Information, quantization of

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The partitioning of a set of possible communications generated by an information source (cf. Information, source of) into a finite (or sometimes countable) number of disjoint subsets $A_i$ in such a way that the information in each class can be represented with a given precision of reproduction of the information (cf. Information, exactness of reproducibility of) by some specially selected element $a_i\in A_i$. To a given quantization of information corresponds a way of coding the information source, defined by a coding function $\phi(x)=a_i$ when $x\in A_i$. Such a quantization enables one to replace the sending of a continuous signal by that of a discrete signal without violating certain conditions on the precision of reproduction of information.


[1] A.A. Kharkevich, "Channels with noise" , Moscow (1965) (In Russian)
[2] C.E. Shannon, "A mathematical theory of communication" Bell Systems Techn. J. , 27 (1948) pp. 379–423; 623–656
[3] R. Gallagher, "Information theory and reliable communication" , Wiley (1968)
[4] T. Berger, "Rate distortion theory" , Prentice-Hall (1971)



[a1] I. Csiszar, J. Körner, "Information theory. Coding theorems for discrete memoryless systems" , Akad. Kiado (1981)
How to Cite This Entry:
Information, quantization of. Encyclopedia of Mathematics. URL:,_quantization_of&oldid=33316
This article was adapted from an original article by R.L. DobrushinV.V. Prelov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article