Abstract
We provide two new results for identification for sources. The first result is about block codes. In [Ahlswede and Cai, IEEE-IT, 52(9), 4198-4207, 2006] it is proven that the q-ary identification entropy HI,q(P) is a lower bound for the average number L(P,P) of expected checkings during the identification process. A necessary assumption for this proof is that the uniform distribution minimizes the symmetric running time \(L_{\mathcal C}(P,P)\) for binary block codes \(\mathcal C=\{0,1\}^k\). This assumption is proved in Sect. 2 not only for binary block codes but for any q-ary block code. The second result is about upper bounds for the worst-case running time. In [Ahlswede, Balkenhol and Kleinewchter, LNCS, 4123, 51-61, 2006] the authors proved in Theorem 3 that L(P) < 3 by an inductive code construction. We discover an alteration of their scheme which strengthens this upper bound significantly.
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References
Ahlswede, R.: Identification Entropy. In: Ahlswede, R., Bäumer, L., Cai, N., Aydinian, H., Blinovsky, V., Deppe, C., Mashurian, H. (eds.) Information Transfer and Combinatorics. LNCS, vol. 4123, pp. 595–613. Springer, Heidelberg (2006)
Ahlswede, R., Balkenhol, B., Kleinewächter, C.: Identification for Sources. In: Ahlswede, R., Bäumer, L., Cai, N., Aydinian, H., Blinovsky, V., Deppe, C., Mashurian, H. (eds.) Information Transfer and Combinatorics. LNCS, vol. 4123, pp. 51–61. Springer, Heidelberg (2006)
Ahlswede, R., Cai, N.: An interpretation of identification entropy. IEEE Trans. Inf. Theory 52(9), 4198–4207 (2006)
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Heup, C. (2013). Two New Results for Identification for Sources. In: Aydinian, H., Cicalese, F., Deppe, C. (eds) Information Theory, Combinatorics, and Search Theory. Lecture Notes in Computer Science, vol 7777. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36899-8_1
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DOI: https://doi.org/10.1007/978-3-642-36899-8_1
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