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Volumn , Issue , 2011, Pages 1-409

Entropy and information theory

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EID: 84892332317     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-1-4419-7970-4     Document Type: Book
Times cited : (1602)

References (201)
  • 2
    • 0009797238 scopus 로고
    • Ergodic and mixing properties of infinite memory channels
    • R. Adler. Ergodic and mixing properties of infinite memory channels. Proc. Amer. Math. Soc., 12:924-930, 1961.
    • (1961) Proc. Amer. Math. Soc. , vol.12 , pp. 924-930
    • Adler, R.1
  • 3
    • 0020542188 scopus 로고
    • Algorithms for sliding-block codes-An application of symbolic dynamics to information theory
    • R. L. Adler, D. Coppersmith, and M. Hassner. Algorithms for sliding-block codes-An application of symbolic dynamics to information theory. IEEE Trans. Inform. Theory, 29:5-22, 1983.
    • (1983) IEEE Trans. Inform. Theory , vol.29 , pp. 5-22
    • Adler, R.L.1    Coppersmith, D.2    Hassner, M.3
  • 4
    • 84892356409 scopus 로고
    • Two contributions to information theory
    • Keszthely, Hungary
    • R. Ahlswede and P. Gács. Two contributions to information theory. In Topics in Information Theory, pages 17-40, Keszthely, Hungary, 1975.
    • (1975) Topics in Information Theory , pp. 17-40
    • Ahlswede, R.1    Gács, P.2
  • 7
    • 0039048754 scopus 로고
    • A sandwich proof of the shannon-MacMillan-breiman theorem
    • P. Algoet and T. Cover. A sandwich proof of the Shannon-MacMillan-Breiman theorem. Ann. Probab., 16:899-909, 1988.
    • (1988) Ann. Probab. , vol.16 , pp. 899-909
    • Algoet, P.1    Cover, T.2
  • 8
    • 0000039074 scopus 로고
    • The strong ergodic theorem for densities: Generalized shannon- MacMillan-breiman theorem
    • A. R. Barron. The strong ergodic theorem for densities: generalized Shannon- MacMillan-Breiman theorem. Ann. Probab., 13:1292-1303, 1985.
    • (1985) Ann. Probab. , vol.13 , pp. 1292-1303
    • Barron, A.R.1
  • 10
    • 0005653424 scopus 로고
    • Rate distortion theory for sources with abstract alphabets and memory
    • T. Berger. Rate distortion theory for sources with abstract alphabets and memory. Inform. and Control, 13:254-273, 1968.
    • (1968) Inform. and Control , vol.13 , pp. 254-273
    • Berger, T.1
  • 11
    • 0004222683 scopus 로고
    • Prentice-Hall Inc. Englewood Cliffs, New Jersey
    • T. Berger. Rate Distortion Theory. Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1971.
    • (1971) Rate Distortion Theory
    • Berger, T.1
  • 14
    • 80955177430 scopus 로고    scopus 로고
    • Some notes on alternating optimization
    • Nikhil Pal and Michio Sugeno, editors, volume 2275 of Lecture Notes in Computer Science, Springer Berlin/Heidelberg, 10.1007/3-540-45631-7-39
    • James Bezdek and Richard Hathaway. Some notes on alternating optimization. In Nikhil Pal and Michio Sugeno, editors, Advances in Soft Computing AFSS 2002, volume 2275 of Lecture Notes in Computer Science, pages 187-195. Springer Berlin/Heidelberg, 2002. 10.1007/3-540-45631-7-39.
    • (2002) Advances in Soft Computing AFSS 2002 , pp. 187-195
    • Bezdek, J.1    Hathaway, R.2
  • 15
    • 0000485156 scopus 로고
    • Some asymptotic theory for the bootstrap
    • P. J. Bickel and D. A. Freedman. Some asymptotic theory for the bootstrap. Annals of Statistics, 9(1):196-1217, 1981.
    • (1981) Annals of Statistics , vol.9 , Issue.1 , pp. 196-1217
    • Bickel, P.J.1    Freedman, D.A.2
  • 17
    • 0001650497 scopus 로고
    • Proof of the ergodic theorem
    • G. D. Birkhoff. Proof of the ergodic theorem. Proc. Nat. Acad. Sci., 17:656-660, 1931.
    • (1931) Proc. Nat. Acad. Sci. , vol.17 , pp. 656-660
    • Birkhoff, G.D.1
  • 18
    • 0015376113 scopus 로고
    • Computation of channel capacity and rate-distortion functions
    • R. E. Blahut. Computation of channel capacity and rate-distortion functions. IEEE Trans. Inform. Theory, 18:460-473, 1972.
    • (1972) IEEE Trans. Inform. Theory , vol.18 , pp. 460-473
    • Blahut, R.E.1
  • 20
    • 0001531440 scopus 로고
    • The individual ergodic theorem of information theory
    • L. Breiman. The individual ergodic theorem of information theory. Ann. of Math. Statist., 28:809-811, 1957.
    • (1957) Ann. of Math. Statist. , vol.28 , pp. 809-811
    • Breiman, L.1
  • 21
    • 0001531440 scopus 로고
    • A correction to the individual ergodic theorem of information theory
    • L. Breiman. A correction to 'The individual ergodic theorem of information theory'. Ann. of Math. Statist., 31:809-810, 1960.
    • (1960) Ann. of Math. Statist. , vol.31 , pp. 809-810
    • Breiman, L.1
  • 23
    • 0000179217 scopus 로고
    • Kolmogorov's contributions to information theory and algorithmic complexity
    • T. M. Cover, P. Gacs, and R. M. Gray. Kolmogorov's contributions to information theory and algorithmic complexity. Ann. Probab., 17:840-865, 1989.
    • (1989) Ann. Probab. , vol.17 , pp. 840-865
    • Cover, T.M.1    Gacs, P.2    Gray, R.M.3
  • 24
    • 0000489740 scopus 로고
    • Information-type measures of difference of probability distributions and indirect observations
    • I. Csiszár. Information-type measures of difference of probability distributions and indirect observations. Studia Scientiarum Mathematicarum Hungarica, 2:299-318, 1967.
    • (1967) Studia Scientiarum Mathematicarum Hungarica , vol.2 , pp. 299-318
    • Csiszár, I.1
  • 26
    • 0000546609 scopus 로고
    • I-divergence geometry of probability distributions and minimization problems
    • I. Csiszár. I-divergence geometry of probability distributions and minimization problems. Ann. Probab., 3(1):146-158, 1975.
    • (1975) Ann. Probab. , vol.3 , Issue.1 , pp. 146-158
    • Csiszár, I.1
  • 28
    • 84892272540 scopus 로고
    • A simplified proof of the sliding-block source coding theorem and its universal extension
    • Toronto
    • L. D. Davisson and R.M. Gray. A simplified proof of the sliding-block source coding theorem and its universal extension. In Conf. Record 1978 Int'l. Conf. on Comm. 2, pages 34-5, Toronto, 1978.
    • (1978) Conf. Record 1978 Int'l. Conf. on Comm. , vol.2 , pp. 34-35
    • Davisson, L.D.1    Gray, R.M.2
  • 32
    • 0003046260 scopus 로고
    • A general formulation of the fundamental shannon theorem in information theory
    • R. L. Dobrushin. A general formulation of the fundamental Shannon theorem in information theory. Uspehi Mat. Akad. Nauk. SSSR, 14:3-104, 1959.
    • (1959) Uspehi Mat. Akad. Nauk. SSSR , vol.14 , pp. 3-104
    • Dobrushin, R.L.1
  • 33
    • 33747478454 scopus 로고
    • Shannon's theorems for channels with synchronization errors
    • R. L. Dobrushin. Shannon's theorems for channels with synchronization errors. Problemy Peredaci Informatsii, 3:18-36, 1967.
    • (1967) Problemy Peredaci Informatsii , vol.3 , pp. 18-36
    • Dobrushin, R.L.1
  • 34
    • 0000080779 scopus 로고
    • Prescribing a system of random variables by conditional distributions
    • R.L. Dobrushin. Prescribing a system of random variables by conditional distributions. Theor. Prob. Appl., 15:458-486, 1970.
    • (1970) Theor. Prob. Appl. , vol.15 , pp. 458-486
    • Dobrushin, R.L.1
  • 35
    • 84980178612 scopus 로고
    • Asymptotic evaluation of certain markov process expectations for large time
    • M. D. Donsker and S. R. S. Varadhan. Asymptotic evaluation of certain Markov process expectations for large time. J. Comm. Pure Appl. Math., 28:1-47, 1975.
    • (1975) J. Comm. Pure Appl. Math. , vol.28 , pp. 1-47
    • Donsker, M.D.1    Varadhan, S.R.S.2
  • 36
    • 0005755803 scopus 로고
    • A note on the abstract alphabet block source coding with a fidelity criterion theorem
    • November
    • J. G. Dunham. A note on the abstract alphabet block source coding with a fidelity criterion theorem. IEEE Trans. Inform. Theory, 24:760, November 1978.
    • (1978) IEEE Trans. Inform. Theory , vol.24 , pp. 760
    • Dunham, J.G.1
  • 41
    • 33747491659 scopus 로고
    • On the coding theorem and its converse for finite-memory channels
    • A. Feinstein. On the coding theorem and its converse for finite-memory channels. Inform. and Control, 2:25-44, 1959.
    • (1959) Inform. and Control , vol.2 , pp. 25-44
    • Feinstein, A.1
  • 42
    • 0018996659 scopus 로고
    • Optimal encoding of discrete-time, continuous-Amplitude, memoryless sources with finite output alphabets
    • Mar.
    • W. A. Finamore and W. A. Pearlman. Optimal encoding of discrete-time, continuous-Amplitude, memoryless sources with finite output alphabets. IEEE Trans. Inform. Theory, 26:144-155, Mar. 1980.
    • (1980) IEEE Trans. Inform. Theory , vol.26 , pp. 144-155
    • Finamore, W.A.1    Pearlman, W.A.2
  • 44
    • 0015600423 scopus 로고
    • The viterbi algorithm
    • March
    • G. D. Forney Jr. The Viterbi algorithm. Proc. IEEE, 61:268-278, March 1973.
    • (1973) Proc. IEEE , vol.61 , pp. 268-278
    • Forney Jr., G.D.1
  • 45
    • 0001309929 scopus 로고
    • Sur la distance de deux lois de probabilit
    • M. Fréchet. Sur la distance de deux lois de probabilité. C. R. Acad. Sci. Paris, 244:689-692, 1957.
    • (1957) C. R. Acad. Sci. Paris , vol.244 , pp. 689-692
    • Fréchet, M.1
  • 49
    • 0005388518 scopus 로고
    • On the general definitions of the quantity of information
    • In Russian
    • I. M. Gelfand, A. N. Kolmogorov, and A. M. Yaglom. On the general definitions of the quantity of information. Dokl. Akad. Nauk, 111:745-748, 1956. (In Russian.).
    • (1956) Dokl. Akad. Nauk , vol.111 , pp. 745-748
    • Gelfand, I.M.1    Kolmogorov, A.N.2    Yaglom, A.M.3
  • 52
    • 0016615526 scopus 로고
    • Sliding-block source coding
    • July
    • R. M. Gray. Sliding-block source coding. IEEE Trans. Inform. Theory, 21(4):357-368, July 1975.
    • (1975) IEEE Trans. Inform. Theory , vol.21 , Issue.4 , pp. 357-368
    • Gray, R.M.1
  • 53
    • 0017431523 scopus 로고
    • Time-invariant trellis encoding of ergodic discrete-time sources with a fidelity criterion
    • R. M. Gray. Time-invariant trellis encoding of ergodic discrete-time sources with a fidelity criterion. IEEE Trans. Inform. Theory, 23:71-83, 1977.
    • (1977) IEEE Trans. Inform. Theory , vol.23 , pp. 71-83
    • Gray, R.M.1
  • 56
    • 0024681085 scopus 로고
    • Spectral analysis of quantization noise in a single-loop sigma-delta modulator with dc input
    • R. M. Gray. Spectral analysis of quantization noise in a single-loop sigma-delta modulator with dc input. IEEE Trans. Comm., 37:588-599, 1989.
    • (1989) IEEE Trans. Comm. , vol.37 , pp. 588-599
    • Gray, R.M.1
  • 59
    • 0016081448 scopus 로고
    • Source coding without the ergodic assumption
    • R. M. Gray and L. D. Davisson. Source coding without the ergodic assumption. IEEE Trans. Inform. Theory, 20:502-516, 1974.
    • (1974) IEEE Trans. Inform. Theory , vol.20 , pp. 502-516
    • Gray, R.M.1    Davisson, L.D.2
  • 61
    • 0020098912 scopus 로고
    • Multiple local optima in vector quantizers
    • March
    • R. M. Gray and E. Karnin. Multiple local optima in vector quantizers. IEEE Trans. Inform. Theory, 28:256-261, March 1982.
    • (1982) IEEE Trans. Inform. Theory , vol.28 , pp. 256-261
    • Gray, R.M.1    Karnin, E.2
  • 62
    • 0001506674 scopus 로고
    • Asymptotically mean stationary measures
    • R. M. Gray and J. C. Kieffer. Asymptotically mean stationary measures. Ann. Probab., 8:962-973, 1980.
    • (1980) Ann. Probab. , vol.8 , pp. 962-973
    • Gray, R.M.1    Kieffer, J.C.2
  • 63
    • 0016549555 scopus 로고
    • Process definitions of distortion rate functions and source coding theorems
    • R. M. Gray, D. L. Neuhoff, and J. K. Omura. Process definitions of distortion rate functions and source coding theorems. IEEE Trans. Inform. Theory, 21:524- 532, 1975.
    • (1975) IEEE Trans. Inform. Theory , vol.21 , pp. 524-532
    • Gray, R.M.1    Neuhoff, D.L.2    Omura, J.K.3
  • 64
    • 0016549555 scopus 로고
    • Process definitions of distortion rate functions and source coding theorems
    • Sept.
    • R. M. Gray, D. L. Neuhoff, and J. K. Omura. Process definitions of distortion rate functions and source coding theorems. IEEE Trans. on Info. Theory, 21(5):524- 532, Sept. 1975.
    • (1975) IEEE Trans. on Info. Theory , vol.21 , Issue.5 , pp. 524-532
    • Gray, R.M.1    Neuhoff, D.L.2    Omura, J.K.3
  • 65
    • 0012788596 scopus 로고
    • Nonblock source coding with a fidelity criterion
    • R. M. Gray, D. L. Neuhoff, and D. Ornstein. Nonblock source coding with a fidelity criterion. Ann. Probab., 3:478-491, 1975.
    • (1975) Ann. Probab. , vol.3 , pp. 478-491
    • Gray, R.M.1    Neuhoff, D.L.2    Ornstein, D.3
  • 66
    • 0001641786 scopus 로고
    • A generalization of ornstein's dbar distance with applications to information theory
    • April
    • R. M. Gray, D. L. Neuhoff, and P. C. Shields. A generalization of ornstein's dbar distance with applications to information theory. Ann. Probab., 3:315-328, April 1975.
    • (1975) Ann. Probab. , vol.3 , pp. 315-328
    • Gray, R.M.1    Neuhoff, D.L.2    Shields, P.C.3
  • 67
    • 0017017306 scopus 로고
    • Sliding-block joint source/noisy-channel coding theorems
    • R. M. Gray and D. S. Ornstein. Sliding-block joint source/noisy-channel coding theorems. IEEE Trans. Inform. Theory, 22:682-690, 1976.
    • (1976) IEEE Trans. Inform. Theory , vol.22 , pp. 682-690
    • Gray, R.M.1    Ornstein, D.S.2
  • 68
    • 15544362346 scopus 로고
    • Block synchronization, slidingblock coding, invulnerable sources and zero error codes for discrete noisy channels
    • R. M. Gray, D. S. Ornstein, and R. L. Dobrushin. Block synchronization, slidingblock coding, invulnerable sources and zero error codes for discrete noisy channels. Ann. Probab., 8:639-674, 1980.
    • (1980) Ann. Probab. , vol.8 , pp. 639-674
    • Gray, R.M.1    Ornstein, D.S.2    Dobrushin, R.L.3
  • 70
    • 0021132425 scopus 로고
    • Block source coding theory for asymptotically mean stationary sources
    • R. M. Gray and F. Saadat. Block source coding theory for asymptotically mean stationary sources. IEEE Trans. Inform. Theory, 30:64-67, 1984.
    • (1984) IEEE Trans. Inform. Theory , vol.30 , pp. 64-67
    • Gray, R.M.1    Saadat, F.2
  • 72
    • 67650697689 scopus 로고    scopus 로고
    • Bits in asymptotically optimal lossy source codes are asymptotically bernoulli
    • J. A. Storer and M. Cohn, editors, March
    • Robert M. Gray and Tamás Linder. Bits in asymptotically optimal lossy source codes are asymptotically bernoulli. In J. A. Storer and M. Cohn, editors, Proceedings 2009 Data Compression Conference (DCC), pages 53-62, March 2009.
    • (2009) Proceedings 2009 Data Compression Conference (DCC) , pp. 53-62
    • Gray, R.M.1    Linder, T.2
  • 75
    • 84980082105 scopus 로고
    • Transmission of information
    • R. V. L. Hartley. Transmission of information. Bell System Tech. J., 7:535-563, 1928.
    • (1928) Bell System Tech. J. , vol.7 , pp. 535-563
    • Hartley, R.V.L.1
  • 76
    • 0019624501 scopus 로고
    • A direct proof of the equality between the block definition and the process definition of distortion-rate functions for stationary ergodic sources
    • Oct.
    • T. Hashimoto. A direct proof of the equality between the block definition and the process definition of distortion-rate functions for stationary ergodic sources. nform. Contr., 51:45-57, Oct. 1981.
    • (1981) Nform. Contr. , vol.51 , pp. 45-57
    • Hashimoto, T.1
  • 77
    • 0004251104 scopus 로고
    • Springer-Verlag, Berlin
    • E. Hoph. Ergodentheorie. Springer-Verlag, Berlin, 1937.
    • (1937) Ergodentheorie
    • Hoph, E.1
  • 78
    • 17844380555 scopus 로고
    • Die Übertragung diskreter informationen durch periodishce und fastperiodische kanale
    • K. Jacobs. Die Übertragung diskreter Informationen durch periodishce und fastperiodische Kanale. Math. Annalen, 137:125-135, 1959.
    • (1959) Math. Annalen , vol.137 , pp. 125-135
    • Jacobs, K.1
  • 79
    • 34250941804 scopus 로고
    • ÜBer die struktur der mittleren entropie
    • K. Jacobs. Über die Struktur der mittleren Entropie. Math. Z., 78:33-43, 1962.
    • (1962) Math. Z. , vol.78 , pp. 33-43
    • Jacobs, K.1
  • 80
    • 33747459126 scopus 로고
    • The ergodic decomposition of the kolmogorov-sinai invariant
    • F. B. Wright and F. B. Wright, editors, Academic Press, New York
    • K. Jacobs. The ergodic decomposition of the Kolmogorov-Sinai invariant. In F. B. Wright and F. B. Wright, editors, Ergodic Theory. Academic Press, New York, 1963.
    • (1963) Ergodic Theory
    • Jacobs, K.1
  • 82
    • 0014869728 scopus 로고
    • Generalization of feinstein's fundamental lemma
    • T. Kadota. Generalization of feinstein's fundamental lemma. IEEE Trans. Inform. Theory, 16:791-792, 1970.
    • (1970) IEEE Trans. Inform. Theory , vol.16 , pp. 791-792
    • Kadota, T.1
  • 84
    • 84858436873 scopus 로고    scopus 로고
    • An outline of ergodic theory
    • Cambridge University Press, Cambridge
    • S. Kalikow and R. McCutcheon. An Outline of Ergodic Theory, Studies in Advanced Mathematics. volume 122 Cambridge University Press, Cambridge, 2010.
    • (2010) Studies in Advanced Mathematics , vol.122
    • Kalikow, S.1    McCutcheon, R.2
  • 85
  • 87
    • 0001010507 scopus 로고
    • On a problem of monge
    • L.V. Kantorovich. On a problem of monge. Dokl. Akad. Nauk, 3:225-226, 1948.
    • (1948) Dokl. Akad. Nauk , vol.3 , pp. 225-226
    • Kantorovich, L.V.1
  • 88
    • 0006339704 scopus 로고
    • The entropy concept in probability theory
    • A. J. Khinchine. The entropy concept in probability theory. Uspekhi Matematicheskikh Nauk., 8:3-20, 1953.
    • (1953) Uspekhi Matematicheskikh Nauk , vol.8 , pp. 3-20
    • Khinchine, A.J.1
  • 89
    • 0346440662 scopus 로고
    • On the fundamental theorems of information theory
    • A. J. Khinchine. On the fundamental theorems of information theory. Uspekhi Matematicheskikh Nauk., 11:17-75, 1957.
    • (1957) Uspekhi Matematicheskikh Nauk , vol.11 , pp. 17-75
    • Khinchine, A.J.1
  • 90
    • 0001529995 scopus 로고
    • A counterexample to Perez's generalization of the Shannon- MacMillan theorem
    • J. C. Kieffer. A counterexample to Perez's generalization of the Shannon- MacMillan theorem. Ann. Probab., 1:362-364, 1973.
    • (1973) Ann. Probab. , vol.1 , pp. 362-364
    • Kieffer, J.C.1
  • 91
    • 0016309184 scopus 로고
    • A general formula for the capacity of stationary nonanticipatory channels
    • J. C. Kieffer. A general formula for the capacity of stationary nonanticipatory channels. Inform. and Control, 26:381-391, 1974.
    • (1974) Inform. and Control , vol.26 , pp. 381-391
    • Kieffer, J.C.1
  • 92
    • 0016487414 scopus 로고
    • On the optimum average distortion attainable by fixed-rate coding of a nonergodic source
    • March
    • J. C. Kieffer. On the optimum average distortion attainable by fixed-rate coding of a nonergodic source. IEEE Trans. Inform. Theory, 21:190-193, March 1975.
    • (1975) IEEE Trans. Inform. Theory , vol.21 , pp. 190-193
    • Kieffer, J.C.1
  • 93
    • 0018036181 scopus 로고
    • A unified approach to weak universal source coding
    • J. C. Kieffer. A unified approach to weak universal source coding. IEEE Trans. Inform. Theory, 24:674-682, 1978.
    • (1978) IEEE Trans. Inform. Theory , vol.24 , pp. 674-682
    • Kieffer, J.C.1
  • 94
    • 0019079362 scopus 로고
    • Extension of source coding theorems for block codes to sliding block codes
    • J. C. Kieffer. Extension of source coding theorems for block codes to sliding block codes. IEEE Trans. Inform. Theory, 26:679-692, 1980.
    • (1980) IEEE Trans. Inform. Theory , vol.26 , pp. 679-692
    • Kieffer, J.C.1
  • 95
    • 0019632726 scopus 로고
    • Block coding for weakly continuous channels
    • J. C. Kieffer. Block coding for weakly continuous channels. IEEE Trans. Inform. Theory, 27:721-727, 1981.
    • (1981) IEEE Trans. Inform. Theory , vol.27 , pp. 721-727
    • Kieffer, J.C.1
  • 96
    • 0019346829 scopus 로고
    • Sliding-block coding for weakly continuous channels
    • J. C. Kieffer. Sliding-block coding for weakly continuous channels. IEEE Trans. Inform. Theory, 28:2-10, 1982.
    • (1982) IEEE Trans. Inform. Theory , vol.28 , pp. 2-10
    • Kieffer, J.C.1
  • 97
    • 84968465513 scopus 로고
    • An ergodic theorem for constrained sequences of functions
    • J. C. Kieffer. An ergodic theorem for constrained sequences of functions. Bulletin American Math Society, 1989.
    • (1989) Bulletin American Math Society
    • Kieffer, J.C.1
  • 100
    • 0026119776 scopus 로고
    • Sample converses in source coding theory
    • March
    • J.C. Kieffer. Sample converses in source coding theory. Information Theory, IEEE Transactions on, 37(2):263 -268, March 1991.
    • (1991) Information Theory, IEEE Transactions on , vol.37 , Issue.2 , pp. 263-268
    • Kieffer, J.C.1
  • 101
    • 0026121389 scopus 로고
    • Strong converses in source coding relative to a fidelity criterion
    • March
    • J.C. Kieffer. Strong converses in source coding relative to a fidelity criterion. Information Theory, IEEE Transactions on, 37(2):257 -262, March 1991.
    • (1991) Information Theory, IEEE Transactions on , vol.37 , Issue.2 , pp. 257-262
    • Kieffer, J.C.1
  • 102
    • 77954824787 scopus 로고
    • On the shannon theory of information in the case of continuous signals
    • A. N. Kolmogorov. On the Shannon theory of information in the case of continuous signals. IRE Transactions Inform, Theory, 2:102-108, 1956.
    • (1956) IRE Transactions Inform, Theory , vol.2 , pp. 102-108
    • Kolmogorov, A.N.1
  • 103
    • 0001450585 scopus 로고
    • A new metric invariant of transitive dynamic systems and automorphisms in lebesgue spaces
    • In Russian
    • A. N. Kolmogorov. A new metric invariant of transitive dynamic systems and automorphisms in lebesgue spaces. Dokl. Akad. Nauk SSR, 119:861-864, 1958. (In Russian.).
    • (1958) Dokl. Akad. Nauk SSR , vol.119 , pp. 861-864
    • Kolmogorov, A.N.1
  • 104
    • 0000419815 scopus 로고
    • On the entropy per unit time as a metric invariant of automorphisms
    • In Russian
    • A. N. Kolmogorov. On the entropy per unit time as a metric invariant of automorphisms. Dokl. Akad. Naud SSSR, 124:768-771, 1959. (In Russian.).
    • (1959) Dokl. Akad. Naud SSSR , vol.124 , pp. 768-771
    • Kolmogorov, A.N.1
  • 105
    • 84892230789 scopus 로고
    • Quantity of information and entropy for continuous distributions
    • Izd. Akad. Nauk. SSSR
    • A. N. Kolmogorov, A. M. Yaglom, and I. M. Gelfand. Quantity of information and entropy for continuous distributions. In Proceedings 3rd All-Union Mat. Conf., volume 3, pages 300-320. Izd. Akad. Nauk. SSSR, 1956.
    • (1956) Proceedings 3rd All-Union Mat. Conf. , vol.3 , pp. 300-320
    • Kolmogorov, A.N.1    Yaglom, A.M.2    Gelfand, I.M.3
  • 106
    • 84941465845 scopus 로고
    • A lower bound for discrimination in terms of variation
    • S. Kullback. A lower bound for discrimination in terms of variation. IEEE Trans. Inform. Theory, 13:126-127, 1967.
    • (1967) IEEE Trans. Inform. Theory , vol.13 , pp. 126-127
    • Kullback, S.1
  • 107
    • 0004257990 scopus 로고
    • Dover, New York, Reprint of 1959 edition published by Wiley
    • S. Kullback. Information Theory and Statistics. Dover, New York, 1968. Reprint of 1959 edition published by Wiley.
    • (1968) Information Theory and Statistics
    • Kullback, S.1
  • 108
    • 0015658962 scopus 로고
    • Bounds on rate-distortion functions for stationary sources and context-dependent fidelity criteria
    • Sept.
    • B. M. Leiner and R. M. Gray. Bounds on rate-distortion functions for stationary sources and context-dependent fidelity criteria. IEEE Trans. Inform. Theory, 19:706-708, Sept. 1973.
    • (1973) IEEE Trans. Inform. Theory , vol.19 , pp. 706-708
    • Leiner, B.M.1    Gray, R.M.2
  • 111
    • 0000749323 scopus 로고
    • Least squares quantization in PCM
    • Unpublished Bell Laboratories Technical Note, Portions presented at the Institute of Mathematical Statistics Meeting Atlantic City New Jersey September 1957. Published in the March 1982 special issue on quantization of the
    • S. P. Lloyd. Least squares quantization in PCM. Unpublished Bell Laboratories Technical Note. Portions presented at the Institute of Mathematical Statistics Meeting Atlantic City New Jersey September 1957. Published in the March 1982 special issue on quantization of the IEEE Transactions on Information Theory, 1957.
    • (1957) IEEE Transactions on Information Theory
    • Lloyd, S.P.1
  • 113
  • 116
    • 0022148098 scopus 로고
    • Vector quantization in speech coding
    • November
    • J. Makhoul, S. Roucos, and H. Gish. Vector quantization in speech coding. Proc. IEEE, 73. No. 11:1551-1587, November 1985.
    • (1985) Proc. IEEE , vol.73 , Issue.11 , pp. 1551-1587
    • Makhoul, J.1    Roucos, S.2    Gish, H.3
  • 117
    • 0001616689 scopus 로고
    • A note on asymptotic joint normality
    • C.L. Mallows. A note on asymptotic joint normality. Ann. Math.l Stat., 43:508- 515, 1972.
    • (1972) Ann. Math.l Stat. , vol.43 , pp. 508-515
    • Mallows, C.L.1
  • 119
    • 0022054529 scopus 로고
    • Sophic systems and encoding data
    • B. Marcus. Sophic systems and encoding data. IEEE Trans. Inform. Theory, 31:366-377, 1985.
    • (1985) IEEE Trans. Inform. Theory , vol.31 , pp. 366-377
    • Marcus, B.1
  • 120
    • 0016665091 scopus 로고
    • On the rate distortion function of stationary sources
    • K. Marton. On the rate distortion function of stationary sources. Problems of Control and Information Theory, 4:289-297, 1975.
    • (1975) Problems of Control and Information Theory , vol.4 , pp. 289-297
    • Marton, K.1
  • 121
    • 0022720166 scopus 로고
    • A simple proof of the blowing-up lemma
    • K. Marton. A simple proof of the blowing-up lemma. TIT, 32:445-446, 1986.
    • (1986) TIT , vol.32 , pp. 445-446
    • Marton, K.1
  • 122
    • 0030514042 scopus 로고    scopus 로고
    • Bounding d-distance by informational divergence: A method to prove measure concentration
    • K. Marton. Bounding d-distance by informational divergence: A method to prove measure concentration. Annals of Probability, 24(2):857-866, 1996.
    • (1996) Annals of Probability , vol.24 , Issue.2 , pp. 857-866
    • Marton, K.1
  • 124
    • 0001413858 scopus 로고
    • The basic theorems of information theory
    • B. MacMillan. The basic theorems of information theory. Ann. of Math. Statist., 24:196-219, 1953.
    • (1953) Ann. of Math. Statist. , vol.24 , pp. 196-219
    • MacMillan, B.1
  • 125
    • 0009302187 scopus 로고
    • A case of isomorphisms of bernoulli scheme
    • In Russian
    • L. D. Meshalkin. A case of isomorphisms of bernoulli scheme. Dokl. Akad. Nauk SSSR, 128:41-44, 1959. (In Russian.).
    • (1959) Dokl. Akad. Nauk SSSR , vol.128 , pp. 41-44
    • Meshalkin, L.D.1
  • 128
    • 84972526459 scopus 로고
    • Generalizations of Shannon-MacMillan theorem
    • Shu-Teh C. Moy. Generalizations of Shannon-MacMillan theorem. Pacific Journal Math., 11:705-714, 1961.
    • (1961) Pacific Journal Math. , vol.11 , pp. 705-714
    • Moy, S.-T.C.1
  • 129
  • 130
    • 27744571100 scopus 로고
    • On the ergodicity and r-ergodicity of stationary probability measures
    • J. Nedoma. On the ergodicity and r-ergodicity of stationary probability measures. Z. Wahrsch. Verw. Gebiete, 2:90-97, 1963.
    • (1963) Z. Wahrsch. Verw. Gebiete , vol.2 , pp. 90-97
    • Nedoma, J.1
  • 133
    • 0016546722 scopus 로고
    • Fixed rate universal block source coding with a fidelity criterion
    • D. L. Neuhoff, R. M. Gray, and L. D. Davisson. Fixed rate universal block source coding with a fidelity criterion. IEEE Trans. Inform. Theory, 21:511-523, 1975.
    • (1975) IEEE Trans. Inform. Theory , vol.21 , pp. 511-523
    • Neuhoff, D.L.1    Gray, R.M.2    Davisson, L.D.3
  • 135
    • 0020190369 scopus 로고
    • Channel distances and exact representation
    • D. L. Neuhoff and P. C. Shields. Channel distances and exact representation. Inform. and Control, 55(1), 1982.
    • (1982) Inform. and Control , vol.55 , Issue.1
    • Neuhoff, D.L.1    Shields, P.C.2
  • 136
    • 84892212991 scopus 로고
    • Channel entropy and primitive approximation
    • D. L. Neuhoff and P. C. Shields. Channel entropy and primitive approximation. Ann. Probab., 10(1):188-198, 1982.
    • (1982) Ann. Probab. , vol.10 , Issue.1 , pp. 188-198
    • Neuhoff, D.L.1    Shields, P.C.2
  • 137
    • 0019348215 scopus 로고
    • Indecomposable finite state channels and primitive approximation
    • D. L. Neuhoff and P. C. Shields. Indecomposable finite state channels and primitive approximation. IEEE Trans. Inform. Theory, 28:11-19, 1982.
    • (1982) IEEE Trans. Inform. Theory , vol.28 , pp. 11-19
    • Neuhoff, D.L.1    Shields, P.C.2
  • 139
    • 0000768820 scopus 로고
    • Bernoulli shifts with the same entropy are isomorphic
    • D. Ornstein. Bernoulli shifts with the same entropy are isomorphic. Advances in Math., 4:337-352, 1970.
    • (1970) Advances in Math , vol.4 , pp. 337-352
    • Ornstein, D.1
  • 140
    • 3042632611 scopus 로고
    • An application of ergodic theory to probability theory
    • D. Ornstein. An application of ergodic theory to probability theory. Ann. Probab., 1:43-58, 1973.
    • (1973) Ann. Probab. , vol.1 , pp. 43-58
    • Ornstein, D.1
  • 142
    • 0002991617 scopus 로고
    • The shannon-MacMillan-breiman theorem for a class of amenable groups
    • D. Ornstein and B. Weiss. The Shannon-MacMillan-Breiman theorem for a class of amenable groups. Israel J. of Math, 44:53-60, 1983.
    • (1983) Israel J. of Math , vol.44 , pp. 53-60
    • Ornstein, D.1    Weiss, B.2
  • 143
    • 0011348143 scopus 로고
    • Robustness of estimators on stationary observations
    • Dec.
    • P. Papantoni-Kazakos and R. M. Gray. Robustness of estimators on stationary observations. Ann. Probab., 7:989-1002, Dec. 1979.
    • (1979) Ann. Probab. , vol.7 , pp. 989-1002
    • Papantoni-Kazakos, P.1    Gray, R.M.2
  • 144
    • 0020168142 scopus 로고
    • Sliding-block and random source coding with constrained size reproduction alphabets
    • Aug.
    • W. A. Pearlman. Sliding-block and random source coding with constrained size reproduction alphabets. IEEE Trans. Commun., 30(8):1859-1867, Aug. 1982.
    • (1982) IEEE Trans. Commun. , vol.30 , Issue.8 , pp. 1859-1867
    • Pearlman, W.A.1
  • 146
    • 0039614532 scopus 로고
    • Notions généralisees d'incertitude, d'entropie et d'information du point de vue de la théorie des martingales
    • Czech. Acad. Sci. Publishing House
    • A. Perez. Notions généralisees d'incertitude, d'entropie et d'information du point de vue de la théorie des martingales. In Transactions First Prague Conf. on Information Theory, Stat. Decision Functions, and Random Processes, pages 183-208. Czech. Acad. Sci. Publishing House, 1957.
    • (1957) Transactions First Prague Conf. on Information Theory, Stat. Decision Functions, and Random Processes , pp. 183-208
    • Perez, A.1
  • 147
    • 84894378131 scopus 로고
    • Sur la convergence des incertitudes, entropies et informations échantillon vers leurs valeurs vraies
    • Czech. Acad. Sci. Publishing House
    • A. Perez. Sur la convergence des incertitudes, entropies et informations échantillon vers leurs valeurs vraies. In Transactions First Prague Conf. on Information Theory, Stat. Decision Functions, and Random Processes, pages 245-252. Czech. Acad. Sci. Publishing House, 1957.
    • (1957) Transactions First Prague Conf. on Information Theory, Stat. Decision Functions, and Random Processes , pp. 245-252
    • Perez, A.1
  • 149
    • 0442300330 scopus 로고
    • Extensions of shannon-MacMillan's limit theorem to more general stochastic processes processes
    • Prague and New York, Publishing House Czech. Akad. Sci. and Academic Press
    • A. Perez. Extensions of Shannon-MacMillan's limit theorem to more general stochastic processes processes. In Third Prague Conf. on Inform. Theory, Decision Functions, and Random Processes, pages 545-574, Prague and New York, 1964. Publishing House Czech. Akad. Sci. and Academic Press.
    • (1964) Third Prague Conf. on Inform. Theory, Decision Functions, and Random Processes , pp. 545-574
    • Perez, A.1
  • 150
    • 0003831421 scopus 로고
    • Cambridge University Press, Cambridge
    • K. Petersen. Ergodic Theory. Cambridge University Press, Cambridge, 1983.
    • (1983) Ergodic Theory
    • Petersen, K.1
  • 151
    • 84892316070 scopus 로고
    • Dynamical systems with completely positive or zero entropy
    • M. S. Pinsker. Dynamical systems with completely positive or zero entropy. Soviet Math. Dokl., 1:937-938, 1960.
    • (1960) Soviet Math. Dokl. , vol.1 , pp. 937-938
    • Pinsker, M.S.1
  • 152
    • 0003818048 scopus 로고
    • Holden Day, San Francisco, Translated by A. Feinstein from the Russian edition published in 1960 by Izd. Akad. Nauk. SSSR
    • M. S. Pinsker. Information and information stability of random variables and processes. Holden Day, San Francisco, 1964. Translated by A. Feinstein from the Russian edition published in 1960 by Izd. Akad. Nauk. SSSR.
    • (1964) Information and Information Stability of Random Variables and Processes
    • Pinsker, M.S.1
  • 153
    • 0003235248 scopus 로고
    • Digital image compression techniques
    • SPIE Optical Engineering Press, Bellingham, Washington
    • M. Rabbani and P. W. Jones. Digital Image Compression Techniques, Tutorial Texts in Optical Engineering. volume 7 SPIE Optical Engineering Press, Bellingham, Washington, 1991.
    • (1991) Tutorial Texts in Optical Engineering , vol.7
    • Rabbani, M.1    Jones, P.W.2
  • 155
    • 0010078599 scopus 로고    scopus 로고
    • Mass transportation problems: Applications
    • Springer- Verlag, New York
    • S.T. Rachev and L. Rüschendorf. Mass Transportation Problems: Applications. Probability and ITS Applications, Vol. II Springer- Verlag, New York, 1998.
    • (1998) Probability and its Applications , vol.2
    • Rachev, S.T.1    Rüschendorf, L.2
  • 156
    • 0007158728 scopus 로고
    • ISI Lecture Notes, Indian Statistical Institute, Calcutta, India
    • D. Ramachandran. Perfect Measures. ISI Lecture Notes, Indian Statistical Institute, Calcutta, India, 1979.
    • (1979) Perfect Measures
    • Ramachandran, D.1
  • 158
    • 0005598060 scopus 로고
    • Construction and properties of invariant measurable partitions
    • V. A. Rohlin and Y. G. Sinai. Construction and properties of invariant measurable partitions. Soviet Math. Dokl., 2:1611-1614, 1962.
    • (1962) Soviet Math. Dokl. , vol.2 , pp. 1611-1614
    • Rohlin, V.A.1    Sinai, Y.G.2
  • 159
    • 0028550580 scopus 로고
    • A mapping approach to rate-distortion computation and analysis
    • Nov.
    • K. Rose. A mapping approach to rate-distortion computation and analysis. EEE Trans. Inform. Theory, 40(6):1939-1952, Nov. 1994.
    • (1994) EEE Trans. Inform. Theory , vol.40 , Issue.6 , pp. 1939-1952
    • Rose, K.1
  • 161
    • 0004218547 scopus 로고    scopus 로고
    • Morgan Kaufmann Publishers, San Francisco, second edition
    • K. Sayood. Introduction to Data Compression. Morgan Kaufmann Publishers, San Francisco, second edition, 2000.
    • (2000) Introduction to Data Compression
    • Sayood, K.1
  • 162
  • 163
    • 84892327233 scopus 로고
    • American Math. Soc. 2, No. 48, pp. 229-254, 1965.
    • (1965) American Math. Soc. , vol.2 , Issue.48 , pp. 229-254
  • 164
    • 84856043672 scopus 로고
    • A mathematical theory of communication
    • C. E. Shannon. A mathematical theory of communication. Bell Syst. Tech. J., 27:379-423, 1948.
    • (1948) Bell Syst. Tech. J. , vol.27 , pp. 379-423
    • Shannon, C.E.1
  • 165
    • 0003214704 scopus 로고
    • Coding theorems for a discrete source with a fidelity criterion
    • C. E. Shannon. Coding theorems for a discrete source with a fidelity criterion. In IRE National Convention Record, Part 4, pages 142-163, 1959.
    • (1959) IRE National Convention Record, Part 4 , pp. 142-163
    • Shannon, C.E.1
  • 167
    • 0023314364 scopus 로고
    • The ergodic and entropy theorems revisited
    • P. C. Shields. The ergodic and entropy theorems revisited. IEEE Trans. Inform. Theory, 33:263-266, 1987.
    • (1987) IEEE Trans. Inform. Theory , vol.33 , pp. 263-266
    • Shields, P.C.1
  • 168
    • 0032184321 scopus 로고    scopus 로고
    • The interactions between ergodic theory and information theory
    • P. C. Shields. The interactions between ergodic theory and information theory. IEEE Trans. Inform. Theory, 40:2079-2093, 1998.
    • (1998) IEEE Trans. Inform. Theory , vol.40 , pp. 2079-2093
    • Shields, P.C.1
  • 170
    • 0000419815 scopus 로고
    • On the concept of entropy of a dynamical system
    • In Russian
    • Y. G. Sinai. On the concept of entropy of a dynamical system. Dokl. Akad. Nauk. SSSR, 124:768-771, 1959. (In Russian.).
    • (1959) Dokl. Akad. Nauk. SSSR , vol.124 , pp. 768-771
    • Sinai, Y.G.1
  • 171
    • 67649301813 scopus 로고
    • Weak isomorphism of transformations with an invariant measure
    • Y. G. Sinai. Weak isomorphism of transformations with an invariant measure. Soviet Math. Dokl., 3:1725-1729, 1962.
    • (1962) Soviet Math. Dokl. , vol.3 , pp. 1725-1729
    • Sinai, Y.G.1
  • 173
    • 0001597243 scopus 로고
    • A class of binary signaling alphabets
    • D. Slepian. A class of binary signaling alphabets. Bell Syst. Tech. J., 35:203-234, 1956.
    • (1956) Bell Syst. Tech. J. , vol.35 , pp. 203-234
    • Slepian, D.1
  • 175
    • 0011355635 scopus 로고
    • A partition on a bernoulli shift which is not weakly bernoulli
    • M. Smorodinsky. A partition on a bernoulli shift which is not weakly bernoulli. Theory of Computing Systems, 5(3):201-203, 1971.
    • (1971) Theory of Computing Systems , vol.5 , Issue.3 , pp. 201-203
    • Smorodinsky, M.1
  • 176
    • 0009150537 scopus 로고
    • Existence of compatible families of proper regular conditional probabilities
    • A. D. Sokai. Existence of compatible families of proper regular conditional probabilities. Z. Wahrsch. Verw. Gebiete, 56:537-548, 1981.
    • (1981) Z. Wahrsch. Verw. Gebiete , vol.56 , pp. 537-548
    • Sokai, A.D.1
  • 177
    • 33747479974 scopus 로고
    • Sur la division des corp materiels en parties
    • H. Steinhaus. Sur la division des corp materiels en parties. Bull. Acad. Polon. Sci., IV(III):801-804, 1956.
    • (1956) Bull. Acad. Polon. Sci. , vol.4 , Issue.3 , pp. 801-804
    • Steinhaus, H.1
  • 179
    • 0020115477 scopus 로고
    • The design of trellis waveform coders
    • April
    • L. C. Stewart, R. M. Gray, and Y. Linde. The design of trellis waveform coders. IEEE Trans. Comm., 30:702-710, April 1982.
    • (1982) IEEE Trans. Comm. , vol.30 , pp. 702-710
    • Stewart, L.C.1    Gray, R.M.2    Linde, Y.3
  • 181
    • 0000925325 scopus 로고
    • Inequalities for distributions with given marginals
    • Aug
    • A. H. Tchen. Inequalities for distributions with given marginals. The Annals of Probability, 8(4):814-827, Aug 1980.
    • (1980) The Annals of Probability , vol.8 , Issue.4 , pp. 814-827
    • Tchen, A.H.1
  • 183
    • 26944500990 scopus 로고
    • Computing the wasserstein distance between probability distributions on the line
    • S. S. Vallender. Computing the wasserstein distance between probability distributions on the line. Theory Probab. Appl., 18:824-827, 1973.
    • (1973) Theory Probab. Appl. , vol.18 , pp. 824-827
    • Vallender, S.S.1
  • 185
    • 0002721507 scopus 로고
    • Markov processes on countable product space describing large systems of automata
    • L. N. Vasershtein. Markov processes on countable product space describing large systems of automata. Problemy Peredachi Informatsii, 5:64-73, 1969.
    • (1969) Problemy Peredachi Informatsii , vol.5 , pp. 64-73
    • Vasershtein, L.N.1
  • 187
    • 77049090012 scopus 로고    scopus 로고
    • The kantorovich metric: The initial history and little-known applications
    • A.M. Vershik. The kantorovich metric: The initial history and little-known applications. POMI, 312:69-85, 2004.
    • (2004) POMI , vol.312 , pp. 69-85
    • Vershik, A.M.1
  • 188
    • 1542342359 scopus 로고    scopus 로고
    • Topics in optimal transportation
    • American Mathematical Society, Providence, RI
    • C. Villani. Topics in Optimal Transportation, Graduate Studies in Mathematics. volume 58, American Mathematical Society, Providence, RI, 2003.
    • (2003) Graduate Studies in Mathematics , vol.58
    • Villani, C.1
  • 190
    • 0016058778 scopus 로고
    • Trellis encoding of memoryless discrete-time sources with a fidelity criterion
    • May
    • A. J. Viterbi and J. K. Omura. Trellis encoding of memoryless discrete-time sources with a fidelity criterion. IEEE Trans. Inform. Theory, 20:325-332, May 1974.
    • (1974) IEEE Trans. Inform. Theory , vol.20 , pp. 325-332
    • Viterbi, A.J.1    Omura, J.K.2
  • 192
    • 0000195485 scopus 로고
    • Zur operatorenmethode in der klassischen mechanik
    • J. vonNeumann. Zur operatorenmethode in der klassischen mechanik. Ann. of Math., 33:587-642, 1932.
    • (1932) Ann. of Math. , vol.33 , pp. 587-642
    • Vonneumann, J.1
  • 193
    • 0004386924 scopus 로고
    • Lecture Notes in Mathematics No. 458, Springer-Verlag, New York
    • P. Walters. Ergodic Theory-Introductory Lectures. Lecture Notes in Mathematics No. 458. Springer-Verlag, New York, 1975.
    • (1975) Ergodic Theory-Introductory Lectures
    • Walters, P.1
  • 195
    • 0017494668 scopus 로고
    • Trellis coding of continuous-Amplitude memoryless sources
    • May
    • S. G. Wilson and D. W. Lytle. Trellis coding of continuous-Amplitude memoryless sources. IEEE Trans. Inform. Theory, 23:404-409, May 1977.
    • (1977) IEEE Trans. Inform. Theory , vol.23 , pp. 404-409
    • Wilson, S.G.1    Lytle, D.W.2
  • 197
    • 33846047612 scopus 로고
    • Strong converse of the coding theorem for the general discrete finite-memory channel
    • J. Wolfowitz. Strong converse of the coding theorem for the general discrete finite-memory channel. Inform. and Control, 3:89-93, 1960.
    • (1960) Inform. and Control , vol.3 , pp. 89-93
    • Wolfowitz, J.1
  • 199
    • 33748322276 scopus 로고
    • A definition of conditional mutual information for arbitrary ensembles
    • A. Wyner. A definition of conditional mutual information for arbitrary ensembles. Inform. and Control, pages 51-59, 1978.
    • (1978) Inform. and Control , pp. 51-59
    • Wyner, A.1
  • 200
    • 0018995553 scopus 로고
    • Distortion-rate theory for individual sequences
    • Mar.
    • J. Ziv. Distortion-rate theory for individual sequences. IEEE Trans. Inform. Theory, 26:137-143, Mar. 1980.
    • (1980) IEEE Trans. Inform. Theory , vol.26 , pp. 137-143
    • Ziv, J.1
  • 201
    • 0022055957 scopus 로고
    • Universal quantization
    • J. Ziv. Universal quantization. IEEE Trans. Inform. Theory, 31:344-347, 1985.
    • (1985) IEEE Trans. Inform. Theory , vol.31 , pp. 344-347
    • Ziv, J.1


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