메뉴 건너뛰기




Volumn 39, Issue 1, 1993, Pages 46-59

Lattice and Trellis Quantization with Lattice- and Trellis-Bounded Codebooks—High-Rate Theory for Memoryless Sources

Author keywords

lattice quantization; Source coding; trellis coded modulation shaping; trellis coded quantization; vector quantization

Indexed keywords

CODES (SYMBOLS); DIGITAL COMMUNICATION SYSTEMS; INFORMATION THEORY; PROBABILITY; SIGNAL DISTORTION; VECTORS;

EID: 0027147870     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/18.179341     Document Type: Article
Times cited : (77)

References (45)
  • 2
    • 84941455682 scopus 로고
    • Full search and tree searched vector quantization of speech waveforms
    • Paris, France, May
    • R. M. Gray and H. Abut, “Full search and tree searched vector quantization of speech waveforms,” Proc. ICASSP, Paris, France, May 1982, pp. 593–596.
    • (1982) Proc. ICASSP , pp. 593-596
    • Gray, R.M.1    Abut, H.2
  • 3
    • 0022148098 scopus 로고
    • Vector quantization in speech coding
    • Nov.
    • J. Makhoul, S. Roucos, and H. Gish, “Vector quantization in speech coding,” Proc. IEEE, vol. 73, pp. 1551–1588, Nov. 1985.
    • (1985) Proc. IEEE , vol.73 , pp. 1551-1588
    • Makhoul, J.1    Roucos, S.2    Gish, H.3
  • 4
    • 0020888029 scopus 로고
    • Vector quantization: A pattern-matching technique for speech coding
    • Dec.
    • A. Gersho and V. Cuperman, “Vector quantization: A pattern-matching technique for speech coding,” IEEE Commun. Mag., pp. 15–21, Dec. 1983.
    • (1983) IEEE Commun. Mag. , pp. 15-21
    • Gersho, A.1    Cuperman, V.2
  • 5
    • 85031487385 scopus 로고
    • Multiple stage vector quantization for speech coding
    • May
    • B.-H. Juang and A. H. Gray, Jr., “Multiple stage vector quantization for speech coding,” Proc. ICASSP, May 1982, pp. 597–600.
    • (1982) Proc. ICASSP , pp. 597-600
    • Juang, B.-H.1    Gray, A.H.2
  • 6
    • 0021445197 scopus 로고
    • Product code vector quantizers for speech and waveform coding
    • June
    • M. J. Sabin and R. M. Gray, “Product code vector quantizers for speech and waveform coding,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-32, pp. 474–488, June 1984.
    • (1984) IEEE Trans. Acoust., Speech, Signal Processing , vol.ASSP-32 , pp. 474-488
    • Sabin, M.J.1    Gray, R.M.2
  • 7
    • 0025659608 scopus 로고
    • Vector sum excited linear prediction (VSELP) speech coding at 8 kb/s
    • Albuquerque, NM, Apr.
    • I. A. Gerson and M.A. Jasuik, “Vector sum excited linear prediction (VSELP) speech coding at 8 kb/s,” in Proc. ICASSP, Albuquerque, NM, Apr. 1989, pp. 461–464.
    • (1989) Proc. ICASSP , pp. 461-464
    • Gerson, I.A.1    Jasuik, M.A.2
  • 8
    • 0020098638 scopus 로고
    • Voronoi regions of lattices, second moments of polytopes, and quantization
    • May
    • J. H. Conway and N.J.A. Sloane, “Voronoi regions of lattices, second moments of polytopes, and quantization,” IEEE Trans. Inform. Theory, vol. IT-28, pp. 211–226, May 1982.
    • (1982) IEEE Trans. Inform. Theory , vol.IT-28 , pp. 211-226
    • Conway, J.H.1    Sloane, N.J.A.2
  • 9
    • 0020102220 scopus 로고
    • Fast quantizing and decoding algorithms for lattice quantizers and codes
    • Mar.
    • —, “Fast quantizing and decoding algorithms for lattice quantizers and codes,” IEEE Trans. Inform. Theory, vol. IT-28, pp. 227–232, Mar. 1982.
    • (1982) IEEE Trans. Inform. Theory , vol.IT-28 , pp. 227-232
  • 10
    • 0020850088 scopus 로고
    • A fast encoding method for lattice codes and quantizers
    • Nov.
    • —, “A fast encoding method for lattice codes and quantizers,” IEEE Trans. Inform. Theory, vol. IT-29, pp. 820–824, Nov. 1983.
    • (1983) IEEE Trans. Inform. Theory , vol.IT-29 , pp. 820-824
  • 11
    • 0021860488 scopus 로고
    • A lower bound on the average error of vector quantizers
    • Jan.
    • —, “A lower bound on the average error of vector quantizers,” IEEE Trans. Inform. Theory, vol. IT-31, pp. 106–109, Jan. 1985.
    • (1985) IEEE Trans. Inform. Theory , vol.IT-31 , pp. 106-109
  • 12
    • 0020098639 scopus 로고
    • On the structure of vector quantizers
    • Mar.
    • A. Gersho, “On the structure of vector quantizers,” IEEE Trans. Inform. Theory, vol. IT-28, pp. 157–166, Mar. 1982.
    • (1982) IEEE Trans. Inform. Theory , vol.IT-28 , pp. 157-166
    • Gersho, A.1
  • 13
    • 0021517874 scopus 로고
    • An algorithm for vector quantizer design
    • K. Sayood, J. D. Gibson, and M. C. Rost, “An algorithm for vector quantizer design,” IEEE Trans. Inform. Theory, vol. IT-30, pp. 805–814, 1984.
    • (1984) IEEE Trans. Inform. Theory , vol.IT-30 , pp. 805-814
    • Sayood, K.1    Gibson, J.D.2    Rost, M.C.3
  • 15
    • 0025434395 scopus 로고
    • A lattice vector quantizer using a geometric decomposition
    • May
    • T.-C. Chen, “A lattice vector quantizer using a geometric decomposition,” IEEE Trans. Commun., vol. 38, pp. 704–714, May 1990.
    • (1990) IEEE Trans. Commun. , vol.38 , pp. 704-714
    • Chen, T.-C.1
  • 18
    • 84941863458 scopus 로고    scopus 로고
    • Cubic lattice vector quantizers for nonuniform sources
    • to appear
    • D.G. Jeong and J.D. Gibson, “Cubic lattice vector quantizers for nonuniform sources,” IEEE Trans. Inform. Theory, to appear.
    • IEEE Trans. Inform. Theory
    • Jeong, D.G.1    Gibson, J.D.2
  • 19
    • 80055077896 scopus 로고
    • A geometric treatment of source encoding of a Gaussian random variable
    • May
    • D. J. Sakrison, “A geometric treatment of source encoding of a Gaussian random variable,” IEEE Trans. Inform. Theory, vol. IT-14, pp. 96–101, May 1968.
    • (1968) IEEE Trans. Inform. Theory , vol.IT-14 , pp. 96-101
    • Sakrison, D.J.1
  • 20
    • 0022756942 scopus 로고
    • A pyramid vector quantizer
    • July
    • T. R. Fischer, “A pyramid vector quantizer,” IEEE Trans. Inform. Theory, vol. IT-32, pp. 568–583, July 1986.
    • (1986) IEEE Trans. Inform. Theory , vol.IT-32 , pp. 568-583
    • Fischer, T.R.1
  • 21
    • 0000467209 scopus 로고
    • Nearest neighbor algorithm for spherical codes from the Leech lattice
    • pt. II, Sept.
    • J.P. Adoul and M. Barth, “Nearest neighbor algorithm for spherical codes from the Leech lattice,” IEEE Trans. Inform. Theory, vol. 34, pt. II, pp. 1188–1202, Sept. 1988.
    • (1988) IEEE Trans. Inform. Theory , vol.34 , pp. 1188-1202
    • Adoul, J.P.1    Barth, M.2
  • 22
    • 34250866133 scopus 로고
    • Geometric source coding and vector quantization
    • Jan.
    • T. R. Fischer, “Geometric source coding and vector quantization,” IEEE Trans. Inform. Theory, vol. 35, pp. 137–145, Jan. 1989.
    • (1989) IEEE Trans. Inform. Theory , vol.35 , pp. 137-145
    • Fischer, T.R.1
  • 23
    • 0024877541 scopus 로고
    • Fast CELP coding based on the Barnes-Wall lattice in 16 dimensions
    • Glasgow, Apr.
    • C. Lamblin, J. P. Adoul, D. Massaloux, and S. Morissette, “Fast CELP coding based on the Barnes-Wall lattice in 16 dimensions,” Proc. ICASSP’89, Glasgow, Apr. 1989, pp. 61–64.
    • (1989) Proc. ICASSP’89 , pp. 61-64
    • Lamblin, C.1    Adoul, J.P.2    Massaloux, D.3    Morissette, S.4
  • 24
    • 0020100081 scopus 로고
    • Asymptotic quantization error of continuous signals and the quantization dimension
    • Mar. also unpublished Bell Labs memo., “Topics in the asymptotic quantization of continuous random variables,” 1966)
    • P. Zador, “Asymptotic quantization error of continuous signals and the quantization dimension,” IEEE Trans. Inform. Theory, vol. IT-28, pp. 139–149, Mar. 1982 (also unpublished Bell Labs memo., “Topics in the asymptotic quantization of continuous random variables,” 1966).
    • (1982) IEEE Trans. Inform. Theory , vol.IT-28 , pp. 139-149
    • Zador, P.1
  • 25
    • 0018491303 scopus 로고
    • Asymptotically optimal block quantization
    • July
    • A. Gersho, “Asymptotically optimal block quantization,” IEEE Trans. Inform. Theory, vol. IT-25, pp. 373–380, July 1979.
    • (1979) IEEE Trans. Inform. Theory , vol.IT-25 , pp. 373-380
    • Gersho, A.1
  • 26
    • 0018845170 scopus 로고
    • Asymptotic performance of block quantizers with difference distortion measures
    • Jan.
    • Y. Yamada, S. Tazaki, and R.M. Gray, “Asymptotic performance of block quantizers with difference distortion measures,” IEEE Trans. Inform. Theory, IT-26, pp. 6–15, Jan. 1984.
    • (1984) IEEE Trans. Inform. Theory , vol.IT-26 , pp. 6-15
    • Yamada, Y.1    Tazaki, S.2    Gray, R.M.3
  • 27
    • 0024735218 scopus 로고
    • High resolution quantization theory and the vector quantizer advantage
    • Sept.
    • T. Lookabaugh and R.M. Gray, “High resolution quantization theory and the vector quantizer advantage,” IEEE Trans. Inform. Theory, vol. 35, pp. 1020–1033, Sept. 1989.
    • (1989) IEEE Trans. Inform. Theory , vol.35 , pp. 1020-1033
    • Lookabaugh, T.1    Gray, R.M.2
  • 28
    • 0021385941 scopus 로고
    • Two results on the asymptotic performance of quantizers
    • J. A. Bucklew, “Two results on the asymptotic performance of quantizers,” IEEE Trans. Inform. Theory, vol. IT-30, pp. 341–348, 1984.
    • (1984) IEEE Trans. Inform. Theory , vol.IT-30 , pp. 341-348
    • Bucklew, J.A.1
  • 29
    • 38349040753 scopus 로고
    • Asymptotically efficient quantizing
    • Sept.
    • H. Gish and J. N. Pierce, “Asymptotically efficient quantizing,” IEEE Trans. Inform. Theory, vol. IT-14, pp. 676–683, Sept. 1968.
    • (1968) IEEE Trans. Inform. Theory , vol.IT-14 , pp. 676-683
    • Gish, H.1    Pierce, J.N.2
  • 30
    • 0021422549 scopus 로고
    • Optimum quantizer performance for a class of non-Gaussian memoryless sources
    • May
    • N. Farvardin and J.W. Modestino, “Optimum quantizer performance for a class of non-Gaussian memoryless sources,” IEEE Trans. Inform. Theory, vol. IT-30, pp. 485–497, May 1984.
    • (1984) IEEE Trans. Inform. Theory , vol.IT-30 , pp. 485-497
    • Farvardin, N.1    Modestino, J.W.2
  • 31
    • 84941860379 scopus 로고
    • Coset codes—Part II: Binary lattices and related codes
    • Sept.
    • G. D. Forney, Jr., “Coset codes—Part II: Binary lattices and related codes,” IEEE Trans. Inform. Theory, vol. 34, pp. 1152–1187, Sept. 1988.
    • (1988) IEEE Trans. Inform. Theory , vol.34 , pp. 1152-1187
    • Forney, G.D.1
  • 32
    • 0024717659 scopus 로고
    • Multidimensional constellations—Part II: Voronoi constellations
    • —, “Multidimensional constellations—Part II: Voronoi constellations,” IEEE J. Select. Areas Commun., vol. 7, pp. 941–958, 1989.
    • (1989) IEEE J. Select. Areas Commun. , vol.7 , pp. 941-958
  • 33
    • 84945713988 scopus 로고
    • Coset codes—Part I: Introduction and geometrical classification
    • pt. II, Sept.
    • —, “Coset codes—Part I: Introduction and geometrical classification,” IEEE Trans. Inform. Theory, vol. 34, pt. II, pp. 1123–1151, Sept. 1988.
    • (1988) IEEE Trans. Inform. Theory , vol.34 , pp. 1123-1151
  • 34
    • 0026834915 scopus 로고
    • Trellis shaping
    • pt. II, Mar.
    • —, “Trellis shaping,” IEEE Trans. Inform. Theory, vol. 38, pt. II, pp. 281–300, Mar. 1992.
    • (1992) IEEE Trans. Inform. Theory , vol.38 , pp. 281-300
  • 35
    • 0025218172 scopus 로고
    • Trellis-coded quantization of memoryless and Gauss-Markov sources
    • Jan.
    • M. W. Marcellin and T. R. Fischer, “Trellis-coded quantization of memoryless and Gauss-Markov sources,” IEEE Trans. Commun., vol. 38, pp. 82–93, Jan. 1990.
    • (1990) IEEE Trans. Commun. , vol.38 , pp. 82-93
    • Marcellin, M.W.1    Fischer, T.R.2
  • 36
    • 0024717169 scopus 로고
    • Some optimal codes have structure
    • Aug.
    • R. deBuda, “Some optimal codes have structure,” IEEE J. Select. Areas Commun., vol. 7, pp. 893–899, Aug. 1989.
    • (1989) IEEE J. Select. Areas Commun. , vol.7 , pp. 893-899
    • deBuda, R.1
  • 39
    • 0023313295 scopus 로고
    • New trellis codes based on lattices and cosets
    • Mar.
    • A. R. Calderbank and N. J. Sloane, “New trellis codes based on lattices and cosets,” IEEE Trans. Inform. Theory, vol. IT-33, pp. 179–195, Mar. 1987.
    • (1987) IEEE Trans. Inform. Theory , vol.IT-33 , pp. 179-195
    • Calderbank, A.R.1    Sloane, N.J.2
  • 40
    • 0026220377 scopus 로고
    • Geometrically uniform codes
    • July
    • G. D. Forney, Jr., “Geometrically uniform codes,” IEEE Trens. Inform. Theory, vol. 36, pp. 1241–1260, July 1991.
    • (1991) IEEE Trens. Inform. Theory , vol.36 , pp. 1241-1260
    • Forney, G.D.1
  • 41
    • 0019343223 scopus 로고
    • Channel coding with multilevel/phase signals
    • Jan.
    • G. Ungerboeck, “Channel coding with multilevel/phase signals,” IEEE Trans. Inform. Theory, vol. IT-28, pp. 55–67, Jan. 1982.
    • (1982) IEEE Trans. Inform. Theory , vol.IT-28 , pp. 55-67
    • Ungerboeck, G.1
  • 42
    • 0023383214 scopus 로고
    • Trellis-coded modulation with multidimensional constellations
    • July
    • L.-F. Wei, “Trellis-coded modulation with multidimensional constellations,” IEEE Trans. Inform. Theory, vol. IT-33, pp. 483–501, July 1987.
    • (1987) IEEE Trans. Inform. Theory , vol.IT-33 , pp. 483-501
    • Wei, L.-F.1
  • 43
    • 0024718199 scopus 로고
    • Multidimensional constellations—Part I: Introduction, figures of merit and generalized cross constellations
    • Aug.
    • G. D. Forney, Jr. and L. F. Wei, “Multidimensional constellations—Part I: Introduction, figures of merit and generalized cross constellations,” IEEE J. Select. Areas Commun., vol. 7, pp. 877–892, Aug. 1989.
    • (1989) IEEE J. Select. Areas Commun. , vol.7 , pp. 877-892
    • Forney, G.D.1    Wei, L.F.2
  • 45
    • 84946245856 scopus 로고
    • Lattice and trellis quantization with lattice-and trellis-bounded codebooks—Implementation techniques for memoryless sources
    • M. V. Eyuboglu and A. Balamesh, “Lattice and trellis quantization with lattice-and trellis-bounded codebooks—Implementation techniques for memoryless sources,” submitted to IEEE Trans. Inform. Theory, 1991.
    • (1991) submitted to IEEE Trans. Inform. Theory
    • Eyuboglu, M.V.1    Balamesh, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.