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Random Correlated Codes for the AVC and the Compound Channels

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Probabilistic Methods and Distributed Information

Part of the book series: Foundations in Signal Processing, Communications and Networking ((SIGNAL,volume 15))

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Abstract

Let \(\bigl \{W(\cdot |\cdot ,s):s\in \mathcal{S}\bigr \}\) be a family of stochastic matrices with common input and output alphabets. A compound channel (CC) (introduced by it) is defined as a family of channels \(W^n(\cdot |\cdot ,s)\), where for all \(x^n\in \mathcal {X}^n\), \(y^n\in \mathcal {Y}^n\), \(s\in \mathcal{S}\) \(W^n(y^n|x^n,s)=\prod \limits _{t=1}^nW(y_t|x_t,s)\).

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Notes

  1. 1.

    The contribution of \(\mathcal {D}^*\) can be found in [4].

References

  1. K. Fan, Minimax theorems. Proc. Natl. Acad. Sci. 39, 42–47 (1958)

    Article  MathSciNet  Google Scholar 

  2. D. Blackwell, L. Breiman, A.J. Thomasian, The capacity of a class of channels. Ann. Math. Stat. 30, 1229–1241 (1959)

    Article  MathSciNet  Google Scholar 

  3. R. Ahlswede, Certain results in coding theory for compound channels I, in Proceedings of the Colloquium on Information Theory, Debrecen, Hungary (1967), pp. 35–60

    Google Scholar 

  4. R. Ahlswede, J. Wolfowitz, The structure of capacity functions for compound channels, in Proceedings of the International Symposium on Probability and Information Theory (McMaster University, Canada, 1968), pp. 12–54

    Google Scholar 

  5. R. Ahlswede, The weak capacity of averaged channels. Z. Wahrscheinlichkeitstheorie Verw. Gebiete 11, 61–73 (1968)

    Google Scholar 

  6. T.S. Han, S. Verdu, Approximation theory of output statistics. IEEE Trans. Inf. Theory IT–39, 752–772 (1993)

    Article  MathSciNet  Google Scholar 

  7. S. Verdu, T.S. Han, A general formula for channel capacity. IEEE Trans. Inf. Theory IT–40, 1147–1157 (1994)

    Article  Google Scholar 

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Authors and Affiliations

  1. Bielefeld, Germany

    Rudolf Ahlswede

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  1. Rudolf Ahlswede
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Correspondence to Rudolf Ahlswede .

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Editors and Affiliations

  1. Bielefeld, Germany

    Alexander Ahlswede

  2. Faculty of Mathematics and Computer Sciences, Friedrich-Schiller-University Jena, Jena, Germany

    Ingo Althöfer

  3. Institute for Communications Engineering, Technical University of Munich, München, Bayern, Germany

    Christian Deppe

  4. Applied Mathematics and Statistics, Quantitative Methods, Bielefeld University of Applied Sciences, Bielefeld, Germany

    Ulrich Tamm

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Ahlswede, R. (2019). Random Correlated Codes for the AVC and the Compound Channels. In: Ahlswede, A., Althöfer, I., Deppe, C., Tamm, U. (eds) Probabilistic Methods and Distributed Information. Foundations in Signal Processing, Communications and Networking, vol 15. Springer, Cham. https://doi.org/10.1007/978-3-030-00312-8_2

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  • DOI: https://doi.org/10.1007/978-3-030-00312-8_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-00310-4

  • Online ISBN: 978-3-030-00312-8

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