Abstract
In [5] Ahlswede and Wolfowitz have obtained the capacities of a.v.ch. with binary output in a number of cases, essentially with the aid of a lemma which relates the capacity of the a.v.ch. to that of a suitable (“underlying”) d.m.c. A generalization of this lemma to a special kind of a.v.ch. with output alphabet b>2, has been given by Ahlswede (Lemma 1 of [1]) and used in [1] and [2] to prove the existence of the weak capacities of various channels under different conditions. We give a detailed proof of a weakened version of Ahlswede's lemma and show, in passing, that his lemma is incorrect. We then define certain special types of a.v.ch and, on the basis of the detailed analysis given by us earlier, we prove lemmas of a similar type for these a.v.ch. We are thus able to extend certain results given for binary output a.v.ch. in [4] and [5] to these special a.v.ch. for which b>2.
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Ahlswede, R.: A note on the existence of the weak capacity for channels with arbitrarily varying channel probability functions. Ann. Math. Statist. 41, No. 3, 1027–1033 (1970)
Ahlswede, R.: Group Codes do not achieve Shannon's channel capacity for the general discrete memoryless channel. Ann. Math. Statist. 42, No. 1, 224–240 (1971)
Ahlswede, R.: The capacity of a channel with arbitrarily varying Gaussian channel probability functions. To appear in the Transactions of the Sixth Prague Conference on Information Theory, Stat. Dec. Functions and Random Processes
Ahlswede, R., Wolfowitz, J.: Correlated decoding for channels with arbitrarily varying channel probability functions. Inform. Control 14, No. 5, 457–473 (1969)
Ahlswede, R., Wolfowitz, J.: The capacity of channels with arbitrarily varying channel probability functions and binary output alphabet. Z. Wahrscheinlichkeitstheorie verw. Gebiete 15, 186–194 (1970)
Berlekamp, E. R., Kleinrock, I.: Analysis of channels with unidirectional drift. JPL Space Programs Summary No. 37–39, Vol. IV, 226–230 (1966)
Blackwell, D., Breiman, L., Thomasian, A. J.: The capacities of certain channel classes under random coding. Ann. Math. Statist. 31, 558–567 (1960)
Gallager, R. G.: Information Theory and Reliable Communication. New York: Wiley 1968
Kiefer, J., Wolfowitz, J.: Channels with arbitrarily verying channel probability functions. Inform. Control 5, 44–54 (1962)
Wolfowitz, J.: Coding Theorems of Information Theory 2nd ed. Berlin-Heidelberg-New York: Springer 1964
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Kambo, N.S., Singh, S. The capacities of certain special channels with arbitrarily varying channel probability functions. Z. Wahrscheinlichkeitstheorie verw Gebiete 29, 331–344 (1974). https://doi.org/10.1007/BF00532717
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DOI: https://doi.org/10.1007/BF00532717