Reliable communication under channel uncertainty

IEEE Transactions on Information Theory

Volumn 44, Issue 6, 1998, Pages 2148-2177

  Lapidoth, Amos ^a,b   Narayan, Prakash ^a,c  

^a IEEE   (United States)

^b Department of Electrical Engineering and Computer Science   (United States)

^c UNIVERSITY OF MARYLAND   (United States)

Author keywords

Arbitrarily varying channel; Compound channel; Deterministic code; Finite state channel; Gaussian arbitrarily varying channel; Jamming; MMI decoder; Multiple access channel; Randomized code; Robustness; Typicality decoder; Universal decoder; Wireless

Indexed keywords

CODES (SYMBOLS); DECODING; JAMMING; ROBUSTNESS (CONTROL SYSTEMS); UNCERTAIN SYSTEMS;

ARBITRARILY VARYING CHANNEL; CHANNEL UNCERTAINTY; COMPOUND CHANNEL; DETERMINISTIC CODE; FINITE STATE CHANNEL; GAUSSIAN ARBITRARILY VARYING CHANNEL; MULTIPLE ACCESS CHANNEL; RANDOMIZED CODE; RELIABLE COMMUNICATION; TYPICALITY DECODER;

COMMUNICATION CHANNELS (INFORMATION THEORY);

EID: 0032182921     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.720535     Document Type: Article

References (131)

1. R. Ahlswede, "Certain results in coding theory for compound channels," in Proc. Coll. Inf. The. Debrecen 1967, A. Rényi, Ed. Budapest, Hungary: J. Bolyai Math. Soc., 1968, vol. 1, pp. 35-60.
2. "A note on the existence of the weak capacity for channels with arbitrarily varying channel probability functions and its relation to Shannon's zero error capacity," Ann. Math. Statist., vol. 41, pp. 1027-1033, 1970.
3. "The capacity of a channel with arbitrary varying Gaussian channel probability functions," in Trans. 6th Prague Conf. Information Theory, Statistical Decision Functions and Random Processes, Sept. 1971, pp. 13-21.
4. "Multi-way communication channels," in Proc. 2nd. Int. Symp. Information Theory. Budapest, Hungary: Hungarian Acad. Sci., 1971, pp. 23-52.
5. "Channel capacities for list codes," J. Appl. Probab., vol. 10, pp. 824-836, 1973.
6. "Elimination of correlation in random codes for arbitrarily varying channels," Z. Wahrscheinlichkeitstheorie Verw. Gebiete, vol. 44, pp. 159-175, 1978.
7. "Elimination of correlation in random codes for arbitrarily varying channels," Z. Wahrscheinlichkeitstheorie Verw. Gebiete, vol. 44, pp. 159-175, 1978
8. "Coloring hypergraphs: A new approach to multiuser source coding, Part I," J. Combin., Inform. Syst. Sci., vol. 4, no. 1, pp. 76-115, 1979
9. "Coloring hypergraphs: A new approach to multiuser source coding, Part II," J. Combin., Inform. Syst. Sci., vol. 5, no. 3, pp. 220-268, 1980.
10. "A method of coding and an application to arbitrarily varying channels," J. Comb., Inform. Syst. Sci.., vol. 5, pp. 10-35, 1980.
11. "Arbitrarily varying channels with states sequence known to the sender," IEEE Trans. Inform. Theory, vol. IT-32, pp. 621-629, Sept. 1986.
12. "The maximal error capacity of arbitrarily varying channels for constant list sizes," IEEE Trans. Inform. Theory, vol. 39, pp. 1416-1417, July 1993.
13. R. Ahlswede, L. A. Bassalygo, and M. S. Pinsker, "Localized random and arbitrary errors in the light of arbitrarily varying channel theory," IEEE Trans. Inform. Theory, vol. 41, pp. 14-25, Jan. 1995.
14. R. Ahlswede and N. Cai, "Two proofs of Pinsker's conjecture concerning arbitrarily varying channels," IEEE Trans. Inform. Theory, vol. 37, pp. 1647-1649, Nov. 1991.
15. "Arbitrarily varying multiple-access channels Part I. Ericson's symmetrizability is adequate, Gubner's conjecture is true," in Proc. IEEE Int. Symp. Information Theory (Ulm, Germany, 1997), p. 22.
16. "Arbitrarily varying multiple-access channels, Part II: Correlated sender's side information, correlated messages, and ambiguous trans-mission," in Proc. IEEE Int. Symp. Information Theory (Ulm, Germany, 1997), p. 23.
17. "Correlated sources help transmission over an arbitrarily varying channel," IEEE Trans. Inform. Theory, vol. 43, pp. 1254-1255, July 1997.
18. R. Ahlswede and I. Csiszâr, "Common randomness in information theory and cryptography: Part II: CR capacity," IEEE Trans. Inform. Theory, vol. 44, pp. 225-240, Jan 1998.
19. R. Ahlswede and J. Wolfowitz, "Correlated decoding for channels with arbitrarily varying channel probability functions," Inform. Contr., vol. 14, pp. 457, 1969.
20. "The capacity of a channel with arbitrarily varying channel probability functions and binary output alphabet," Z. Wahrscheinlichkeit-stheorie Verw. Gebiete, vol. 15, pp. 186-194, 1970.
21. V. B. Balakirsky, "Coding theorem for discrete memoryless channels with given decision rules," in Proc. 1st French-Soviet Workshop on Algebraic Coding (Lecture Notes in Computer Science 573), G. Cohen, S. Litsyn, A. Lobstein, and G. Zémor, Eds. Berlin, Germany: Springer-Verlag, July 1991, pp. 142-150.
22. "A converse coding theorem for mismatched decoding at the output of binary-input memoryless channels," IEEE Trans. Inform. Theory, vol. 41, pp. 1889-1902, Nov. 1995.
23. A. Barron, J. Rissanen, and B. Yu, "Minimum description length principle in modeling and coding," this issue, pp. 2743-2760.
24. T. Berger, "Multiterminal source coding," in The Information Theory Approach to Communications (CISM Course and Lecture Notes, no. 229), G. Longo, Ed. Berlin, Germany: Springer-Verlag, 1977, pp. 172-231.
25. T. Berger and J. Gibson, "Lossy data compression," this issue, pp. 2693-2723.
26. E. Biglieri, J. Proakis, and S. Shamai, "Fading channels: Information theoretic and communications aspects," this issue, pp. 2619-2692.
27. N. M. Blachman, "The effect of statistically dependent interference upon channel capacity," IRE Trans. Inform. Theory, vol. IT-8, pp. 553-557, Sept. 1962.
28. "On the capacity of a band-limited channel perturbed by statistically dependent interference," IRE Trans. Inform. Theory, vol. IT-8, pp. 48-55, Jan. 1962.
29. D. Blackwell, L. Breiman, and A. J. Thomasian, "Proof of Shannon's transmission theorem for finite-state indecomposable channels," Ann. Math. Statist., vol. 29, no. 4, pp. 1209-1220, 1958.
30. "The capacity of a class of channels," Ann. Math. Statist., vol. 30, pp. 1229-1241, Dec. 1959.
31. "The capacities of certain channel classes under random coding," Ann. Math. Statist., vol. 31, pp. 558-567, 1960.
32. R. E. Blahut, Principles and Practice of Information Theory. Reading, MA: Addison-Wesley, 1987.
33. V. Blinovsky, P. Narayan, and M. Pinsker, "Capacity of an arbitrarily varying channel under list decoding," Probl. Pered. Inform., vol. 31, pp. 99-113, 1995, English translation.
34. V. Blinovsky and M. Pinsker, "Estimation of the size of the list when decoding over an arbitrarily varying channel," in Proc. 1st French-Israeli Workshop on Algebraic Coding, G. Cohen et al., Eds. (Paris, France, July 1993). Berlin, Germany: Springer, 1993, pp. 28-33.
35. "One method of the estimation of the size for list decoding in arbitrarily varying channel," in Proc. of ISITA-94 (Sidney, Australia, 1994), pp. 607-609.
36. J. M. Borden, D. J. Mason, and R. J. McEliece, "Some information theoretic saddlepoints," SIAM Contr. Opt., vol. 23, no. 1, Jan. 1985.
37. M. H. M. Costa, "Writing on dirty paper," IEEE Trans. Inform. Theory, vol. IT-29, pp. 439-441, May 1983.
38. T. M. Cover, "Broadcast channels," IEEE Trans. Inform. Theory, vol. IT-18, pp. 2-14, Jan. 1972.
39. T. M. Cover and J. A. Thomas, Elements of Information Theory. New York: Wiley, 1991
40. I. Csiszär, "The method of types," this issue, pp. 2505-2523.
41. "Arbitrarily varying channels with general alphabets and states," IEEE Trans. Inform. Theory, vol. 38, pp. 1725-1742, Nov. 1992.
42. I. Csiszâr and J. Körner, "Many coding theorems follow from an elementary combinatorial lemma," in Proc. 3rd Czechoslovak-Soviet-Hungarian Sem. Information Theory (Liblice, Czechoslovakia, 1980), pp. 25-44.
43. "Graph decomposition: A new key to coding theorems," IEEE Trans. Inform. Theory, vol. IT-27, pp. 5-12, Jan. 1981.
44. Information Theory: Coding Theorems for Discrete Memoryless Systems. New York: Academic, 1981.
45. "On the capacity of the arbitrarily varying channel for maximum probability of error," Z. Wahrscheinlichkeitstheorie Verw. Gebiete, vol. 57, pp. 87-101, 1981.
46. I. Csiszâr, J. Körner, and K. Marton, "A new look at the error exponent of discrete memoryless channels," in IEEE Int. Symp. Information Theory (Cornell Univ., Ithaca, NY, Oct. 1977), unpublished preprint.
47. I. Csiszâr and P. Narayan, "Arbitrarily varying channels with constrained inputs and states," IEEE Trans. Inform. Theory, vol. 34, pp. 27-34, Jan. 1988.
48. "The capacity of the arbitrarily varying channel revisited: Ca-pacity, constraints," IEEE Trans. Inform. Theory, vol. 34, pp. 181-193, Jan. 1988.
49. "Capacity and decoding rules for classes of arbitrarily varying channels," IEEE Trans. Inform. Theory, vol. 35, pp. 752-769, July 1989.
50. "Capacity of the Gaussian arbitrarily varying channel," IEEE Trans. Inform. Theory, vol. 37, no. 1, pp. 18-26, Jan. 1991.
51. "Channel capacity for a given decoding metric," IEEE Trans. Inform. Theory, vol. 41, pp. 3543, Jan. 1995.
52. R. L. Dobrushin, "Optimum information transmission through a channel with unknown parameters," Radio Eng. Electron., vol. 4, no. 12, pp. 1-8, 1959.
53. R. L. Dobrushin and S. Z. Stambler, "Coding theorems for classes of arbitrarily varying discrete memoryless channels," Probl. Pered. Inform., vol. 11, no. 2, pp. 3-22, 1975, English translation.
54. G. Dueck, "Maximal error capacity regions are smaller than average error capacity regions for multi-user channels," Probl. Contr. Inform. Theory, vol. 7, pp. 11-19, 1978.
55. P. Elias, "List decoding for noisy channels," in IRE WESCON Conv. Rec., 1957, vol. 2, pp. 94-104.
56. "Zero error capacity under list decoding," IEEE Trans. Infam. Theory, vol. 34, pp. 1070-1074, Sept. 1988.
57. E. O. Elliott, "Estimates of error rates for codes on burst-noise channels," Bell Syst. Tech. J., pp. 1977-1997, Sept. 1963.
58. T. Ericson, "A min-max theorem for antijamming group codes," IEEE Trans. Inform. Theory, vol. IT-30, pp. 792-799, Nov. 1984.
59. "Exponential error bounds for random codes in the arbitrarily varying channel," IEEE Trans. Inform. Theory, vol. IT-31, pp. 42-48, Jan. 1985.
60. M. Feder and A. Lapidoth, "Universal decoding for channels with memory," IEEE Trans. Inform. Theory, vol. 44, pp. 1726-1745, Sept. 1998.
61. N. Merhav and M. Feder, "Universal prediction," this issue, pp. 2124-2147.
62. G. D. Forney, "Exponential error bounds for erasure, list and deci-sion feedback systems," IEEE Trans. Inform. Theory, vol. IT-14, pp. 206-220, Mar. 1968.
63. L. J. Forys and P. P. Varaiya, "The e-capacity of classes of unknown channels," Inform. Contr., vol. 14, pp. 376-406, 1969.
64. R. G. Gallager, Information Theory and Reliable Communication. New York: Wiley, 1968.
65. "The random coding bound is tight for the average code," IEEE Trans. Inform. Theory, vol. IT-19, pp. 244-246, Mar. 1973.
66. "Energy limited channels: Coding, multiaccess, and spread spectrum," Tech. Rep. LIDS-P-1714, Lab. Inform. Decision Syst., Mass. Inst. Technol., Cambridge, MA, Nov. 1988.
67. S. I. Gel'fand and M. S. Pinsker, "Coding for channel with random parameters," Probl. Contr. Inform. Theory, vol. 9, no. 1, pp. 19-31, 1980.
68. E. N. Gilbert, "Capacity of burst-noise channels," Bell Syst. Tech. J., vol. 39, pp. 1253-1265, Sept. 1960.
69. A. J. Goldsmith and P. P. Varaiya, "Capacity, mutual information, and coding for finite-state Markov channels," IEEE Trans. Inform. Theory, vol. 42, pp. 868-886, May 1996.
70. A. Grant, R. Rimoldi, R. Urbanke, and P. Whiting, "Rate-splitting multiple access for discrete memoryless channels," IEEE Trans. Inform. Theory, to be published
71. R. Gray and D. Neuhoff, "Quantization," this issue, pp. 2325-2383.
72. J. A. Gubner, "On the deterministic-code capacity of the multiple-access arbitrarily varying channel," IEEE Trans. Inform. Theory, vol. 36, pp. 262-275, Mar. 1990.
73. "State constraints for the multiple-access arbitrarily varying channel," IEEE Trans. Inform. Theory, vol. 37, pp. 27-35, Jan. 1991.
74. "On the capacity region of the discrete additive multiple-access arbitrarily varying channel," IEEE Trans. Inform. Theory, vol. 38, pp. 1344-1346, July 1992.
75. J. A. Gubner and B. L. Hughes, "Nonconvexity of the capacity region of the multiple-access arbitrarily varying channel subject to constraints," IEEE Trans. Inform. Theory, vol. 41, pp. 3-13, Jan. 1995.
76. D. Hajela and M. Honig, "Bounds on e-rate for linear, time-invariant, multi-input/multi-output channels," IEEE Trans. Inform. Theory, vol. 36, Sept. 1990
77. T. S. Han, "Information-spectrum methods in information theory," Grad-uate School of Inform. Syst., Univ. Electro-Communications, Chofu, Tokyo 182 Japan, Tech. Rep., 1997.
78. C. Heegard and A. El Gamal, "On the capacity of computer memory with defects," IEEE Trans. Inform. Theory, vol. IT-29, pp. 731-739, Sept. 1983.
79. M. Hegde, W. E. Stark, and D. Teneketzis, "On the capacity of channels with unknown interference," IEEE Trans. Inform. Theory, vol. 35, pp. 770-783, July 1989.
80. B. Hughes and P. Narayan, "Gaussian arbitrarily varying channels," IEEE Trans. Inform. Theory, vol. IT-33, pp. 267-284, Mar. 1987.
81. "The capacity of a vector Gaussian arbitrarily varying channel," IEEE Trans. Inform. Theory, vol. 34, pp. 995-1003, Sept. 1988.
82. B. L. Hughes, "The smallest list size for the arbitrarily varying channel," in Proc. 1993 IEEE Int. Symp. Information Theory (San Antonio, TX, Jan. 1993).
83. "The smallest list for the arbitrarily varying channel," IEEE Trans. Inform. Theory, vol. 43, pp. 803-815, May 1997.
84. J. Y. N. Hui, "Fundamental issues of multiple accessing," Ph.D. disser-tation, Mass. Inst. Technol., Cambridge, MA, 1983.
85. J. H. Jahn, "Coding for arbitrarily varying multiuser channels," IEEE Trans. Inform. Theory, vol. IT-27, pp. 212-226, Mar. 1981.
86. F. Jelinek, "Indecomposable channels with side information at the transmitter," Inform. Contr., vol. 8, pp. 36-55, 1965.
87. A. Lapidoth, "Mismatched decoding and the multiple-access channel," IEEE Trans. Inform. Theory, vol. 42, pp. 1439-1452, Sept. 1996.
88. "Nearest-neighbor decoding for additive non-Gaussian noise channels," IEEE Trans. Inform. Theory, vol. 42, pp. 1520-1529, Sept. 1996.
89. "On the role of mismatch in rate distortion theory," IEEE Trans. Inform. Theory, vol. 43, pp. 387, Jan. 1997
90. A. Lapidoth and \. E. Telatar, private communication, Dec. 1997.
91. "The compound channel capacity of a class of finite-state channels," IEEE Trans. Inform. Theory, vol. 44, pp. 973-983, May 1998.
92. A. Lapidoth and J. Ziv, "On the universality of the LZ-based decoding algorithm," IEEE Trans. Inform. Theory, vol. 44, pp. 1746-1755, Sept. 1998.
93. "Universal sequential decoding," presented at the 1998 Infor-mation Theory Workshop, Kerry, Killarney Co., Ireland.
94. H. Liao, "Multiple access channels," Ph.D. dissertation, Dept. Elec. Eng., Univ. Hawaii, 1972.
95. Y.-S. Liu and B. L. Hughes, "A new universal random coding bound for the multiple-access channel," IEEE Trans. Inform. Theory, vol. 42, pp. 376-386, Mar. 1996.
96. L. Lovâsz, "On the Shannon capacity of a graph," IEEE Trans. Inform. Theory, vol. IT-25, pp. 1-7, Jan. 1979.
97. R. J. McEliece, "CISM courses and lectures," in Communication in the Presence of Jamming-An Information Theory Approach, no. 279. New York: Springer, 1983.
98. N. Merhav, "Universal decoding for memoryless Gaussian channels with deterministic interference," IEEE Trans. Inform. Theory, vol. 39, pp. 1261-1269, July 1993.
99. "How many information bits does a decoder need about the channel statistics," IEEE Trans. Inform. Theory, vol. 43, pp. 1707-1714, Sept. 1997.
100. N. Merhav, G. Kaplan, A. Lapidoth, and S. Shamai (Shitz), "On in-formation rates for mismatched decoders," IEEE Trans. Inform. Theory, vol. 40, pp. 1953-1967, Nov. 1994.
101. M. Mushkin and I. Bar-David, "Capacity and coding for the Gilbert-Elliott channel," IEEE Trans. Inform. Theory, vol. 35, pp. 1277-1290, Nov. 1989.
102. L. H. Ozarow, S. Shamai, and A. D. Wyner, "Information theoretic considerations for cellular mobile radio," IEEE Trans. Veh. TechnoL, vol. 43, pp. 359-378, May 1994.
103. J. Pokorny and H. M. Wallmeier, "Random coding bound and codes produced by permutations for the multiple access channel," IEEE Trans. Inform. Theory, 1985.
104. T. S. Rappaport, Wireless Communications, Principles and Practice. Englewood Cliffs, NJ: Prentice-Hall, 1996.
105. B. Rimoldi and R. Urbanke, "A rate-splitting approach to the Gaussian multiple-access channel," IEEE Trans. Inform. Theory, vol. 42, pp. 364-375, Mar. 1996.
106. W. L. Root, "Estimates of e capacity for certain linear communication channels," IEEE Trans. Inform. Theory, vol. IT-14, pp. 361-369, May 1968.
107. W. L. Root and P. P. Varaiya, "Capacity of classes of Gaussian channels," SIAM J. Appl. Math., vol. 16, no. 6, pp. 1350-1393, Nov. 1968.
108. J. Salz and E. Zehavi, "Decoding under integer metrics constraints," IEEE Trans. Commun., vol. 43, nos. 2/3/4, pp. 307-317, Feb./Mar./Apr. 1995.
109. S. Shamai, "A broadcast transmission strategy of the Gaussian slowly fading channel," in Proc. Int. Symp. Information Theory ISIT'97 (Ulm, Germany, 1997), p. 150
110. S. Shamai (Shitz) and A. D. Wyner, "Information-theoretic consider-ations for systematic, cellular, multiple-access fading channels, Parts I and II," IEEE Trans. Inform. Theory, vol. 43, pp. 1877-1894, Nov. 1997.
111. C. E. Shannon, "A mathematical theory of communication," Bell Syst. Tech. J., vol. 27,pp. 379-423, 623-656, 1948.
112. "The zero error capacity of a noisy channel," IRE Trans. Inform. Theory, vol. IT-2, pp. 8-19, 1956.
113. "Certain results in coding theory for noisy channels," Inform. Contr., vol. 1, pp. 6-25, 1957.
114. "Channels with side information at the transmitter," IBM J. Res. Develop., vol. 2, no. 4, pp. 289-293, 1958.
115. C. E. Shannon, R. G. Gallager, and E. R. Berlekamp, "Lower bounds to error probability for coding on discrete memoryless channels," Infom. Contr., vol. 10, pp. 65-103, pt. I,
116. Infom. Contr.,ibid pp. 522-552, pt. II, 1967.
117. C. E. Shannon, "Probability of error for optimal codes in a Gaussian channel," Bell Syst. Tech. J., vol. 38, pp. 611-656, May 1959.
118. M. K. Simon, J. K. Omura, R. A. Scholtz, and B. K. Levitt, Spread Spectrum Communications Handbook. New York: McGraw-Hill, 1994, revised edition.
119. S.Z. Stambler, "Shannon theorems for a full class of channels with state known at the output," Probl. Pered. Inform., vol. 14, no. 4, pp. 3-12, 1975, English translation.
120. I. G. Stiglitz, "Coding for a class of unknown channels," IEEE Trans. Inform. Theory, vol. IT-12, pp. 189-195, Apr. 1966.
121. I. E. Telatar, "Zeroor list capacities of discrete memoryless chan-nels," IEEE Trans. Inform. Theory, vol. 43, pp. 1977-1982, Nov. 1997.
122. S. Verdü, "On channel capacity per unit cost," IEEE Trans. Inform. Theory, vol. 36, pp. 1019-1030, Sept. 1990.
123. S. Verdü and T. S. Han, "A general formula for channel capacity," IEEE Trans. Inform. Theory, vol. 40, pp. 1147-1157, July 1994.
124. H. S. Wang and N. Moayeri, "Finite-state Markov channel-A useful model for radio communication channels," IEEE Trans. Veh. Technol., vol. 44, pp. 163-171, Feb. 1995.
125. J. Wolfowitz, "The coding of messages subject to chance errors," Illinois J. Math., vol. 1, pp. 591-606, Dec. 1957.
126. "Simultaneous channels," Arch. Rat. Mech. Anal, vol. 4, pp. 371-386, 1960
127. Coding Theorems of Information Theory, 3rd ed. Berlin, Ger-many: Springer-Verlag, 1978.
128. A. D. Wyner, "Shannon-theoretic approach to a Gaussian cellular multiple-access channel," IEEE Trans. Inform. Theory, vol. 40, pp. 1713-1727, Nov. 1994.
129. A. D. Wyner, J. Ziv, and A. J. Wyner, "On the role of pattern matching in information theory," this issue, pp. 2045-2056.
130. J. Ziv, "Universal decoding for finite-state channels," IEEE Trans. Inform. Theory, vol. IT-31,pp. 453-460, July 1985.
131. J. Ziv and A. Lempel, "Compression of individual sequences via variable-rate coding," IEEE Trans. Inform. Theory, vol. IT-24, pp. 530-536, Sept. 1978.