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On Concepts of Performance Parameters for Channels

  • Chapter
General Theory of Information Transfer and Combinatorics

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4123))

Abstract

Among the mostly investigated parameters for noisy channels are code size, error probability in decoding, block length; rate, capacity, reliability function; delay, complexity of coding. There are several statements about connections between these quantities. They carry names like “coding theorem”, “converse theorem” (weak, strong, ...), “direct theorem”, “capacity theorem”, “lower bound”, “upper bound”, etc. There are analogous notions for source coding.

This note has become necessary after the author noticed that Information Theory suffers from a lack of precision in terminology. Its purpose is to open a discussion about this situation with the goal to gain more clarity.

There is also some confusion concerning the scopes of analytical and combinatorial methods in probabilistic coding theory, particularly in the theory of identification. We present a covering (or approximation) lemma for hypergraphs, which especially makes strong converse proofs in this area transparent and dramatically simplifies them.

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Author information

Authors and Affiliations

  1. Fakultät für Mathematik, Universität Bielefeld, Universitätsstr. 25, 33615, Bielefeld, Germany

    R. Ahlswede

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  1. R. Ahlswede
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Editor information

Editors and Affiliations

  1. Fakultät für Mathematik, Universität Bielefeld, 100131, 33501, Bielefeld, Germany

    Rudolf Ahlswede

  2. Fakultät für Mathematik, Universität Bielefeld, Universitätsstr. 25, 33615, Bielefeld, Germany

    Lars Bäumer , Ning Cai , Harout Aydinian  & Christian Deppe , ,  & 

  3. Russian Academy of Sciences Institute of Problems of Information Transmission, Bol’shoi Karetnyi per. 19, 101447, Moscow, Russia

    Vladimir Blinovsky

  4. Universität Bielefeld, Fakultät für Mathematik, Universitätsstr. 25, 33615, Bielefeld, Germany

    Haik Mashurian

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Ahlswede, R. (2006). On Concepts of Performance Parameters for Channels. In: Ahlswede, R., et al. General Theory of Information Transfer and Combinatorics. Lecture Notes in Computer Science, vol 4123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11889342_40

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  • DOI: https://doi.org/10.1007/11889342_40

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-46244-6

  • Online ISBN: 978-3-540-46245-3

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