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Data Compression

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Storing and Transmitting Data

Abstract

The source model discussed throughout this chapter is the Discrete Source (DS). Such a source is a pair \((\mathcal{X},P)\), where \(\mathcal{X}\triangleq \{1,\dots ,a\}\), say, is a finite alphabet and \(P\triangleq (P(1),\dots ,P(a))\) is a probability distribution on \(\mathcal{X}\). A discrete source can also be described by a random variable \(X:\mathcal{X}\rightarrow \mathcal{X}\), where \(\text {Prob}(X=x)=P(x)\) for all \(x\in \mathcal{X}\).

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Notes

  1. 1.

    As for entropy-typical sequences we use analogous abbreviations for typical sequences in terms of \(n\), \(P\), and \(\delta \).

References

  1. R. Ahlswede, B. Verboven, On identification via multi-way channels with feedback. IEEE Trans. Inf. Theory 37(5), 1519–1526 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  2. R.B. Ash, Information Theory (Interscience Publishers, New York, 1965)

    Google Scholar 

  3. R.E. Blahut, Theory and Practice of Error Control Codes (Addison-Wesley Publishing Company, Advanced Book Program, Reading, MA, 1983)

    MATH  Google Scholar 

  4. I. Csiszár, J. Körner, Coding Theorems for Discrete Memoryless Systems, Probability and Mathematical Statistics (Academic Press, New York, 1981)

    Google Scholar 

  5. R.M. Fano, The Transmission of Information, Technical Report No. 65, Research Laboratory of Electronics, M.I.T. (Cambridge, Mass, 1949)

    Google Scholar 

  6. J.C. Harsanyi, Game and decision theoretic models in ethics. in Handbook of Game Theory with Economic Applications, vol. 1, 1st edn, ed. by R.J. Aumann, S. Hart (1992), pp. 669–707

    Google Scholar 

  7. D.A. Huffman, A method for the construction of minimum-redundancy codes. Proc. Inst. Radio Eng. 40(9), 1098–1101 (1952)

    Google Scholar 

  8. L.G. Kraft, A device for quantizing, grouping, and coding amplitude modulated pulses. MS Thesis Electrical Engineering Department (Institute of Technology, Cambridge, 1949)

    Google Scholar 

  9. B. McMillan, Two inequalities implied by unique decipherability. IEEE Trans. Inf. Theor. 2(4), 115–116 (1956)

    Article  MathSciNet  Google Scholar 

  10. F.M. Reza, An Introduction to Information Theory (McGraw-Hill, New York, 1961)

    Google Scholar 

  11. C.E. Shannon, A mathematical theory of communication. Bell Sys. Tech. Jour. 27, 398–403 (1948)

    MathSciNet  Google Scholar 

  12. D. Welsh, Codes and Cryptography (Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1988)

    Google Scholar 

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Correspondence to Rudolf Ahlswede .

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Ahlswede, R., Ahlswede, A., Althöfer, I., Deppe, C., Tamm, U. (2014). Data Compression. In: Ahlswede, A., Althöfer, I., Deppe, C., Tamm, U. (eds) Storing and Transmitting Data. Foundations in Signal Processing, Communications and Networking, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-319-05479-7_2

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  • DOI: https://doi.org/10.1007/978-3-319-05479-7_2

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