Channel Capacity for a Given Decoding Metric

IEEE Transactions on Information Theory

Volumn 41, Issue 1, 1995, Pages 35-43

  Csiszár, Imre ^a   Narayan, Prakash ^b  

^a ALFRÉD RÉNYI INSTITUTE OF MATHEMATICS   (Hungary)

^b UNIVERSITY OF MARYLAND   (United States)

Author keywords

arbitrarily varying channel; d capacity; d decoder; erasures only capacity; mismatch; Shannon capacity; Sperner capacity

Indexed keywords

BLOCK CODES; CODES (SYMBOLS); CODING ERRORS; COMMUNICATION CHANNELS (INFORMATION THEORY); DECODING; FUNCTIONS; GRAPH THEORY; PERFORMANCE;

ARBITRARY VARYING CHANNEL; DECODER; ERASURES ONLY CAPACITY; MISMATCH; SHANNON CAPACITY; SPERNER CAPACITY;

CHANNEL CAPACITY;

EID: 0029219819     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/18.370120     Document Type: Article

References (34)

1. R. Ahlswede, “Elimination of correlation in random codes for arbitrarily varying channels,” Z. Wahrscheinlichkeitstheorie Verw. Gebiete, vol. 44, pp. 159–175, 1978.
2. —, “A method of coding and an application to arbitrarily varying channels,” J. Combin., Inform. Syst. Sci., vol. 5, pp. 10–35, 1980.
3. R. Ahlswede, N. Cai, and Z. Zhang, “Erasure, list and detection zero-error capacities for low noise and a relation to identification,” in Proc. IEEE Int. Symp. on Information Theory (Trondheim, Norway, June–July 1994), p. 380; also, Preprint 93–068, Sonderforschungsbereich 343, Discrete Strukturen in der Mathematik, Universität Bielefeld, 1993.
4. V. B. Balakirsky, “Coding theorems for discrete memoryless channels with given decision rule,” in Lecture Notes in Comp. Sci., Proc. 1st French-Soviet Workshop on Algebraic Coding, July 1991, pp. 142–150.
5. V. B. Balakirsky, “A converse coding theorem for mismatched decoding at the output of binary-input memoryless channels,” preprint, 1994.
6. D. Blackwell, L. Breiman, and A. J. Thomasian, “The capacities of certain channel classes under random coding,” Ann. Math. Statist., vol. 31, pp. 558–567, 1960.
7. T. M. Cover and J. A. Thomas, Elements of Information Theory, New York: Wiley, 1991.
8. I. Csiszár and J. Körner, “Many coding theorems follow from an elementary combinatorial lemma,” in Proc. 3rd Czechoslovak-Soviet-Hungarian Sem on Information Theory (Liblice, Czechoslovakia, 1980, pp. 25–44.
9. —, Information Theory: Coding Theorems for Discrete Memoryless Systems. New York: Academic Press, 1981.
10. —, “Graph decomposition: A new key to coding theorems,” IEEE Trans. Inform. Theory, vol. IT-27, pp. 5–12, 1981.
11. —, “On the capacity of the arbitrarily varying channel for maximum probability of error,” Z. Wahrscheinlichkeitstheorie Verw. Gebiete, vol. 57, pp. 87–101, 1981.
12. I. Csiszár and P. Narayan, “The capacity of the arbitrarily varying channel revisited: Capacity, constraints,” IEEE Trans. Inform. Theory, vol. 34, pp. 181–193, Mar. 1988.
13. —, “Capacity and decoding rules for classes or arbitrarily varying channels,” IEEE Trans. Inform. Theory, vol. 35, pp. 752–769, July 1989.
14. I. Csiszár, “Channel capacity for minimum distance decoding,” in Open Problems, 4th Joint Swedish-Soviet Workshop on Information Theory, (Gotland, Sweden, 1989), pp. 8–11.
15. R. L. Dobrushin and S. Z. Stambler, “Coding theorems for classes of arbitrarily varying discrete memoryless channels,” Probl. Peredach. Inform., vol. 11, no. 2, pp. 3–22, 1975 (English translation).
16. W. Feller, An Introduction to Probability Theory and Its Applications, vol. II. New York: Wiley, 1971.
17. T. R. M. Fischer, “Some remarks on the role of inaccuracy in Shannon's theory of information transmission,” in Trans. 8th Prague Conf. on Information Theory, 1971, pp. 211–226.
18. R. G. Gallager, Information Theory and Reliable Communication. New York: Wiley, 1968.
19. —, “A simple derivation of the coding theorem and some applications,” IEEE Trans. Inform. Theory, vol. IT-11, pp. 3–18, Jan. 1965.
20. L. Gargano, J. Körner, and U. Vaccaro, “Sperner capacities,” Graphs and Combinatorics, vol. 9, pp. 31–46, 1993.
21. V. D. Goppa, “Nonprobabilistic mutual information without memory,” Probl. Contr. Inform. Theory, vol. 4, pp. 97–102, 1975.
22. J. Y. N. Hui, “Fundamental issues of multiple accessing,” Ph.D. dissertation, MIT, 1983.
23. G. Kaplan and S. Shamai (Shitz:), “Information rates and error exponents of compound channels with application to antipodal signaling in a fading environment,” AEU, vol. 47, no. 4, pp. 228–239, 1993.
24. A. Lapidoth, “Information rates for mismatched decoders,” in Proc. 2nd Int. Winter Meeting on Coding and Information Theory (Essen, Germany, Dec. 1993), pp. 12–15.
25. —, “Mismatched decoding for the multiple access channel, in Proc. IEEE Int. Symp. on Information Theory (Trondheim, Norway, June–July 1994), p. 382.
26. L. Lovàsz, “On the Shannon capacity of a graph,” IEEE Trans. Inform. Theory, vol. IT-25, pp. 1–7, 1979.
27. N. Merhav, G. Kaplan, A. Lapidoth, and S. Shamai (Shitz), “On information rates for mismatched decoders,” in Proc. 1993 IEEE Int. Symp. on Information Theory, (San Antonio, TX, Jan. 1993), p. 266, also, preprint, 1993.
28. M. S. Pinsker and A. Sheverdjaev, “Zero error capacity with erasure,” Probl. Peredach. Inform., vol. 6, no. 1, pp. 20–24 (in Russian), 1970.
29. C. E. Shannon, “The zero error capacity of a noisy channel,” IRE Trans. Inform. Theory, vol. IT-2, pp. 8–19, 1956. (Reprinted in Key Papers in the Development of Information Theory, D. Slepian, Ed. New York: IEEE Press, 1974.)
30. M. Simon, J. Omura, R. Sholtz, and B. Levitt, Spread Spectrum Communications, vol. I, New York: Computer Science Press, 1985, ch. 4.
31. I. G. Stiglitz, “Coding for a class of unknown channels,” IEEE Trans. Inform. Theory, vol. IT-12, pp. 189–195, Apr. 1966.
32. I. E. Telatar and R. G. Gallager, “New exponential upper bounds to error and erasure probabilities,” in Proc. IEEE Int. Symp. on Information Theory (Trondheim, Norway, June–July 1994), p. 379; also, preprint, 1993.
33. J. Wolfowitz, Coding Theorems of Information Theory. Berlin-Heidelberg, Germany: Springer Verlag, 1961; 2nd ed., 1964; 3rd ed., 1978.
34. J. Ziv, “Universal decoding for finite-state channels,” IEEE Trans. Inform. Theory, vol. IT-31, no. 4, pp. 453–460, July 1985.