    • R. Kannan, "Minkowski's convex body theorem and integer programming," Math. Oper. Res., vol.12, no.3, pp. 415-440, 1987.
    • (1987) Math. Oper. Res. , vol.12 , Issue.3 , pp. 415-440
    • Kannan, R.1
  • 19
    • 0022563696 scopus 로고
    • Soft decoding techniques for codes and lattices, including the Golay code and the Leech lattice
    • Jan.
    • J. H. Conway and N. J. A. Sloane, "Soft decoding techniques for codes and lattices, including the Golay code and the Leech lattice," IEEE Trans. Inf. Theory, vol.32, pp. 41-50, Jan. 1986.
    • (1986) IEEE Trans. Inf. Theory , vol.32 , pp. 41-50
    • Conway, J.H.1    Sloane, N.J.A.2
  • 20
    • 51349083795 scopus 로고    scopus 로고
    • An algorithm to compute the nearest point in the lattice an
    • Sep.
    • R. G. McKilliam, I. V. L. Clarkson, and B. G. Quinn, "An algorithm to compute the nearest point in the lattice A*n," IEEE Trans. Inf. Theory, vol.54, pp. 4378-4381, Sep. 2008.
    • (2008) IEEE Trans. Inf. Theory , vol.54 , pp. 4378-4381
    • McKilliam, R.G.1    Clarkson, I.V.L.2    Quinn, B.G.3
  • 22
    • 0001590074 scopus 로고
    • Extreme forms
    • H. S. M. Coxeter, "Extreme forms," Canad. J. Math., vol.3, pp. 391-441, 1951.
    • (1951) Canad. J. Math. , vol.3 , pp. 391-441
    • Coxeter, H.S.M.1
  • 24
    • 0022719093 scopus 로고
    • An eight-dimensional trellis code
    • May
    • A. R. Calderbank and N. J. A. Sloane, "An eight-dimensional trellis code," Proc. IEEE, vol.74, pp. 757-759, May 1986.
    • (1986) Proc. IEEE , vol.74 , pp. 757-759
    • Calderbank, A.R.1    Sloane, N.J.A.2
  • 25
    • 0023383214 scopus 로고
    • Trellis-coded modulation with multidimensional constellations
    • Jul.
    • L.-F. Wei, "Trellis-coded modulation with multidimensional constellations," IEEE Trans. Inf. Theory, vol.33, pp. 483-501, Jul. 1987.
    • (1987) IEEE Trans. Inf. Theory , vol.33 , pp. 483-501
    • Wei, L.-F.1
  • 26
    • 84945713988 scopus 로고
    • Coset codes I: Introduction and geometrical classification
    • Sep.
    • G. D. Forney, Jr, "Coset codes I: Introduction and geometrical classification," IEEE Trans. Inf. Theory, vol.34, pp. 1123-1151, Sep. 1988.
    • (1988) IEEE Trans. Inf. Theory , vol.34 , pp. 1123-1151
    • Forney Jr., G.D.1
  • 27
    • 84941860379 scopus 로고
    • Coset codes II: Binary lattices and related codes
    • Sep.
    • G. D. Forney, Jr, "Coset codes II: Binary lattices and related codes," IEEE Trans. Inf. Theory, vol.34, pp. 1152-1187, Sep. 1988.
    • (1988) IEEE Trans. Inf. Theory , vol.34 , pp. 1152-1187
    • Forney Jr., G.D.1
  • 28
    • 0020098638 scopus 로고
    • Voronoi regions of lattices, second moments of polytopes, and quantization
    • Mar.
    • J. H. Conway and N. J. A. Sloane, "Voronoi regions of lattices, second moments of polytopes, and quantization," IEEE Trans. Inf. Theory, vol.28, pp. 211-226, Mar. 1982.
    • (1982) IEEE Trans. Inf. Theory , vol.28 , pp. 211-226
    • Conway, J.H.1    Sloane, N.J.A.2
  • 29
    • 0036215391 scopus 로고    scopus 로고
    • Some newlattice quantization algorithms for video compression coding
    • Jan.
    • M. S. Postol, "Some newlattice quantization algorithms for video compression coding," IEEE Trans. Circuits Syst., vol.12, no.1, pp. 53-60, Jan. 2002.
    • (2002) IEEE Trans. Circuits Syst. , vol.12 , Issue.1 , pp. 53-60
    • Postol, M.S.1
  • 30
    • 0024627104 scopus 로고
    • Demodulation of a Gosset lattice code having a spectral null at DC
    • Mar.
    • N. Secord and R. de Buda, "Demodulation of a Gosset lattice code having a spectral null at DC," IEEE Trans. Inf. Theory, vol.35, pp. 472-477, Mar. 1989.
    • (1989) IEEE Trans. Inf. Theory , vol.35 , pp. 472-477
    • Secord, N.1    De Buda, R.2
  • 31
    • 0032665718 scopus 로고    scopus 로고
    • Frequency estimation, phase unwrapping and the nearest lattice point problem
    • Mar.
    • I. V. L. Clarkson, "Frequency estimation, phase unwrapping and the nearest lattice point problem," in Proc. Int. Conf. Acoust. Speech Signal Process., Mar. 1999, vol.3, pp. 1609-1612.
    • (1999) Proc. Int. Conf. Acoust. Speech Signal Process. , vol.3 , pp. 1609-1612
    • Clarkson, I.V.L.1
  • 35
    • 84976747133 scopus 로고
    • The algorithm SELECT-For finding the ith smallest of elements
    • R. W. Floyd and R. L. Rivest, "The algorithm SELECT-For finding the ith smallest of- elements," Commun. ACM, vol.18, no.3, pp. 173-173, 1975.
    • (1975) Commun. ACM , vol.18 , Issue.3 , pp. 173-173
    • Floyd, R.W.1    Rivest, R.L.2
  • 36
    • 0016485958 scopus 로고
    • Expected time bounds for selection
    • Mar.
    • R. W. Floyd and R. L. Rivest, "Expected time bounds for selection," Commun. ACM, vol.18, pp. 165-172, Mar. 1975.
    • (1975) Commun. ACM , vol.18 , pp. 165-172
    • Floyd, R.W.1    Rivest, R.L.2
  • 37
    • 0003657590 scopus 로고    scopus 로고
    • 3rd ed. Reading, MA: Addison-Wesley ,Seminumerical Algorithms
    • D. E. Knuth, The Art of Computer Programming, 3rd ed. Reading, MA: Addison-Wesley, 1997, vol.2, Seminumerical Algorithms.
    • (1997) The Art of Computer Programming , vol.2
    • Knuth, D.E.1
  • 38
    • 0030519162 scopus 로고    scopus 로고
    • Polytope projection and projection polytopes
    • Nov.
    • T. Burger, P. Gritzmann, and V. Klee, "Polytope projection and projection polytopes," The Amer. Math. Monthly, vol.103, no.9, pp. 742-755, Nov. 1996.
    • (1996) The Amer. Math. Monthly , vol.103 , Issue.9 , pp. 742-755
    • Burger, T.1    Gritzmann, P.2    Klee, V.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.