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 \(x\in \mathcal{X}\).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
As for entropy-typical sequences we use analogous abbreviations for typical sequences in terms of \(n\), \(P\), and \(\delta \).
References
R. Ahlswede, B. Verboven, On identification via multi-way channels with feedback. IEEE Trans. Inf. Theory 37(5), 1519–1526 (1991)
R.B. Ash, Information Theory (Interscience Publishers, New York, 1965)
R.E. Blahut, Theory and Practice of Error Control Codes (Addison-Wesley Publishing Company, Advanced Book Program, Reading, MA, 1983)
I. Csiszár, J. Körner, Coding Theorems for Discrete Memoryless Systems, Probability and Mathematical Statistics (Academic Press, New York, 1981)
R.M. Fano, The Transmission of Information, Technical Report No. 65, Research Laboratory of Electronics, M.I.T. (Cambridge, Mass, 1949)
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
D.A. Huffman, A method for the construction of minimum-redundancy codes. Proc. Inst. Radio Eng. 40(9), 1098–1101 (1952)
L.G. Kraft, A device for quantizing, grouping, and coding amplitude modulated pulses. MS Thesis Electrical Engineering Department (Institute of Technology, Cambridge, 1949)
B. McMillan, Two inequalities implied by unique decipherability. IEEE Trans. Inf. Theor. 2(4), 115–116 (1956)
F.M. Reza, An Introduction to Information Theory (McGraw-Hill, New York, 1961)
C.E. Shannon, A mathematical theory of communication. Bell Sys. Tech. Jour. 27, 398–403 (1948)
D. Welsh, Codes and Cryptography (Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1988)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-319-05479-7_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-05478-0
Online ISBN: 978-3-319-05479-7
eBook Packages: EngineeringEngineering (R0)