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Published in:
2013 | OriginalPaper | Chapter
Two New Results for Identification for Sources
Author : Christian Heup
Published in: Information Theory, Combinatorics, and Search Theory
Publisher: Springer Berlin Heidelberg
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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
H
I
,
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.