# Information, quantization of

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.

#### References

[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) |

#### Comments

#### References

[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: http://encyclopediaofmath.org/index.php?title=Information,_quantization_of&oldid=33316