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Multiple-user communication

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Abstract

The survey is devoted to the theory of multiple-user communication (coding of dependent sources, one-way multicomponent channels, and multiway channels).

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Literature cited

  1. E. A. Arutyunyan, “A lower bound of the probability of error for multiway channels,” Probl. Peredachi Inf.,11, No. 2, 23–36 (1975).

    Google Scholar 

  2. R. G. Gallager, “The throughput capacity and coding for several broadcast channels,” Probl. Peredachi Inf.,10, No. 3, 3–14 (1974).

    Google Scholar 

  3. S. I. Gel'fand, “The throughput capacity of a broadcast channel,” Probl. Peredachi Inf.,13, No. 3, 106–108 (1977).

    Google Scholar 

  4. V. N. Koshelev, “On the problem of separate coding of two dependent sources,” Probl. Peredachi Inf.,13, No. 1, 26–32 (1977).

    Google Scholar 

  5. A. V. Kuznetsov and B. S. Tsybakov, “Coding in memory with defect cells,” Probl. Peredachi Inf.,10, No. 2, 52–60 (1974).

    Google Scholar 

  6. L. M. Libkind, “Two-way discrete communication channels without memory,” Probl. Peredachi Inf.,3, No. 2, 37–46 (1967).

    Google Scholar 

  7. G. A. Margulis, “Probabilistic characteristics of graphs with large connectivity,” Probl. Peredachi Inf.,10, No. 2, 101–108 (1974).

    Google Scholar 

  8. A. S. Nemirovskii, “On the throughput capacity of a multiray channel with dispersed reception and automatic election,” Radiotekhnika,16, No. 9, 34–38 (1961).

    Google Scholar 

  9. I. A. Ovseevich, “The throughput capacity of a multipath system,” Probl. Peredachi Inf., No. 14, 43–58 (1963).

    Google Scholar 

  10. I. A. Ovseevich and M. S. Pinsker, “Rate of information transmission, the throughput capacity of a multipath system, and reception by the method of linear operative transformation,” Radiotekhnika,14, No. 3, 9–21 (1959).

    Google Scholar 

  11. I. A. Ovseevich and M. S. Pinsker, “On the throughput capacity of a multipath information system,” Izv. Akad. Nauk SSSR, Otd. Tekh. Energ. Avtom., No. 1, 133–135 (1959).

    Google Scholar 

  12. I. A. Ovseevich and M. S. Pinsker, “Optimal linear prediction and correction of the signal during its transmission over a multipath system,” Izv. Akad. Nauk SSSR, Otd. Tekh. Energ. Avtom., No. 2, 49–59 (1959).

    Google Scholar 

  13. I. A. Ovseevich and M. S. Pinsker, “On the throughput capacity of a multipath system,” Izv. Akad. Nauk SSSR, Otd. Tekh. Energ. Avtom., No. 4, 208–210 (1961).

    Google Scholar 

  14. G. Sh. Poltyrev, “On the admissible transmission speeds in discrete broadcast channels,” in: VI Conf. po Teorii Kodir. i Peredachi Inform., Ch. I, Doklady, Moscow-Tomsk (1975), pp. 150–155.

    Google Scholar 

  15. G. Sh. Poltyrev, “Throughput capacity of parallel broadcast channels with degraded components,” Probl. Peredachi Inf.,13, No. 2, 23–35 (1977).

    Google Scholar 

  16. V. L. Stefanyuk, “On ‘mutualhelp’ in an assemblage of radio stations,” Probl. Peredachi Inf.,7, No. 3, 103–107 (1971).

    Google Scholar 

  17. V. L. Stefanyuk and M. L. Tsetlin, “On the regulation of power in an assemblage of radio stations,” Probl. Peredachi Inf.,3, No. 4, 49–57 (1967).

    Google Scholar 

  18. B. S. Tsybakov, “Group additive codes for correction of defects,” Probl. Peredachi Inf.,11, No. 1, 111–113 (1975).

    Google Scholar 

  19. B. S. Tsybakov, “Correcting defects and errors,” Probl. Peredachi Inf.,11, No. 3, 21–30 (1975).

    Google Scholar 

  20. R. Ahlswede, “On two-way communication channels and a problem by Zarankiewicz,” Trans. 6th Prague Conf. Inform. Theory, Statist. Decis. Function., Random Proces., Prague, 1971, Prague (1973), pp. 23–27.

  21. R. Ahlswede, “Multiway communication channels,” in: 2nd Intern. Symp. Inf. Theory, Tsahkadsor, 1971, Budapest (1973), pp. 23–52.

  22. R. Ahlswede, “The capacity region of a channel with two senders and two receivers,” Ann. Probab.,2, No. 5, 805–814 (1974).

    Google Scholar 

  23. R. Ahlswede and G. Dueck, “Every bad code has a good subcode: a local converse to the coding theorem,” Z. Wahrscheinlichkeitstheorie Verw. Geb.,34, No. 2, 179–182 (1976).

    Google Scholar 

  24. R. Ahlswede, P. Gács, and J. Körner, “Bounds on conditional probabilities with application in multiuser communication,” Z. Wahrscheinlichkeitstheorie Verw. Geb.,34, No. 2, 157–177 (1976).

    Google Scholar 

  25. R. Ahlswede and J. Körner, “Source coding with side information and a converse for degraded broadcast channels,” IEEE Trans. Inf. Theory,21, No. 6, 629–637 (1975).

    Google Scholar 

  26. T. Berger, Rate Distortion Theory, Prentice-Hall, New Jersey (1971).

    Google Scholar 

  27. T. Berger and S. Y. Tung, “Encoding of correlated analog sources,” in: Proc. 1975 IEEE-USSR Joint Workshop on Inform. Theory, Moscow, December, 1975, New York (1976), pp. 7–10.

  28. P. P. Bergmans, “Random coding theorem for broadcast channels with degraded components,” IEEE Trans. Inf. Theory,19, No. 2, 197–207 (1973).

    Google Scholar 

  29. P. P. Bergmans, “A simple converse for broadcast channels with additive white Gaussian noise,” IEEE Trans. Inf. Theory,20, No. 2, 279–280 (1974).

    Google Scholar 

  30. P. P. Bergmans and T. M. Cover, “Cooperative broadcasting,” IEEE Trans. Inf. Theory,20, No. 3, 317–324 (1974).

    Google Scholar 

  31. N. M. Blachman, “The convolution inequality for entropy powers,” IEEE Trans. Inf. Theory,11, No. 2, 267–271 (1965).

    Google Scholar 

  32. A. B. Carleial, “A case where interference does not reduce capacity,” IEEE Trans. Inf. Theory,21, No. 5, 569–570 (1975).

    Google Scholar 

  33. T. M. Cover, “Broadcast channels,” IEEE Trans. Inf. Theory,18, No. 1, 2–14 (1972).

    Google Scholar 

  34. T. M. Cover, “A proof of the data compression theorem of Slepian and Wolf for ergodic sources,” IEEE Trans. Inf. Theory,21, No. 2, 226–228 (1975).

    Google Scholar 

  35. T. M. Cover, “An achievable rate region for the broadcast channel,” IEEE Trans. Inf. Theory,21, No. 4, 399–404 (1975).

    Google Scholar 

  36. T. M. Cover, “Some advances in broadcast channels,” Adv. Commun. Systems,4, 229–266 (1975).

    Google Scholar 

  37. T. M. Cover, “Open problems in information theory,” Proc. 1975 IEEE — USSR Joint Workshop on Inform. Theory, Moscow, December, 1975, New York (1976), pp. 35–36.

  38. I. Csiszár and J. Körner, “Broadcast channels with confidential messages,” Preprint, Mathematical Institute of the Hungarian Academy of Sciences (1976).

  39. P. Elias, “Networks of Gaussian channels with applications to feedback systems,” EEEE Trans. Inf. Theory,13, No. 4, 493–501 (1967).

    Google Scholar 

  40. N. T. Gaarder and J. K. Wolf, “The capacity region of a multiple-access discrete rnemoryless channel can increase with feedback,” IEEE Trans. Inf. Theory,21, No. 1, 100–102 (1975).

    Google Scholar 

  41. P. Gács and J. Körner, “Common information is far less than mutual information,” Probl. Upr. Teor. Inf. (Hung.),2, No. 2, 149–162 (1973).

    Google Scholar 

  42. R. G. Gallager, Information Theory and Reliable Communication, Wiley, New York (1968).

    Google Scholar 

  43. R. G. Gallager, “Basic limits on protocol information in data communication networks,” IEEE Trans. Inf. Theory,22, No. 4, 385–398 (1976).

    Google Scholar 

  44. R. M. Gray, “A new class of lower bounds to information rates of stationary sources via conditional rate-distortion functions,” IEEE Trans. Inf. Theory,19, No. 4, 480–489 (1973).

    Google Scholar 

  45. R. M. Gray and P. P. Bergmans, “Problems in simultaneous communication,” IEEE Trans. Commun.,21, No. 5, 763–767 (1973).

    Google Scholar 

  46. R. M. Gray and A. D. Wyner, “Source coding for a simple network,” Bell. Syst. Tech. J.,53, No. 9, 1681–1721 (1974).

    Google Scholar 

  47. D. Horwood and R. Gagliardi, “Signal design for digital multiple access communications,” IEEE Trans. Commun.,23, No. 3, 378–383 (1975).

    Google Scholar 

  48. F. Jelinek, “Loss in information transmission through two-way channels,” Inf. Control,6, No. 4, 337–371 (1963).

    Google Scholar 

  49. F. Jelinek, “Coding for and decomposition of two-way channels,” IEEE Trans. Inf. Theory,10, No. 1, 5–17 (1964).

    Google Scholar 

  50. T. Kasami and Lin Shu, “Coding for a multiple-access channel,” IEEE Trans. Inf. Theory,22, No. 2, 129–137 (1976).

    Google Scholar 

  51. L. Kleinrock and F. A. Tobagi, “Packet switching in radio channels. Part I. Carrier sense multiple-access modes and their throughput-delay characteristics,” IEEE Trans. Commun.,23, No. 12, 1400–1416 (1975).

    Google Scholar 

  52. J. Körner and K. Marton, “A source network problem involving the comparison of two channels. I,” Preprint No. 22, Math. Inst. Hung. Acad. Sci., Budapest (1975).

    Google Scholar 

  53. J. Körner and K. Marton, “A source network problem involving the comparison of two channels. II,” Preprint (1975).

  54. J. Körner and K. Marton, “General broadcast channels with degraded message sets,” IEEE Trans. Inf. Theory,23, No. 1, 60–64 (1977).

    Google Scholar 

  55. H. J. Liao, “Channel capacity for nonorthogonal multiple access communications,” Proc. 5th Ann. Princeton Conf. Inf. Sci. and Syst., Princeton, New Jersey (1971), pp. 140–144.

  56. E. C. van der Meulen, “A note and counterexample on the two-way channel,” Univ. Rochester (1970).

  57. E. C. van der Meulen, “Three-terminal communication channels,” Adv. Appl. Probab.,3, 120–154 (1971).

    Google Scholar 

  58. E. C. van der Meulen, “The discrete memoryless channel with two senders and one receiver,” 2nd Intern. Symp. Inform. Theory, Tsakhadsor, 1971, Budapest (1973), pp. 103–135.

  59. E. C. van der Meulen, “Multiterminal communication channels,” Adv. Appl. Probab.,15, No. 1, 32–33 (1973).

    Google Scholar 

  60. E. C. van der Meulen, “On a problem by Ahlswede regarding the capacity region of certain multiway channels,” M. Control,25, No. 4, 351–356 (1974).

    Google Scholar 

  61. E. C. van der Meulen, “Random coding theorems for the general discrete memoryless broadcast channel,” IEEE Trans. Inf. Theory,21, No. 2, 180–190 (1975).

    Google Scholar 

  62. E. C. van der Meulen, “Advances in multiple-user communication channels,” Proc. 1975 IEEE — USSR Joint Workshop on Inform. Theory, Moscow, December, 1975, New York (1976), pp. 227–247.

  63. E. C. van der Meulen, “A survey of multiway channels in information theory: 1961–1976,” IEEE Trans. Inf. Theory,23, No. 1, 1–37 (1977).

    Google Scholar 

  64. M. Ohkubo, “Studies on multiple access channels,” Densi Pusin Gakkai Rombunsi,A59, No. 8, 652–659 (1976).

    Google Scholar 

  65. J. N. Pierce and S. Stein, “Multiple diversity with nonindependent fading,” PIRE,48, No. 1 (1960).

  66. E. C. Posner, “Broadcasting and covering,” Util. Math.,5, 323–333 (1974).

    Google Scholar 

  67. A. Rényi, “On measures of dependence,” Acta Math. Acad. Sci. Hung.,10, No. 3–4, 441–451 (1959).

    Google Scholar 

  68. I. Rubin, “Communication network message path delays,” IEEE Trans. Inf. Theory,20, No. 5, 738–745 (1974).

    Google Scholar 

  69. H. Sato, “An upper bound to the capacity region of a broadcast channel,” Preprint (1975).

  70. J. E. Savage, “Signal detection in the presence of multiple-access noise,” IEEE Trans. Inf. Theory,20, No. 1, 42–49 (1974).

    Google Scholar 

  71. C. E. Shannon, “Communication theory of secrecy systems,” Bell Syst. Tech. J.,28, No. 4, 656–715 (1949).

    Google Scholar 

  72. C. E. Shannon, “A note on a partial ordering for communication channels,” Inf. Control,1, No. 4, 390–397 (1958).

    Google Scholar 

  73. C. E. Shannon, “Two-way communication channels,” Proc. 4th Berkeley Symp. Math. Stat. and Prob., 1960, Vol. 1, Berkeley-Los Angeles, Univ. Calif. Press (1961), pp. 611–644.

    Google Scholar 

  74. Bhu Dev Sharma, “Multiple decoding scheme and bounds on the probability of error and erasure over a multiple channel,” Kybernetika,12, No. 4, 213–222 (1976).

    Google Scholar 

  75. P. Shields and J.-P. Thouvenot, “Une remarque sur les isomorphismes de schemas de Bernoulli qui préservent certains facteurs,” Isr. J. Math.,21, No. 2–3, 173–176 (1975).

    Google Scholar 

  76. D. Slepian and J. K. Wolf, “Noiseless coding for correlated information sources,” IEEE Trans. Inf. Theory,19, No. 4, 471–480 (1973).

    Google Scholar 

  77. D. Slepian and J. K. Wolf, “A coding theorem for multiple access channels with correlated sources,” Bell Syst. Tech. J.,52, No. 7, 1037–1076 (1973).

    Google Scholar 

  78. I. G. Stiglitz, “Multiple access consideration. A satellite example,” IEEE Trans. Commun.,21, No. 5, 577–582 (1973).

    Google Scholar 

  79. I. G. Stiglitz, “Packet switching in radio channels. Part II. The hidden terminal problem in carrier sense multiple-access and the busy-tone solution,” IEEE Trans. Commun.,23, No. 12, 1417–1433 (1975).

    Google Scholar 

  80. J.-P. Thouvenot, “Remarques sur les systémes dinamiques donnés avec plusieurs facteurs,” Isr. J. Math.,21, No. 2–3, 215–232 (1975).

    Google Scholar 

  81. M. L. Ulrey, “The capacity region of a channel with s senders and r receivers,” Inf. Control,29, No. 3, 185–203 (1975).

    Google Scholar 

  82. H. S. Witsenhausen, “Entropy inequalities for discrete channels,” IEEE Trans. Inf. Theory,20, No. 5, 610–616 (1974).

    Google Scholar 

  83. H. S. Witsenhausen, “On sequences of pairs of dependent random variables,” SIAM J. Appl. Math.,28, No. 1, 100–113 (1975).

    Google Scholar 

  84. H. S. Witsenhausen, “Values and bounds for the common information of two discrete random variables,” SIAM J. Appl. Math.,31, No. 2, 313–333 (1976).

    Google Scholar 

  85. H. S. Witsenhausen, “The zero-error side information problem and chromatic numbers,” IEEE Trans. Inf. Theory,22, No. 5, 592–593 (1976).

    Google Scholar 

  86. H. S. Witsenhausen and A. D. Wyner, “A conditional entropy bound for a pair of discrete random variables,” IEEE Trans. Inf. Theory,21, No. 5, 493–501 (1975).

    Google Scholar 

  87. J. K. Wolf, “Multiple-user communications,” NTC 73, Nat. Telecommun. Conf., Atlanta, Ga., 1973, Vol. 2, New York (1973), 28E/1–28E/11.

  88. J. K. Wolf, “Data reduction for multiple correlated sources,” Proc. of the 5th Colloquium on Microwave Communications, Budapest, Hungary, June 24–30 (1974).

  89. J. Wolfowitz, Coding Theorems of Information Theory, Springer, Berlin-Gottingen-Heidelberg (1961).

    Google Scholar 

  90. J. Wolfowitz, “The method of random codes for two-way channels without feedback,” (1965).

  91. A. D. Wyner, “Another look at the coding theorem of information theory. A tutorial,” Proc. IEEE,58, No. 6, 894–913 (1970).

    Google Scholar 

  92. A. D. Wyner, “A theorem on the entropy of certain binary sequences and applications. II,” IEEE Trans. Inf. Theory,19, No. 6, 772–777 (1973).

    Google Scholar 

  93. A. D. Wyner, “Recent results in the Shannon theory,” IEEE Trans. Inf. Theory,20, No. 1, 2–10 (1974).

    Google Scholar 

  94. A. D. Wyner, “The common information of two dependent random variables,” IEEE Trans. Inf. Theory,21, No. 2, 163–179 (1975).

    Google Scholar 

  95. A. D. Wyner, “On source coding with side information at the decoder,” IEEE Trans. Inf. Theory,21, No. 3, 294–300 (1975).

    Google Scholar 

  96. A. D. Wyner, “The wire-tap channel,” Bell Syst. Tech. J.,54, No. 8, 1355–1387 (1975).

    Google Scholar 

  97. A. D. Wyner and J. Ziv, “A theorem on the entropy of certain binary sequences and applications. I,” IEEE Trans. Inf. Theory,19, No. 6, 769–772 (1973).

    Google Scholar 

  98. A. D. Wyner and J. Ziv, “The rate-distortion function for source coding with side information at the decoder,” IEEE Trans. Inf. Theory,22, No. 1, 1–10 (1976).

    Google Scholar 

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Translated from Itogi Nauki i Tekhniki. Teoriya Veroyatnostei, Matematicheskaya Statistika, Teoreticheskaya Kibernetika, Vol. 15, pp. 123–162, 1978.

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Gel'fand, S.I., Prelov, V.V. Multiple-user communication. J Math Sci 13, 386–408 (1980). https://doi.org/10.1007/BF01088987

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