Erasure, list, and detection zero-error capacities for low noise and a relation to identification

Ahlswede R, Cai N, Zhang Z (1996)
IEEE TRANSACTIONS ON INFORMATION THEORY 42(1): 55-62.

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Abstract
For the discrete memoryless channel (X, Y, W) we give characterizations of the zero-error erasure capacity C-er and the zero-error average list size capacity C-al in terms of limits of suitable information (respectively, divergence) quantities (Theorem 1). However, they do not ''single-letterize.'' Next we assume that X subset of Y and W(x/x) > 0 for all x is an element of X, and we associate with W the low-noise channel W-epsilon, where for Y+ (x) = {y : W(y/x) > 0} [GRAPHICS] Our Theorem 2 says that as epsilon tends to zero the capacities C-er(W-epsilon) and C-al(W-epsilon) relate to the zero-error detection capacity C-de(W). Our third result is a seemingly basic contribution to the theory of identification via channels. We introduce the (second-order) identification capacity C-oid for identification codes with zero misrejection probability and misacceptance probability tending to zero. Our Theorem 3 says that C-oid equals the zero-error erasure capacity for transmission C-er.
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Ahlswede R, Cai N, Zhang Z. Erasure, list, and detection zero-error capacities for low noise and a relation to identification. IEEE TRANSACTIONS ON INFORMATION THEORY. 1996;42(1):55-62.
Ahlswede, R., Cai, N., & Zhang, Z. (1996). Erasure, list, and detection zero-error capacities for low noise and a relation to identification. IEEE TRANSACTIONS ON INFORMATION THEORY, 42(1), 55-62.
Ahlswede, R., Cai, N., and Zhang, Z. (1996). Erasure, list, and detection zero-error capacities for low noise and a relation to identification. IEEE TRANSACTIONS ON INFORMATION THEORY 42, 55-62.
Ahlswede, R., Cai, N., & Zhang, Z., 1996. Erasure, list, and detection zero-error capacities for low noise and a relation to identification. IEEE TRANSACTIONS ON INFORMATION THEORY, 42(1), p 55-62.
R. Ahlswede, N. Cai, and Z. Zhang, “Erasure, list, and detection zero-error capacities for low noise and a relation to identification”, IEEE TRANSACTIONS ON INFORMATION THEORY, vol. 42, 1996, pp. 55-62.
Ahlswede, R., Cai, N., Zhang, Z.: Erasure, list, and detection zero-error capacities for low noise and a relation to identification. IEEE TRANSACTIONS ON INFORMATION THEORY. 42, 55-62 (1996).
Ahlswede, Rudolf, Cai, N, and Zhang, Z. “Erasure, list, and detection zero-error capacities for low noise and a relation to identification”. IEEE TRANSACTIONS ON INFORMATION THEORY 42.1 (1996): 55-62.
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