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Volumn 44, Issue 6, 1998, Pages 2561-2595

The art of signaling: fifty years of coding theory

Author keywords

Algebraic; Information and coding theory; Quantum and space time codes; Trellis

Indexed keywords

ALGEBRA; BLOCK CODES; CHANNEL CAPACITY; COMMUNICATION CHANNELS (INFORMATION THEORY); CRYPTOGRAPHY; GEOMETRY; INFORMATION THEORY; POLYNOMIALS; PROBABILITY; TRELLIS CODES;

EID: 0032183145     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.720549     Document Type: Article
Times cited : (46)

References (234)
  • 1
    • 33747266524 scopus 로고    scopus 로고
    • Space block coding: A simple transmitter diversity scheme for wireless communications
    • S. Alamouti, Space block coding: A simple transmitter diversity scheme for wireless communications, submitted to IEEE J. Select. Areas Commun., 1997.
    • (1997) IEEE J. Select. Areas Commun.
    • Alamouti, S.1
  • 3
    • 0016037512 scopus 로고
    • Optimal decoding of linear codes for minimizing symbol error rate
    • L. R. Bahl, J. Cocke, F. Jelinek, and J. Raviv, Optimal decoding of linear codes for minimizing symbol error rate, IEEE Trans. Inform. Theory, vol. IT-20, pp. 284-287, 1974.
    • (1974) IEEE Trans. Inform. Theory, . , vol.IT-20 , pp. 284-287
    • Bahl, L.R.1    Cocke, J.2    Jelinek, F.3    Raviv, J.4
  • 4
    • 0026155822 scopus 로고
    • Dual diversity combining and equalization in digital cellular mobile radio
    • N. Balaban and J. Salz, Dual diversity combining and equalization in digital cellular mobile radio, IEEE Trans. Veh. Tech.nol, vol. 40, pp. 342-354, 1991.
    • (1991) IEEE Trans. Veh. Tech.nol , vol.40 , pp. 342-354
    • Balaban, N.1    Salz, J.2
  • 5
    • 3643119399 scopus 로고
    • At the dawn of the theory of codes
    • A. Barg, At the dawn of the theory of codes, Math. Intelligencer, vol. 15, pp. 20-26, 1993.
    • (1993) Math. Intelligencer , vol.15 , pp. 20-26
    • Barg, A.1
  • 6
    • 0000342467 scopus 로고
    • Statistical inference for probabilistic functions of finite-state Markov chains
    • L. E. Baum and T. Pétrie, Statistical inference for probabilistic functions of finite-state Markov chains, Ann. Math. Statist., vol. 37, pp. 1554-1563, 1966.
    • (1966) Ann. Math. Statist. , vol.37 , pp. 1554-1563
    • Baum, L.E.1    Pétrie, T.2
  • 7
    • 0030106621 scopus 로고    scopus 로고
    • Unveiling turbo codes: Some results on parallel concatenated coding schemes
    • S. Benedetto and G. Montorsi, Unveiling turbo codes: Some results on parallel concatenated coding schemes, IEEE Trans. Inform. Theory, vol. 42, pp. 409-428, 1996.
    • (1996) IEEE Trans. Inform. Theory , vol.42 , pp. 409-428
    • Benedetto, S.1    Montorsi, G.2
  • 8
    • 4243789313 scopus 로고    scopus 로고
    • Purification of noisy entanglement and faithful teleportation via noisy channels
    • also LANL eprint quant-ph/9511027.
    • C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, Purification of noisy entanglement and faithful teleportation via noisy channels, Phys. Rev. Lett., vol. 76, pp. 722-725, 1996; also LANL eprint quant-ph/9511027.
    • (1996) Phys. Rev. Lett. , vol.76 , pp. 722-725
    • Bennett, C.H.1    Brassard, G.2    Popescu, S.3    Schumacher, B.4    Smolin, J.A.5    Wootters, W.K.6
  • 12
  • 13
    • 0028514145 scopus 로고
    • Performance of nonuniform constellations on the Gaussian channel
    • W. Betts, A. R. Calderbank, and R. Laroia, Performance of nonuniform constellations on the Gaussian channel, IEEE Trans. Inform. Theory, vol. 40, pp. 1633-1638, 1994
    • (1994) IEEE Trans. Inform. Theory , vol.40 , pp. 1633-1638
    • Betts, W.1    Calderbank, A.R.2    Laroia, R.3
  • 17
    • 0000945803 scopus 로고
    • Circuitry for performing error correction calculations on baseband encoded data to eliminate error propagation
    • W. G. Bliss, Circuitry for performing error correction calculations on baseband encoded data to eliminate error propagation, IBM Tech. Disci. Bull., vol. 23, pp. 4633-4634, 1981.
    • (1981) IBM Tech. Disci. Bull. , vol.23 , pp. 4633-4634
    • Bliss, W.G.1
  • 18
    • 33747503366 scopus 로고
    • Quasisymmetric designs and the smith normal form
    • A. Blokhuis and A. R. Calderbank, Quasisymmetric designs and the smith normal form, Des., Codes Cryptogr., vol. 2, pp. 189-206, 1992.
    • (1992) Des., Codes Cryptogr. , vol.2 , pp. 189-206
    • Blokhuis, A.1    Calderbank, A.R.2
  • 19
    • 0029272035 scopus 로고
    • Quaternary quadratic residue codes and unimodular lattices
    • A. Bonnecaze, A. R. Calderbank, and P. Sole, Quaternary quadratic residue codes and unimodular lattices, IEEE Trans. Inform. Theory, vol. 41, pp. 366-377, 1995.
    • (1995) IEEE Trans. Inform. Theory , vol.41 , pp. 366-377
    • Bonnecaze, A.1    Calderbank, A.R.2    Sole, P.3
  • 20
    • 0002541684 scopus 로고
    • On linear associative algebras corresponding to association schemes of partially balanced designs
    • R. C. Bose and D. M. Mesner, On linear associative algebras corresponding to association schemes of partially balanced designs, Ann. Math. Statist., vol. 30, pp. 21-38, 1959.
    • (1959) Ann. Math. Statist. , vol.30 , pp. 21-38
    • Bose, R.C.1    Mesner, D.M.2
  • 22
    • 0024627773 scopus 로고
    • Multilevel codes and multistage decoding
    • A. R. Calderbank, Multilevel codes and multistage decoding, IEEE Trans Commun., vol. 37, pp. 222-229, 1989.
    • (1989) IEEE Trans Commun. , vol.37 , pp. 222-229
    • Calderbank, A.R.1
  • 27
    • 0032137638 scopus 로고    scopus 로고
    • Partial response codes for electron trapping optical memories
    • A. R. Calderbank, R. Laroia, and S. W. McLaughlin, Partial response codes for electron trapping optical memories, IEEE Trans. Commun., vol. 46, pp. 1011-1019, 1998.
    • (1998) IEEE Trans. Commun. , vol.46 , pp. 1011-1019
    • Calderbank, A.R.1    Laroia, R.2    McLaughlin, S.W.3
  • 30
    • 0024719206 scopus 로고
    • Baseband line codes via spectral factorization
    • A. R. Calderbank and J. E. Mazo, Baseband line codes via spectral factorization, IEEE J. Select. Areas Commun., vol. 7, pp. 914-928, 1989.
    • (1989) IEEE J. Select. Areas Commun. , vol.7 , pp. 914-928
    • Calderbank, A.R.1    Mazo, J.E.2
  • 31
    • 0025462466 scopus 로고
    • Nonequiprobable signaling on the Gaussian channel
    • A. R. Calderbank and L. H. Ozarow, Nonequiprobable signaling on the Gaussian channel, IEEE Trans. Inform. Theory, vol. 33, pp. 726-740, 1990.
    • (1990) IEEE Trans. Inform. Theory , vol.33 , pp. 726-740
    • Calderbank, A.R.1    Ozarow, L.H.2
  • 32
    • 0001060859 scopus 로고    scopus 로고
    • Quantum error correction and orthogonal geometry
    • also LANL eprint quant-ph/9605005.
    • A. R. Calderbank, E. M. Rains, P. W. Shor, and N. J. A. Sloane, Quantum error correction and orthogonal geometry, Phys. Rev. Lett., vol. 78, pp. 405-409, 1997; also LANL eprint quant-ph/9605005.
    • (1997) Phys. Rev. Lett. , vol.78 , pp. 405-409
    • Calderbank, A.R.1    Rains, E.M.2    Shor, P.W.3    Sloane, N.J.A.4
  • 34
    • 0027634580 scopus 로고
    • Multilevel codes for unequal error protection
    • A. R. Calderbank and N. Seshadri, Multilevel codes for unequal error protection, IEEE Trans. Inform. Theory, vol. 39, pp. 1234-1248, 1993.
    • (1993) IEEE Trans. Inform. Theory , vol.39 , pp. 1234-1248
    • Calderbank, A.R.1    Seshadri, N.2
  • 35
    • 0001398327 scopus 로고    scopus 로고
    • Good quantum error-correcting codes exist
    • also LANL eprint quant-ph/9512032.
    • A. R. Calderbank and P. W. Shor, Good quantum error-correcting codes exist, Phys. Rev. A, vol. 54, pp. 1098-1105, 1996; also LANL eprint quant-ph/9512032.
    • (1996) Phys. Rev. a , vol.54 , pp. 1098-1105
    • Calderbank, A.R.1    Shor, P.W.2
  • 36
    • 0023313295 scopus 로고
    • New trellis codes based on lattices and cosets
    • A. R. Calderbank and N. J. A. Sloane, New trellis codes based on lattices and cosets, IEEE Trans. Inform. Theory, vol. 33, pp. 177-195, 1987.
    • (1987) IEEE Trans. Inform. Theory , vol.33 , pp. 177-195
    • Calderbank, A.R.1    Sloane, N.J.A.2
  • 37
    • 49549167853 scopus 로고
    • Quadratic forms over GF(2)
    • P. J. Cameron and J. J. Seidel, Quadratic forms over GF(2), Indag. Math., vol. 35, pp. 1-8, 1973.
    • (1973) Indag. Math. , vol.35 , pp. 1-8
    • Cameron, P.J.1    Seidel, J.J.2
  • 38
    • 0013197963 scopus 로고    scopus 로고
    • Codes and association schemes, in
    • R. A. Brualdi, W. C. Huffman, and V. Pless, Eds. Amsterdam, The Netherlands: Else vier, to be published.
    • P. Camion, Codes and association schemes, in Handbook of Coding Theory, R. A. Brualdi, W. C. Huffman, and V. Pless, Eds. Amsterdam, The Netherlands: Else vier, to be published.
    • Handbook of Coding Theory
    • Camion, P.1
  • 39
    • 0033184694 scopus 로고    scopus 로고
    • On minimum Lee weights of Hensel lifts of some binary BCH codes
    • submitted for publication.
    • H. Chen, On minimum Lee weights of Hensel lifts of some binary BCH codes, IEEE Trans. Inform. Theory, submitted for publication.
    • IEEE Trans. Inform. Theory
    • Chen, H.1
  • 40
    • 5244282087 scopus 로고
    • Cyclic decoding procedure for the Bose-Chaudhuri-Hocquengham codes
    • R. T. Chien, Cyclic decoding procedure for the Bose-Chaudhuri-Hocquengham codes, IEEE Trans. Inform. Theory, vol. IT-10, pp. 357-363, 1964.
    • (1964) IEEE Trans. Inform. Theory , vol.VOL. IT-10 , pp. 357-363
    • Chien, R.T.1
  • 41
    • 0003734035 scopus 로고
    • The subtleties and intricacies of building a constraint length 15 convolutional decoder
    • O. M. Collins, The subtleties and intricacies of building a constraint length 15 convolutional decoder, IEEE Trans. Commun., vol. 40, pp. 1810-1819, 1992.
    • (1992) IEEE Trans. Commun. , vol.40 , pp. 1810-1819
    • Collins, O.M.1
  • 42
    • 0020850088 scopus 로고
    • A fast encoding method for lattice codes and quantizers
    • J. H. Conway and N. J. A. Sloane, A fast encoding method for lattice codes and quantizers, IEEE Trans. Inform. Theory, vol. IT-29, pp. 820-824, 1983.
    • (1983) IEEE Trans. Inform. Theory , vol.IT-29 , pp. 820-824
    • Conway, J.H.1    Sloane, N.J.A.2
  • 43
    • 0022563696 scopus 로고
    • Soft decoding techniques for codes and lattices including the Golay code and the Leech lattice
    • Soft decoding techniques for codes and lattices including the Golay code and the Leech lattice, IEEE Trans. Inform. Theory, vol. IT-32, pp. 41-50, 1986
    • (1986) IEEE Trans. Inform. Theory , vol.IT , pp. 41-50
  • 47
    • 0026205301 scopus 로고
    • Variable rate sub-band speech coding and matched convolutional channel coding for mobile radio channels
    • R. V. Cox, J. Hagenauer, N. Seshadri, and C.-E. Sundberg, Variable rate sub-band speech coding and matched convolutional channel coding for mobile radio channels, IEEE Trans. Signal Processing, vol. 39, pp. 1717-1731, 1991.
    • (1991) IEEE Trans. Signal Processing , vol.39 , pp. 1717-1731
    • Cox, R.V.1    Hagenauer, J.2    Seshadri, N.3    Sundberg, C.-E.4
  • 48
    • 85041979556 scopus 로고
    • An algebraic approach to the association schemes of coding theory
    • P. Delsarte, An algebraic approach to the association schemes of coding theory, Philips Res. Rep. Suppl, no. 10, 1973.
    • (1973) Philips Res. Rep. Suppl , Issue.10
    • Delsarte, P.1
  • 49
    • 0015735548 scopus 로고
    • Four fundamental parameters of a code and their combinatorial significance
    • Four fundamental parameters of a code and their combinatorial significance, Inform. Contr., vol. 23, pp. 407-438, 1973.
    • (1973) Inform. Contr. , vol.23 , pp. 407-438
  • 50
    • 0142002530 scopus 로고
    • Hahn polynomials, discrete harmonics and i-designs
    • Hahn polynomials, discrete harmonics and i-designs, SIAM J. Appl. Math., vol. 34, pp. 157-166, 1978.
    • (1978) SIAM J. Appl. Math. , vol.34 , pp. 157-166
  • 51
    • 33747483945 scopus 로고
    • Application and generalization of the Mac Williams transform in coding theory, in
    • Louvain-la-Neuve, Belgium
    • Application and generalization of the Mac Williams transform in coding theory, in P roc. 15th Symp. Information Theory in the Benelux (Louvain-la-Neuve, Belgium, 1989), pp. 9-14.
    • (1989) P Roc. 15th Symp. Information Theory in the Benelux , pp. 9-14
  • 52
    • 0038257909 scopus 로고
    • Alternating bilinear forms over GF(g)
    • P. Delsarte and J.-M. Goethals, Alternating bilinear forms over GF(g), J. Comb. Theory (A), vol. 19, pp. 26-50, 1975.
    • (1975) J. Comb. Theory (A) , vol.19 , pp. 26-50
    • Delsarte, P.1    Goethals, J.-M.2
  • 53
    • 0016599548 scopus 로고
    • Bounds for systems of lines and Jacobi polynomials
    • P. Delsarte, J.-M. Goethals, and J. J. Seidel, Bounds for systems of lines and Jacobi polynomials, Philips Res. Rep., vol. 30, pp. 91-105, 1975.
    • (1975) Philips Res. Rep. , vol.30 , pp. 91-105
    • Delsarte, P.1    Goethals, J.-M.2    Seidel, J.J.3
  • 54
    • 65649140960 scopus 로고
    • Spherical codes and designs
    • Spherical codes and designs, Geom. Dedicata, vol. 6, pp. 363-388, 1977.
    • (1977) Geom. Dedicata , vol.6 , pp. 363-388
  • 56
    • 5144230689 scopus 로고
    • Zeros of functions in finite abelian group algebras
    • P. Delsarte and R. J. McEliece, Zeros of functions in finite abelian group algebras, Amer. J. Math., vol. 98, pp. 197-224, 1976.
    • (1976) Amer. J. Math. , vol.98 , pp. 197-224
    • Delsarte, P.1    McEliece, R.J.2
  • 57
    • 0043156236 scopus 로고
    • Fisher type inequalities for euclidean -designs
    • P. Delsarte and J. J. Seidel, Fisher type inequalities for euclidean -designs, Lin. Alg. Appl., vols. 114/115, pp. 213-230, 1989.
    • (1989) Lin. Alg. Appl., Vols. , vol.114-115 , pp. 213-230
    • Delsarte, P.1    Seidel, J.J.2
  • 58
    • 0001799628 scopus 로고
    • Essai experimentalle et analytique
    • M. R. de Prony, Essai experimentalle et analytique, J. École Polytech. Paris, vol. 1, pp. 24-76, 1795.
    • (1795) J. École Polytech. Paris , vol.1 , pp. 24-76
    • De Prony, M.R.1
  • 59
    • 0027597079 scopus 로고
    • Majority coset decoding
    • I. Duursma, Majority coset decoding, IEEE Trans. Inform. Theory, vol. 39, pp. 1067-1071, 1993.
    • (1993) IEEE Trans. Inform. Theory , vol.39 , pp. 1067-1071
    • Duursma, I.1
  • 60
    • 0028460333 scopus 로고
    • Error-locating pairs for cyclic codes
    • I. Duursma and R. Kotier, Error-locating pairs for cyclic codes, IEEE Trans. Inform. Theory, vol. 40, pp. 1108-1121, 1994.
    • (1994) IEEE Trans. Inform. Theory , vol.40 , pp. 1108-1121
    • Duursma, I.1    Kotier, R.2
  • 61
    • 0027596957 scopus 로고
    • Achieving the designed error capacity in decoding algebraic-geometric codes
    • D. Ehrhard, Achieving the designed error capacity in decoding algebraic-geometric codes, IEEE Trans. Inform. Theory, vol. 39, pp. 743-751, 1993
    • (1993) IEEE Trans. Inform. Theory , vol.39 , pp. 743-751
    • Ehrhard, D.1
  • 62
    • 0000619946 scopus 로고    scopus 로고
    • Error correction in quantum communication
    • also LANL eprint quant-phi/9602022.
    • A. Ekert and C. Macchiavello, Error correction in quantum communication, Phys. Rev. Lett., vol. 77, pp. 2585-2588, 1996; also LANL eprint quant-phi/9602022.
    • (1996) Phys. Rev. Lett. , vol.77 , pp. 2585-2588
    • Ekert, A.1    Macchiavello, C.2
  • 63
    • 0026223105 scopus 로고
    • On codes satisfying Mth order running digital sum constraints
    • E. Eleftheriou and R. Cideciyan, On codes satisfying Mth order running digital sum constraints, IEEE Trans. Inform. Theory, vol. 37, pp. 1294-1313, 1991.
    • (1991) IEEE Trans. Inform. Theory , vol.37 , pp. 1294-1313
    • Eleftheriou, E.1    Cideciyan, R.2
  • 64
    • 84948588467 scopus 로고
    • Achievable rates for multiple descriptions
    • A. A. El Gamal and T. M. Cover, Achievable rates for multiple descriptions, IEEE Trans. Inform. Theory, vol. IT-28, pp. 851-857, 1982
    • (1982) IEEE Trans. Inform. Theory , vol.IT-28 , pp. 851-857
    • El Gamal, A.A.1    Cover, T.M.2
  • 65
  • 66
    • 84960611591 scopus 로고
    • Intersection theorems for systems of finite sets
    • P. Erdös, C. Ko, and R. Rado, Intersection theorems for systems of finite sets, Quart. J. Math. Oxford, vol. 12, pp. 313-320, 1961.
    • (1961) Quart. J. Math. Oxford , vol.12 , pp. 313-320
    • Erdös, P.1    Ko, C.2    Rado, R.3
  • 67
    • 0002834913 scopus 로고
    • The use of coding theory in computational complexity
    • Providence, RI: Amer. Math. Soci.
    • J. Feigenbaum, The use of coding theory in computational complexity, in Different Aspects of Coding Theory, Proc. Symp. in Appl. Math., vol. 50. Providence, RI: Amer. Math. Soci., 1995, pp. 207-233.
    • (1995) Different Aspects of Coding Theory, Proc. Symp. in Appl. Math. , vol.50 , pp. 207-233
    • Feigenbaum, J.1
  • 68
    • 0001817861 scopus 로고    scopus 로고
    • Data Networks As Cascades: Investigating the Multifractal Nature of Internet WAN Traffic
    • A. Feldmann, A. C. Gilbert, and W. Willinger, Data networks as cascades: Investigating the multifractal nature of internet WAN traffic, to be published in Proc. ACM/SIGCOMM'98.
    • Proc. ACM/SIGCOMM'98.
    • Feldmann, A.1    Gilbert, A.C.2    Willinger, W.3
  • 69
    • 0027311434 scopus 로고
    • G.-L. Feng and T. R. N. Rao, Decoding of algebraic geometric codes up to the designed minimum distance, IEEE Trans. Inform. Theory, vol. 39, pp. 37-45, 1993.
    • (1993) IEEE Trans. Inform. Theory , vol.39 , pp. 37-45
    • Feng, G.-L.1
  • 70
    • 0028514932 scopus 로고
    • A new procedure for decoding cyclic and BCH codes up to the actual minimum distance
    • G.-L. Feng and K. K. Tzeng, A new procedure for decoding cyclic and BCH codes up to the actual minimum distance, IEEE Trans. Inform. Theory, vol. 40, pp. 1364-1374, 1994.
    • (1994) IEEE Trans. Inform. Theory , vol.40 , pp. 1364-1374
    • Feng, G.-L.1    Tzeng, K.K.2
  • 71
    • 0040642567 scopus 로고
    • The theory of confounding in factorial experiments in relation to the theory of groups
    • R. A. Fisher, The theory of confounding in factorial experiments in relation to the theory of groups, Ann. Eugenics, vol. 11, pp. 341-353, 1942.
    • (1942) Ann. Eugenics , vol.11 , pp. 341-353
    • Fisher, R.A.1
  • 72
    • 0011416193 scopus 로고
    • A system of confounding for factors with more than two alternatives, giving completely orthogonal cubes and higher powers
    • R. A. Fisher, A system of confounding for factors with more than two alternatives, giving completely orthogonal cubes and higher powers, Ann. Eugenics, vol. 12, pp. 2283-2290, 1945.
    • (1945) Ann. Eugenics , vol.12 , pp. 2283-2290
    • Fisher, R.A.1
  • 74
    • 0004137776 scopus 로고
    • Cambridge, MA: MIT Press
    • Concatenated Codes. Cambridge, MA: MIT Press, 1966.
    • (1966) Concatenated Codes.
  • 75
    • 0014869779 scopus 로고
    • Convolutional codes I: Algebraic structure
    • correction in vol. IT-17, p. 360
    • Convolutional codes I: Algebraic structure, IEEE Trans. Inform. Theory, vol. IT-16, pp. 720-738, 1970; correction in vol. IT-17, p. 360, 1971.
    • (1971) IEEE Trans. Inform. Theory , vol.VOL. IT-16 , pp. 720-738
  • 76
    • 0015346024 scopus 로고
    • Maximum likelihood sequence estimation in the presence of intersymbol interference
    • Maximum likelihood sequence estimation in the presence of intersymbol interference, IEEE Trans. Inform. Theory, vol. IT-18, pp. 363-378, 1972
    • (1972) IEEE Trans. Inform. Theory , vol.IT-18 , pp. 363-378
  • 77
    • 0015600423 scopus 로고
    • The Viterbi algorithm
    • The Viterbi algorithm, Proc. IEEE, vol. 61, pp. 267-278, 1973.
    • (1973) Proc. IEEE , vol.61 , pp. 267-278
  • 78
    • 0016508669 scopus 로고
    • Minimal bases of rational vector spaces wtih applications to multivariable linear systems
    • Minimal bases of rational vector spaces wtih applications to multivariable linear systems, SIAM J. Contr., vol. 13, pp. 439-520, 1975
    • (1975) SIAM J. Contr. , vol.13 , pp. 439-520
  • 79
    • 84945713988 scopus 로고
    • Coset codes-Part I: Introduction and geometrical classification
    • Coset codes-Part I: Introduction and geometrical classification, IEEE Trans. Inform. Theory, vol. 34, pp. 1123-1151, 1988.
    • (1988) IEEE Trans. Inform. Theory , vol.34 , pp. 1123-1151
  • 80
    • 84941860379 scopus 로고
    • Coset codes-Part II: Binary lattices and related codes
    • Coset codes-Part II: Binary lattices and related codes, IEEE Trans. Inform. Theory, vol. 34, pp. 1152-1187, 1988.
    • (1988) IEEE Trans. Inform. Theory , vol.34 , pp. 1152-1187
  • 81
    • 0026220377 scopus 로고
    • Geometrically uniform codes
    • Geometrically uniform codes, IEEE Trans. Inform. Theory, vol. 37, pp. 1241-1260, 1991.
    • (1991) IEEE Trans. Inform. Theory , vol.37 , pp. 1241-1260
  • 82
    • 0026834915 scopus 로고
    • Trellis shaping
    • Trellis shaping, IEEE Trans. Inform. Theory, vol. 38, pp. 281-300, 1992.
    • (1992) IEEE Trans. Inform. Theory , vol.38 , pp. 281-300
  • 84
    • 0024733925 scopus 로고
    • Coset codes for partial response channels; or coset codes with spectral nulls
    • G. D. Forney, Jr. and A. R. Calderbank, Coset codes for partial response channels; or coset codes with spectral nulls, IEEE Trans. Inform. Theory, vol. 35, pp. 925-943, 1989.
    • (1989) IEEE Trans. Inform. Theory , vol.35 , pp. 925-943
    • Forney Jr., G.D.1    Calderbank, A.R.2
  • 85
    • 0027668052 scopus 로고
    • The dynamics of group codes: State spaces, trellis diagrams and canonical encoders
    • G. D. Forney, Jr. and M. Trott, The dynamics of group codes: State spaces, trellis diagrams and canonical encoders, IEEE Trans. Inform. Theory, vol. 39, pp. 1491-1513, 1993.
    • (1993) IEEE Trans. Inform. Theory , vol.39 , pp. 1491-1513
    • Forney Jr., G.D.1    Trott, M.2
  • 87
    • 0030286484 scopus 로고    scopus 로고
    • Generalized minimum distance decoding of euclidean-space codes and lattices
    • G. D. Forney, Jr. and A. Vardy, Generalized minimum distance decoding of euclidean-space codes and lattices, IEEE Trans. Inform. Theory, vol. 42, pp. 1992-2026, 1996.
    • (1996) IEEE Trans. Inform. Theory , vol.42 , pp. 1992-2026
    • Forney Jr., G.D.1    Vardy, A.2
  • 88
    • 70349677822 scopus 로고    scopus 로고
    • On limits of wireless communication in a fading environment when using multiple antennas
    • to be published.
    • G. J. Foschini, Jr. and M. J. Gans, On limits of wireless communication in a fading environment when using multiple antennas, Wireless Personal Commun., to be published.
    • Wireless Personal Commun.
    • Foschini Jr., G.J.1    Gans, M.J.2
  • 91
    • 84925405668 scopus 로고
    • Low-density parity-check codes
    • R. G. Gallager, Low-density parity-check codes, IEEE Trans. Inform. Theory, vol. IT-8, pp. 21-28, 1962.
    • (1962) IEEE Trans. Inform. Theory , vol.IT-8 , pp. 21-28
    • Gallager, R.G.1
  • 93
    • 0003092390 scopus 로고
    • A tower of Artin-Schreier extensions of function fields attaining the Drinfeld-Vlädut bound
    • A. Garcia and H. Stichtenoth, A tower of Artin-Schreier extensions of function fields attaining the Drinfeld-Vlädut bound, Invent. Math., vol. 121, pp. 211-222, 1995.
    • (1995) Invent. Math. , vol.121 , pp. 211-222
    • Garcia, A.1    Stichtenoth, H.2
  • 94
    • 0003418704 scopus 로고
    • Orthogonal designs, quadratic forms and Hadamard matrices, in
    • New York and Basel: Marcel Decker
    • A. V. Geramita and J. Seberry, Orthogonal designs, quadratic forms and Hadamard matrices, in Lecture Notes in Pure and Applied Mathematics, vol. 43. New York and Basel: Marcel Decker, 1979.
    • (1979) Lecture Notes in Pure and Applied Mathematics , vol.43
    • Geramita, A.V.1    Seberry, J.2
  • 95
    • 0001287361 scopus 로고
    • A comparison of signalling alphabets
    • E. N. Gilbert, A comparison of signalling alphabets, Bell Syst. Tech. J.. vol. 31, pp. 504-522, 1952.
    • (1952) Bell Syst. Tech. J.. , vol.31 , pp. 504-522
    • Gilbert, E.N.1
  • 96
    • 33747492558 scopus 로고    scopus 로고
    • The capacity of wireless communications systems can be substantially increased by the use of antenna diversity
    • to be published.
    • R. D. Gitlin, J. Salz, and J. H. Winters, The capacity of wireless communications systems can be substantially increased by the use of antenna diversity, IEEE J. Select. Areas Commun., to be published.
    • IEEE J. Select. Areas Commun.
    • Gitlin, R.D.1    Salz, J.2    Winters, J.H.3
  • 97
    • 0001298679 scopus 로고
    • Weight polynomials of self-dual codes and the MacWilliams identities
    • A. M. Gleason, Weight polynomials of self-dual codes and the MacWilliams identities, in Actes Congrès Int. de Math., vol. 3, pp. 211-215, 1970.
    • (1970) Actes Congrès Int. de Math. , vol.3 , pp. 211-215
    • Gleason, A.M.1
  • 98
    • 0016128565 scopus 로고
    • Two dual families of nonlinear binary codes
    • J.-M. Goethals, Two dual families of nonlinear binary codes, Electron. Lett., vol. 10, pp. 471-472, 1974.
    • (1974) Electron. Lett. , vol.10 , pp. 471-472
    • Goethals, J.-M.1
  • 99
    • 0016953735 scopus 로고
    • Nonlinear codes defined by quadratic forms over GF(2)
    • Nonlinear codes defined by quadratic forms over GF(2), Inform. Contr., vol. 31, pp. 43-74, 1976.
    • (1976) Inform. Contr. , vol.31 , pp. 43-74
  • 102
    • 0000499681 scopus 로고
    • Notes on digital coding
    • M. J. E. Golay, Notes on digital coding, Proc. IEEE, vol. 37, p. 657, 1949.
    • (1949) Proc. IEEE , vol.37 , pp. 657
    • Golay, M.J.E.1
  • 103
    • 0000942249 scopus 로고
    • Codes on algebraic curves
    • V. D. Goppa, Codes on algebraic curves, Sov. Math.-Dokl., vol. 24, pp. 170-172, 1981.
    • (1981) Sov. Math.-Dokl. , vol.24 , pp. 170-172
    • Goppa, V.D.1
  • 104
    • 0000588580 scopus 로고
    • Translation from Dokl. Akad. Nauk S.S.S.R., vol. 259, pp. 1289-1290, 1981.
    • (1981) Dokl. Akad. Nauk S.S.S.R. , vol.259 , pp. 1289-1290
  • 105
    • 0000830897 scopus 로고
    • A class of error correcting codes in pm symbols
    • D. C. Gorenstein and N. Zierler, A class of error correcting codes in pm symbols, SIAM J., vol. 9, pp. 207-214, 1971.
    • (1971) SIAM J. , vol.9 , pp. 207-214
    • Gorenstein, D.C.1    Zierler, N.2
  • 106
    • 0000132422 scopus 로고    scopus 로고
    • A class of quantum error-correcting codes saturating the quantum Hamming bound
    • also LANL eprint quant-ph/9604038
    • D. Gottesman, A class of quantum error-correcting codes saturating the quantum Hamming bound, Phys. Rev. A, vol. 54, pp. 1862-1868, 1996; also LANL eprint quant-ph/9604038
    • (1996) Phys. Rev. a , vol.54 , pp. 1862-1868
    • Gottesman, D.1
  • 107
    • 0024908946 scopus 로고    scopus 로고
    • A Viterbi algorithm with soft-decision out-puts and its applications
    • J. Hagenauer and P. Hoeher, A Viterbi algorithm with soft-decision out-puts and its applications, in IEEE Globecom'89, 1989, pp. 1680-1685.
    • IEEE Globecom' , vol.89 , pp. 1989
    • Hagenauer, J.1    Hoeher, P.2
  • 108
    • 33747454442 scopus 로고
    • Matching Viterbi decoders and Reed-Solomon decoders in concatenated systems
    • S. B. Wicker and V. K. Bhargava, Eds. Piscataway, NJ: IEEE Press
    • J. Hagenauer, E. Offer, and L. Papke, Matching Viterbi decoders and Reed-Solomon decoders in concatenated systems, in Reed-Solomon Codes and Their Applications, S. B. Wicker and V. K. Bhargava, Eds. Piscataway, NJ: IEEE Press, 1994, pp. 242-271.
    • (1994) Reed-Solomon Codes and Their Applications , pp. 242-271
    • Hagenauer, J.1    Offer, E.2    Papke, L.3
  • 111
    • 84907867509 scopus 로고
    • On the decoding of algebraic-geometric codes
    • T. Høholdt and R. Pellikaan, On the decoding of algebraic-geometric codes, IEEE Trans. Inform. Theory, vol. 41, pp. 1589-1614, 1995.
    • (1995) IEEE Trans. Inform. Theory , vol.41 , pp. 1589-1614
    • Høholdt, T.1    Pellikaan, R.2
  • 113
    • 11144343315 scopus 로고
    • A new multi-level coding method using error correcting codes
    • H. Imai and S. Hirakawa, A new multi-level coding method using error correcting codes, IEEE Trans. Inform. Theory, vol. IT-23, pp. 371-377, 1977.
    • (1977) IEEE Trans. Inform. Theory , vol.IT-23 , pp. 371-377
    • Imai, H.1    Hirakawa, S.2
  • 114
    • 56349098139 scopus 로고
    • RS codes and the compact disk
    • S. B. Wicker and V. K. Bhargava, Eds. Piscataway, NJ: IEEE Press
    • K. A. S. Immink, RS codes and the compact disk, in Reed-Solomon Codes and Their Applications, S. B. Wicker and V. K. Bhargava, Eds. Piscataway, NJ: IEEE Press, 1994, pp. 41-59.
    • (1994) Reed-Solomon Codes and Their Applications , pp. 41-59
    • Immink, K.A.S.1
  • 115
    • 0031234312 scopus 로고    scopus 로고
    • A practical method for approaching the channel capacity of constrained channels
    • A practical method for approaching the channel capacity of constrained channels, IEEE Trans. Inform. Theory, vol. 43, pp. 1389-1399, 1997.
    • (1997) IEEE Trans. Inform. Theory , vol.43 , pp. 1389-1399
  • 116
    • 0023345320 scopus 로고
    • Binary transmission codes with higher order spectral nulls at zero frequency
    • K. A. S. Immink and G. Beenker, Binary transmission codes with higher order spectral nulls at zero frequency, IEEE Trans. Inform. Theory, vol. IT-33, pp. 452-454, 1987.
    • (1987) IEEE Trans. Inform. Theory , vol.IT-33 , pp. 452-454
    • Immink, K.A.S.1    Beenker, G.2
  • 118
    • 0015404701 scopus 로고
    • A class of constructive asymptotically good algebraic codes
    • J. Justesen, A class of constructive asymptotically good algebraic codes, IEEE Trans. Inform. Theory, vol. IT-18, pp. 652-656, 1972.
    • (1972) IEEE Trans. Inform. Theory , vol.IT-18 , pp. 652-656
    • Justesen, J.1
  • 119
    • 0020126782 scopus 로고
    • Information rates and power spectra of digital codes
    • Information rates and power spectra of digital codes, IEEE Trans. Inform. Theory, vol. IT-28, pp. 457-472, 1982.
    • (1982) IEEE Trans. Inform. Theory , vol.IT-28 , pp. 457-472
  • 122
    • 0026157741 scopus 로고
    • Matched spectral null codes for partial response channels
    • R. Karabed and P. H. Siegel, Matched spectral null codes for partial response channels, IEEE Trans. Inform. Theory, vol. 37, pp. 818-855, 1991.
    • (1991) IEEE Trans. Inform. Theory , vol.37 , pp. 818-855
    • Karabed, R.1    Siegel, P.H.2
  • 123
    • 0038257908 scopus 로고
    • A class of low-rate nonlinear binary codes
    • A. M. Kerdock, A class of low-rate nonlinear binary codes, Inform. Contr., vol. 20, pp. 182-187, 1972.
    • (1972) Inform. Contr. , vol.20 , pp. 182-187
    • Kerdock, A.M.1
  • 124
    • 0000258946 scopus 로고
    • The minimum distance of codes in an array coming from telescopic subgroups
    • C. Kirfel and R. Pellikaan, The minimum distance of codes in an array coming from telescopic subgroups, IEEE Trans. Inform. Theory, vol. 41, pp. 1720-1731, 1995.
    • (1995) IEEE Trans. Inform. Theory , vol.41 , pp. 1720-1731
    • Kirfel, C.1    Pellikaan, R.2
  • 125
    • 0015129510 scopus 로고
    • Correlative level coding and maximum likelihood decoding
    • H. Kobayashi, Correlative level coding and maximum likelihood decoding, IEEE Trans. Inform. Theory, vol. IT-17, pp. 586-594, 1971.
    • (1971) IEEE Trans. Inform. Theory , vol.IT-17 , pp. 586-594
    • Kobayashi, H.1
  • 126
    • 0000102940 scopus 로고
    • Applications of partial response channel coding to magnetic recording systems
    • H. Kobayashi and D. T. Tang, Applications of partial response channel coding to magnetic recording systems, IBM J. Res. Develop., vol. 14, pp. 368-375, 1970.
    • (1970) IBM J. Res. Develop. , vol.14 , pp. 368-375
    • Kobayashi, H.1    Tang, D.T.2
  • 128
    • 0019585653 scopus 로고
    • Estimation of mean error for a discrete successive approximation scheme
    • V. Koshélev, Estimation of mean error for a discrete successive approximation scheme, Probl. Inform. Transm., vol. 17, pp. 20-33, 1981.
    • (1981) Probl. Inform. Transm. , vol.17 , pp. 20-33
    • Koshélev, V.1
  • 129
    • 0003650642 scopus 로고
    • London Math. Soc. Lecture Notes, London/New York: Cambridge Univ. Press
    • E. S. Lander, Symmetric Designs: An Algebraic Approach (London Math. Soc. Lecture Notes, vol. 74). London/New York: Cambridge Univ. Press, 1983.
    • (1983) Symmetric Designs: An Algebraic Approach , vol.74
    • Lander, E.S.1
  • 130
    • 0030196751 scopus 로고    scopus 로고
    • Coding for intersymbol interference channels-Combined coding and preceding
    • R. Laroia, Coding for intersymbol interference channels-Combined coding and preceding, IEEE Trans. Inform. Theory, vol. 42, pp. 1053-1061, 1996.
    • (1996) IEEE Trans. Inform. Theory , vol.42 , pp. 1053-1061
    • Laroia, R.1
  • 131
    • 0028461532 scopus 로고
    • On optimal shaping of mul-tidimensional constellations
    • R. Laroia, N. Farvardin, and S. Tretter, On optimal shaping of mul-tidimensional constellations, IEEE Trans. Inform. Theory, vol. 40, pp. 1044-1056, 1994.
    • (1994) IEEE Trans. Inform. Theory , vol.40 , pp. 1044-1056
    • Laroia, R.1    Farvardin, N.2    Tretter, S.3
  • 132
    • 0001654568 scopus 로고
    • Notes on sphere packings
    • J. Leech, Notes on sphere packings, Canadian J. Math., vol. 19, pp. 251-267, 1967.
    • (1967) Canadian J. Math. , vol.19 , pp. 251-267
    • Leech, J.1
  • 133
    • 0001017029 scopus 로고
    • Sphere packings and error-correcting codes
    • J. Leech and N. J. A. Sloane, Sphere packings and error-correcting codes, Canadian J. Math., vol. 23, pp. 718-745, 1971.
    • (1971) Canadian J. Math. , vol.23 , pp. 718-745
    • Leech, J.1    Sloane, N.J.A.2
  • 135
    • 0038247240 scopus 로고
    • On bounds for packings in n-dimensional euclidean space
    • V. I. Levenshtein, On bounds for packings in n-dimensional euclidean space, Sov. Math.-Dokl, vol. 20, no. 2, pp. 417-421, 1979.
    • (1979) Sov. Math.-Dokl , vol.20 , Issue.2 , pp. 417-421
    • Levenshtein, V.I.1
  • 136
    • 3643078812 scopus 로고
    • Bounds on the maximum cardinality of a code with bounded modulus of the inner product
    • Bounds on the maximum cardinality of a code with bounded modulus of the inner product, Sov. Math.-Dokl., vol. 25, pp. 526-531, 1982.
    • (1982) Sov. Math.-Dokl. , vol.25 , pp. 526-531
  • 137
    • 34249842879 scopus 로고
    • Designs as maximum codes in polynomial metric spaces
    • Designs as maximum codes in polynomial metric spaces, Acta Applic. Math., vol. 29, pp. 1-82, 1992.
    • (1992) Acta Applic. Math. , vol.29 , pp. 1-82
  • 138
    • 0011271568 scopus 로고
    • Long BCH codes are bad
    • S. Lin and E. J. Weldon, Jr., Long BCH codes are bad, Inform. Contr., vol. 11, pp. 452-495, 1967.
    • (1967) Inform. Contr. , vol.11 , pp. 452-495
    • Lin, S.1    Weldon Jr., E.J.2
  • 140
    • 33747506752 scopus 로고
    • Berlin-Heidelberg-New York: Springer
    • Coding theory, in Springer Lecture Notes, vol. 201. Berlin-Heidelberg-New York: Springer, 1971.
    • (1971) Springer Lecture Notes , vol.201
    • Theory, C.1
  • 141
    • 0022564721 scopus 로고
    • On the minimum distance of cyclic codes
    • J. H. van Lint and R. M. Wilson, On the minimum distance of cyclic codes, IEEE Trans. Inform. Theory, vol. IT-32, pp. 23-40, 1986.
    • (1986) IEEE Trans. Inform. Theory , vol.IT-32 , pp. 23-40
    • Van Lint, J.H.1    Wilson, R.M.2
  • 142
    • 0005076525 scopus 로고
    • Binary block coding
    • S. P. Lloyd, Binary block coding, Bell Syst. Tech. J., vol. 36, pp. 517-535, 1957.
    • (1957) Bell Syst. Tech. J. , vol.36 , pp. 517-535
    • Lloyd, S.P.1
  • 143
    • 0031276871 scopus 로고    scopus 로고
    • Averaging bounds for lattices and linear codes
    • [ 142] H.-A. Loeliger, Averaging bounds for lattices and linear codes, IEEE Trans. Inform. Theory, vol. 43, pp. 1767-1773, 1997.
    • (1997) IEEE Trans. Inform. Theory , vol.43 , pp. 1767-1773
    • Loeliger, H.-A.1
  • 144
    • 0024735218 scopus 로고
    • High-resolution quantization theory and the vector quantizer advantage
    • T. D. Lookabaugh and R. M. Gray, High-resolution quantization theory and the vector quantizer advantage, IEEE Trans. Inform. Theory, vol. 35, pp. 1020-1033, 1989.
    • (1989) IEEE Trans. Inform. Theory , vol.35 , pp. 1020-1033
    • Lookabaugh, T.D.1    Gray, R.M.2
  • 145
    • 0018292109 scopus 로고
    • On the Shannon capacity of a graph
    • L. Lovâsz, On the Shannon capacity of a graph, IEEE Trans. Inform. Theory, vol. IT-25, pp. 1-7, 1979.
    • (1979) IEEE Trans. Inform. Theory , vol.IT-25 , pp. 1-7
    • Lovâsz, L.1
  • 146
    • 0030219216 scopus 로고    scopus 로고
    • Near Shannon limit performance of low density parity check codes
    • reprinted vol. 33, pp. 457-458, 1997.
    • D. J. C. MacKay and R. M. Neil, Near Shannon limit performance of low density parity check codes, Electron. Lett., vol. 32, pp. 1645-1646, 1996 (reprinted vol. 33, pp. 457-458, 1997).
    • (1996) Electron. Lett. , vol.32 , pp. 1645-1646
    • MacKay, D.J.C.1    Neil, R.M.2
  • 148
    • 0002627993 scopus 로고
    • A theorem on the distribution of weights in a systematic code
    • A theorem on the distribution of weights in a systematic code, Bell Syst. Tech. J., vol. 42, pp. 79-94, 1963.
    • (1963) Bell Syst. Tech. J. , vol.42 , pp. 79-94
  • 151
    • 0025218172 scopus 로고
    • Trellis-coded quantization of memoryless and Gauss-Markov sources
    • M. W. Marcellin and T. R. Fischer, Trellis-coded quantization of memoryless and Gauss-Markov sources, IEEE Trans. Commun., vol. 38, pp. 82-93, 1993.
    • (1993) IEEE Trans. Commun. , vol.38 , pp. 82-93
    • Marcellin, M.W.1    Fischer, T.R.2
  • 152
    • 0000987356 scopus 로고
    • Symbolic dynamics and connections to coding theory automata theory and system theory
    • Providence, RI: Amer. Math. Soc.
    • B. Marcus, Symbolic dynamics and connections to coding theory automata theory and system theory, in Different Aspects of Coding Theory, Proc. Symp. Applied Mathematics, vol. 50. Providence, RI: Amer. Math. Soc., 1995, pp. 95-108.
    • (1995) Different Aspects of Coding Theory, Proc. Symp. Applied Mathematics , vol.50 , pp. 95-108
    • Marcus, B.1
  • 154
    • 84937740421 scopus 로고
    • Shift register synthesis and BCH decoding
    • J. L. Massey, Shift register synthesis and BCH decoding, IEEE Trans. Inform. Theory, vol. IT-15, pp. 122-127, 1969.
    • (1969) IEEE Trans. Inform. Theory, . , vol.IT-15 , pp. 122-127
    • Massey, J.L.1
  • 155
    • 11344281140 scopus 로고
    • A new treatment of Bose-Chaudhuri codes
    • H. F. Mattson, Jr. and G. Solomon, A new treatment of Bose-Chaudhuri codes, SIAM J., vol. 9, pp. 654-669, 1961.
    • (1961) SIAM J. , vol.9 , pp. 654-669
    • Mattson Jr., H.F.1    Solomon, G.2
  • 157
    • 0017468074 scopus 로고
    • New upper bounds on the rate of a code via the Delsarte-MacWilliams inequalities
    • R. J. McEliece, E. R. Rodemich, H. Rumsey, Jr., and L. R. Welch, New upper bounds on the rate of a code via the Delsarte-MacWilliams inequalities, IEEE Trans. Inform. Theory, vol. IT-23, pp. 157-166, 1977.
    • (1977) IEEE Trans. Inform. Theory , vol.IT-23 , pp. 157-166
    • McEliece, R.J.1    Rodemich, E.R.2    Rumsey, H.3    Jr4    Welch, L.R.5
  • 158
    • 33747475391 scopus 로고
    • Capacity of channels with matched transmission technique for peak transmitting power limitation
    • H. Miyakawa and H. Harashima, Capacity of channels with matched transmission technique for peak transmitting power limitation, in Nat. Conv. Rec. IECE Japan, 1969, pp. 1268-1264.
    • (1969) Nat. Conv. Rec. IECE Japan , pp. 1268-11264
    • Miyakawa, H.1    Harashima, H.2
  • 159
    • 0024078703 scopus 로고
    • Minimal trellises for block codes
    • D. J. Muder, Minimal trellises for block codes, IEEE Trans. Inform. Theory, vol. 34, pp. 1049-1053, 1988.
    • (1988) IEEE Trans. Inform. Theory , vol.34 , pp. 1049-1053
    • Muder, D.J.1
  • 162
    • 0018809684 scopus 로고    scopus 로고
    • A class of error correcting codes for DPSK channels
    • K. Nakamura, A class of error correcting codes for DPSK channels, in Proc. Int. Conf. Communication, 1979, pp. 45.4.1-45.4.5.
    • Proc. Int. Conf. Communication , vol.1979 , pp. 4541-4545
    • Nakamura, K.1
  • 163
    • 0023329840 scopus 로고
    • 256-QAM modem for multi-carrier 400 Mb/s digital radio
    • Y. Nakamura, Y. Saito, and S. Aikawa, 256-QAM modem for multi-carrier 400 Mb/s digital radio, IEEE J. Select. Areas. Commun., vol. JSAC-5, pp. 329-335, 1987.
    • (1987) IEEE J. Select. Areas. Commun. , vol.JSAC-5 , pp. 329-335
    • Nakamura, Y.1    Saito, Y.2    Aikawa, S.3
  • 165
  • 166
    • 0001179224 scopus 로고
    • New bounds on the number of spheres that can touch a unit sphere in n-dimensions
    • A. M. Odlyzko and N. J. A. Sloane, New bounds on the number of spheres that can touch a unit sphere in n-dimensions, J. Combin. Theory, vol. (A)26, pp. 210-214, 1979.
    • (1979) J. Combin. Theory , vol.A26 , pp. 210-214
    • Odlyzko, A.M.1    Sloane, N.J.A.2
  • 167
    • 0019178773 scopus 로고
    • On a source coding problem with two channels and three receivers
    • L. H. Ozarow, On a source coding problem with two channels and three receivers, Bell Syst. Tech. J., vol. 59, pp. 1909-1921, 1980.
    • (1980) Bell Syst. Tech. J. , vol.59 , pp. 1909-1921
    • Ozarow, L.H.1
  • 169
    • 0022015348 scopus 로고
    • Communications aspects of the compact disk digital audio system
    • Feb.
    • J. B. H. Peek, Communications aspects of the compact disk digital audio system, IEEE Commun. Mag., vol. 23, pp. 7-15, Feb. 1985.
    • (1985) IEEE Commun. Mag. , vol.23 , pp. 7-15
    • Peek, J.B.H.1
  • 170
    • 38249008268 scopus 로고
    • On the decoding by error location and the number of dependent error positions
    • R. Pellikaan, On the decoding by error location and the number of dependent error positions, Discr. Math., vols. 106/107, pp. 369-381, 1992.
    • (1992) Discr. Math. , vol.106-107 , pp. 369-381
    • Pellikaan, R.1
  • 171
    • 0000808175 scopus 로고
    • Encoding and error correction procedures for the Bose-Chaudhuri codes
    • W. W. Peterson, Encoding and error correction procedures for the Bose-Chaudhuri codes, IEEE Trans. Inform. Theory, vol. 6, pp. 459-470, 1960.
    • (1960) IEEE Trans. Inform. Theory , vol.6 , pp. 459-470
    • Peterson, W.W.1
  • 173
    • 0026953491 scopus 로고
    • On decoding geometric Goppa codes using an extra place
    • S. C. Porter, B.-Z. Shen, and R. Pellikaan, On decoding geometric Goppa codes using an extra place, IEEE Trans. Inform. Theory, vol. 38, pp. 1663-1676, 1992.
    • (1992) IEEE Trans. Inform. Theory , vol.38 , pp. 1663-1676
    • Porter, S.C.1    Shen, B.-Z.2    Pellikaan, R.3
  • 174
    • 34250844514 scopus 로고
    • Multilevel codes based on partitioning
    • G. J. Pottie and D. P. Taylor, Multilevel codes based on partitioning, IEEE Trans. Inform. Theory, vol. 35, pp. 87-98, 1989.
    • (1989) IEEE Trans. Inform. Theory , vol.35 , pp. 87-98
    • Pottie, G.J.1    Taylor, D.P.2
  • 175
    • 0038257910 scopus 로고
    • A class of optimum nonlinear double error correcting codes
    • F. P. Preparata, A class of optimum nonlinear double error correcting codes, Inform. Contr., vol. 13, pp. 378-400, 1968.
    • (1968) Inform. Contr. , vol.13 , pp. 378-400
    • Preparata, F.P.1
  • 176
    • 0027188053 scopus 로고
    • Multiresolution broadcast for digital HDTV using joint source/channel coding
    • K. Ramchandran, A. Ortega, K. M. Uz, and M. Vetterli, Multiresolution broadcast for digital HDTV using joint source/channel coding, IEEE J. Select. Areas Commun., vol. 11, pp. 6-23, 1993.
    • (1993) IEEE J. Select. Areas Commun. , vol.11 , pp. 6-23
    • Ramchandran, K.1    Ortega, A.2    Uz, K.M.3    Vetterli, M.4
  • 177
    • 0000580915 scopus 로고
    • Factorial experiments derivable from combinatorial arrangements of arrays
    • C. R. Rao, Factorial experiments derivable from combinatorial arrangements of arrays, J. Roy. Statist. Soc., vol. 9, pp. 128-139, 1947.
    • (1947) J. Roy. Statist. Soc. , vol.9 , pp. 128-139
    • Rao, C.R.1
  • 180
    • 0001174154 scopus 로고
    • Polynomial codes over certain finite fields
    • I. S. Reed and G. Solomon, Polynomial codes over certain finite fields, SIAM J., vol. 8, pp. 300-304, 1960.
    • (1960) SIAM J. , vol.8 , pp. 300-304
    • Reed, I.S.1    Solomon, G.2
  • 181
    • 33747274267 scopus 로고
    • Finding a minimal set of linear recurring relations capable of generating a given finite two-dimensional array
    • S. Sakata, Finding a minimal set of linear recurring relations capable of generating a given finite two-dimensional array, J. Symbolic Comput., vol. 5, pp. 321-337, 1988
    • (1988) J. Symbolic Comput. , vol.5 , pp. 321-337
    • Sakata, S.1
  • 182
    • 0025383036 scopus 로고
    • Extension of the Berlekamp-Massey algorithm to N dimen-sions
    • S. Sakata, Extension of the Berlekamp-Massey algorithm to N dimen-sions, Inform. Comput., vol. 84, pp. 207-239, 1990.
    • (1990) Inform. Comput. , vol.84 , pp. 207-239
    • Sakata, S.1
  • 183
  • 185
    • 0024946642 scopus 로고
    • Generalized Viterbi detection with convolutional codes
    • N. Seshadri and C.-E. Sundberg, Generalized Viterbi detection with convolutional codes, in IEEE Globecom'89, 1989, pp. 1534-1538.
    • (1989) IEEE Globecom'89 , pp. 1534-1538
    • Seshadri, N.1    Sundberg, C.-E.2
  • 186
    • 0028014792 scopus 로고
    • Two signaling schemes for improving the error performance of frequency-division-duplex (FDD) transmission systems using transmitter antenna diversity
    • N. Seshadri and J. H. Winters, Two signaling schemes for improving the error performance of frequency-division-duplex (FDD) transmission systems using transmitter antenna diversity, Int. J. Wireless Inform. Networks, vol. 1, pp. 49-60, 1994.
    • (1994) Int. J. Wireless Inform. Networks , vol.1 , pp. 49-60
    • Seshadri, N.1    Winters, J.H.2
  • 187
  • 188
    • 84940644968 scopus 로고
    • A mathematical theory of communication I, II
    • Reprinted in C. E. Shannon and W. Weaver, A Mathematical Theory of Communication. Urbana, IL: Univ. Illinois Press
    • C. E. Shannon, A mathematical theory of communication I, II, Bell Syst. Tech. J., vol. 27, pp. 379-423; 623-656, 1948; Reprinted in C. E. Shannon and W. Weaver, A Mathematical Theory of Communication. Urbana, IL: Univ. Illinois Press, 1949.
    • (1949) Bell Syst. Tech. J. , vol.27 , pp. 379-423
    • Shannon, C.E.1
  • 189
    • 84938009281 scopus 로고
    • The zero-error capacity of a noisy channel
    • The zero-error capacity of a noisy channel, IRE Trans. Inform. Theory, vol. IT-2, pp. 8-19, 1956.
    • (1956) IRE Trans. Inform. Theory , vol.IT-2 , pp. 8-19
  • 191
  • 192
    • 33746738958 scopus 로고
    • Scheme for reducing deroherence in quantum computer memory
    • Scheme for reducing deroherence in quantum computer memory, Phys. Rev. A., vol. 52, pp. 2493-2496, 1995.
    • (1995) Phys. Rev. A. , vol.52 , pp. 2493-2496
  • 193
    • 0001267593 scopus 로고    scopus 로고
    • Quantum analog of the Mac Williams identities in classical coding theory
    • also LANL eprint quant-ph/9610040.
    • P. W. Shor and R. Laflamme, Quantum analog of the Mac Williams identities in classical coding theory, Phys. Rev. Lett., vol. 78, pp. 1600-1602, 1997; also LANL eprint quant-ph/9610040.
    • (1997) Phys. Rev. Lett. , vol.78 , pp. 1600-1602
    • Shor, P.W.1    Laflamme, R.2
  • 194
    • 0011592043 scopus 로고
    • Extremal polynomials used in bounds of code volume
    • in Russian
    • V. M. Sidel'nikov, Extremal polynomials used in bounds of code volume, Probt. Pered. Inform., vol. 16, pp. 17-39, 1980 (in Russian).
    • (1980) Probt. Pered. Inform. , vol.16 , pp. 17-39
    • Sidel'Nikov, V.M.1
  • 195
    • 0019032458 scopus 로고
    • English translation in Probl. Inform. Transm., vol. 16, pp. 174-186, 1980.
    • (1980) Probl. Inform. Transm. , vol.16 , pp. 174-186
  • 197
    • 0025484013 scopus 로고
    • On the decoding of algebraic geometric codes
    • A. N. Skorobogatov and S. G. Vlädu;, On the decoding of algebraic geometric codes, IEEE Trans. Inform. Theory, vol. 36, pp. 1461-1463, 1990.
    • (1990) IEEE Trans. Inform. Theory , vol.36 , pp. 1461-1463
    • Skorobogatov, A.N.1    Vlädu, S.G.2
  • 198
    • 0001597243 scopus 로고
    • A class of binary signaling alphabets
    • D. Slepian, A class of binary signaling alphabets, Bell Syst. Tech. J., vol. 35, pp. 203-234, 1956.
    • (1956) Bell Syst. Tech. J. , vol.35 , pp. 203-234
    • Slepian, D.1
  • 199
    • 33747478843 scopus 로고
    • A note on two binary signaling alphabets
    • A note on two binary signaling alphabets, IRE Trans. Inform. Theory, vol. IT-2, pp. 84-86, 1956.
    • (1956) IRE Trans. Inform. Theory , vol.IT-2 , pp. 84-86
  • 200
    • 0004635627 scopus 로고
    • Some further theory of group codes
    • Some further theory of group codes, Bell Syst. Tech. J., vol. 39, pp. 1219-1252, 1960.
    • (1960) Bell Syst. Tech. J. , vol.39 , pp. 1219-1252
  • 201
    • 80054814722 scopus 로고
    • Group codes for the Gaussian channel
    • Group codes for the Gaussian channel, Bell Syst. Tech. ]., vol. 47, pp. 575-602, 1968.
    • (1968) Bell Syst. Tech. . , vol.47 , pp. 575-602
  • 202
    • 0015648934 scopus 로고
    • Noiseless coding of correlated information
    • D. Slepian and J. K. Wolf, Noiseless coding of correlated information, IEEE Trans. Inform. Theory, vol. IT-19, pp. 471-480, 1973.
    • (1973) IEEE Trans. Inform. Theory , vol.IT-19 , pp. 471-480
    • Slepian, D.1    Wolf, J.K.2
  • 203
    • 0002144660 scopus 로고
    • Error-correcting codes and invariant theory: New applications of a nineteenth century technique
    • N. J. A. Sloane, Error-correcting codes and invariant theory: New applications of a nineteenth century technique, Amer. Math. Monthly, vol. 84, pp. 82-107, 1977.
    • (1977) Amer. Math. Monthly , vol.84 , pp. 82-107
    • Sloane, N.J.A.1
  • 204
    • 0018530717 scopus 로고
    • A connection between block and convolutional codes
    • G. Solomon and H. C. A. van Tilborg, A connection between block and convolutional codes, SIAM J. Appl. Math., vol. 37, pp. 358-369, 1979.
    • (1979) SIAM J. Appl. Math. , vol.37 , pp. 358-369
    • Solomon, G.1    Van Tilborg, H.C.A.2
  • 205
    • 4043092517 scopus 로고    scopus 로고
    • Error correcting codes in quantum theory
    • A. M. Steane, Error correcting codes in quantum theory, Phys. Rev. Lett., vol. 77, pp. 793-797, 1996.
    • (1996) Phys. Rev. Lett. , vol.77 , pp. 793-797
    • Steane, A.M.1
  • 207
    • 0031097176 scopus 로고    scopus 로고
    • Decoding of Reed-Solomon codes beyond the error-correction bound
    • M. Sudan, Decoding of Reed-Solomon codes beyond the error-correction bound, J. Complexity, vol. 13, pp. 180-193, 1997.
    • (1997) J. Complexity , vol.13 , pp. 180-193
    • Sudan, M.1
  • 208
    • 0025547666 scopus 로고
    • Digital cellular systems for North America, in
    • C.-E. Sundberg and N. Seshadri, Digital cellular systems for North America, in IEEE Globecom'90, 1990, pp. 533-537.
    • (1990) IEEE Globecom'90 , pp. 533-537
    • Sundberg, C.-E.1    Seshadri, N.2
  • 209
    • 0019608335 scopus 로고
    • A recursive approach to low complexity codes
    • R. M. Tanner, A recursive approach to low complexity codes, IEEE Trans. Inform. Theory, vol. IT-27, pp. 533-547, 1981.
    • (1981) IEEE Trans. Inform. Theory , vol.IT-27 , pp. 533-547
    • Tanner, R.M.1
  • 210
    • 0030289445 scopus 로고    scopus 로고
    • Trellis complexity versus the coding gain of lattices, parts I and II
    • V. Tarokh and I. F. Blake, Trellis complexity versus the coding gain of lattices, parts I and II, IEEE Trans. Inform. Theory, vol. 42, pp. 1796-1807 and 1808-1816, 1996.
    • IEEE Trans. Inform. Theory , vol.42 , pp. 1796-1807
    • Tarokh, V.1    Blake, I.F.2
  • 211
    • 0032023863 scopus 로고    scopus 로고
    • Space-time codes for high data rate wireless communication: Performance criterion and code construction
    • V. Tarokh, N. Seshadri, and A. R. Calderbank, Space-time codes for high data rate wireless communication: Performance criterion and code construction, IEEE Trans. Inform. Theory, vol. 44, pp. 744-765, 1998.
    • (1998) IEEE Trans. Inform. Theory , vol.44 , pp. 744-765
    • Tarokh, V.1    Seshadri, N.2    Calderbank, A.R.3
  • 213
    • 84859625236 scopus 로고
    • On Goppa codes which are better than the Varshamov-Gilbert bound
    • M. A. Tsfasman, S. G. Vlädu;, and T. Zink, On Goppa codes which are better than the Varshamov-Gilbert bound, Math. Nach., vol. 109, pp. 21-28, 1982.
    • (1982) Math. Nach. , vol.109 , pp. 21-28
    • Tsfasman S G Vlädu, M.A.1    Zink, T.2
  • 214
    • 0001920780 scopus 로고
    • On the nonexistence of perfect codes over finite fields
    • A. Tietâvâinen, On the nonexistence of perfect codes over finite fields, SIAM J. Appl. Math., vol. 24, pp. 88-96, 1973.
    • (1973) SIAM J. Appl. Math. , vol.24 , pp. 88-96
    • Tietâvâinen, A.1
  • 215
    • 0015033920 scopus 로고
    • New automatic equalizer employing modulo arith-metic
    • M. Tomlinson, New automatic equalizer employing modulo arith-metic, Electron. Lett., vol. 7, pp. 138-139, 1971.
    • (1971) Electron. Lett. , vol.7 , pp. 138-139
    • Tomlinson, M.1
  • 216
    • 0027597173 scopus 로고
    • Design of multiple description scalar quantizers
    • V. A. Vaishampayan, Design of multiple description scalar quantizers, IEEE Trans. Inform. Theory, vol. 39, pp. 821-834, 1993.
    • (1993) IEEE Trans. Inform. Theory , vol.39 , pp. 821-834
    • Vaishampayan, V.A.1
  • 217
    • 0019343223 scopus 로고
    • Channel coding with multilevel/phase signals
    • G. Ungerboeck, Channel coding with multilevel/phase signals, IEEE Trans. Inform. Theory, vol. IT-28, pp. 55-67, 1982.
    • (1982) IEEE Trans. Inform. Theory , vol.IT-28 , pp. 55-67
    • Ungerboeck, G.1
  • 218
    • 0026157330 scopus 로고
    • More efficient soft decoding of the Golay codes
    • A. Vardy and Y. Be'ery, More efficient soft decoding of the Golay codes, IEEE Trans. Inform. Theory, vol. 37, pp. 667-672, 1991.
    • (1991) IEEE Trans. Inform. Theory , vol.37 , pp. 667-672
    • Vardy, A.1    Be'Ery, Y.2
  • 219
    • 0027634536 scopus 로고
    • Maximum-likelihood decoding of the Leech lattice
    • Maximum-likelihood decoding of the Leech lattice, IEEE Trans. Inform. Theory, vol. 39, pp. 1435-1444, 1993.
    • (1993) IEEE Trans. Inform. Theory , vol.39 , pp. 1435-1444
  • 220
    • 0000479182 scopus 로고
    • Estimate of the number of signals in error correcting codes
    • R. R. Varshamov, Estimate of the number of signals in error correcting codes, Dokl. Akad. Nauk. SSSR, vol. 117, pp. 739-741, 1957.
    • (1957) Dokl. Akad. Nauk. SSSR , vol.117 , pp. 739-741
    • Varshamov, R.R.1
  • 221
    • 84935113569 scopus 로고
    • Error bounds for convolutional codes and an asymptot-ically optimal decoding algorithm
    • A. J. Viterbi, Error bounds for convolutional codes and an asymptot-ically optimal decoding algorithm, IEEE Trans. Inform. Theory, vol. IT-13, pp. 260-269, 1967.
    • (1967) IEEE Trans. Inform. Theory , vol.IT-13 , pp. 260-269
    • Viterbi, A.J.1
  • 222
    • 0029371581 scopus 로고
    • Power and bandwidth efficient digital communication using turbo codes in multilevel codes
    • U. Wachsmann and J. Huber, Power and bandwidth efficient digital communication using turbo codes in multilevel codes, Euro. Trans. Telecommun., vol. 6, pp. 557-567, 1995.
    • (1995) Euro. Trans. Telecommun. , vol.6 , pp. 557-567
    • Wachsmann, U.1    Huber, J.2
  • 223
  • 226
    • 0000484483 scopus 로고    scopus 로고
    • A bibliographical guide to self-similar traffic and performance modeling for modern high-speed networks
    • F. P. Kelly, S. Zachary, and I. Ziedins, Eds. Oxford, U.K.: Clarendon Press
    • W. Willinger, M. S. Taqqu, and A. Erramilli, A bibliographical guide to self-similar traffic and performance modeling for modern high-speed networks, in Stochastic Networks: Theory and Applications, Royal Statistical Lecture Note Series, vol. 4, F. P. Kelly, S. Zachary, and I. Ziedins, Eds. Oxford, U.K.: Clarendon Press, 1996, pp. 339-366.
    • Stochastic Networks: Theory and Applications, Royal Statistical Lecture Note Series , vol.4 , pp. 339-366
    • Willinger, W.1    Taqqu, M.S.2    Erramilli, A.3
  • 227
    • 51249186924 scopus 로고
    • The exact bound in the Erdos-Ko-Rado theorem
    • R. M. Wilson, The exact bound in the Erdos-Ko-Rado theorem, Combinatorica, vol. 4, pp. 247-257, 1984.
    • (1984) Combinatorica , vol.4 , pp. 247-257
    • Wilson, R.M.1
  • 228
    • 0001093296 scopus 로고
    • Base station modulation diversity for digital SIMULCAST
    • A. Wittneben, Base station modulation diversity for digital SIMULCAST, in Proc. IEEE Vehicular Technology Conf., 1993, pp. 505-511.
    • (1993) Proc. IEEE Vehicular Technology Conf. , pp. 505-511
    • Wittneben, A.1
  • 229
    • 11844274087 scopus 로고
    • Decoding of Bose-Chaudhuri-Hocquenghem codes and Prony's method for curve fitting
    • J. K. Wolf, Decoding of Bose-Chaudhuri-Hocquenghem codes and Prony's method for curve fitting, IEEE Trans. Inform. Theory, vol. IT-3, p. 608, 1967.
    • (1967) IEEE Trans. Inform. Theory , vol.IT-3 , pp. 608
    • Wolf, J.K.1
  • 232
    • 0016915623 scopus 로고
    • Generalized cascade codes
    • V. A. Zinoviev, Generalized cascade codes, Probl. Pered. Inform., vol. 12, pp. 2-9, 1976 (in Russian).
    • (1976) Probl. Pered. Inform. , vol.12 , pp. 2-9
    • Zinoviev, V.A.1
  • 233
    • 0015764354 scopus 로고
    • V. A. Zinoviev and V. K. Leontiev, The nonexistence of perfect codes over Galois fields, Probl. Contr. Inform. Theory, vol. 2, pp. 123-132, 1973.
    • (1973) Probl. Contr. Inform. Theory , vol.2 , pp. 123-132
    • Zinoviev, V.A.1
  • 234
    • 0016419451 scopus 로고
    • V. V. Zyablov and M. S. Pinsker, Estimates of the error-correction complexity of Gallager's low density codes, Probl. Inform. Transm., vol. 11, pp. 18-28, 1976.
    • (1976) Probl. Inform. Transm. , vol.11 , pp. 18-28
    • Zyablov, V.V.1


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