Equivocation

Equivocation (from latin aequus equal 'and vocare call') which is information received by the transmission over a channel between an information source ( transmitter ) and an information sink ( receiver ) lost about. The term is to be understood in this context as information content and goes back to the information theory of Claude Shannon , who laid the foundations for this in the 1940s.
In practical implementations, the abstract concept of an “information channel ” can extend over location (e.g. a communication link between two points; → PTP ) or over time (e.g. in the form of a data memory ).

definition

Model of a channel with source H (X) and sink H (Y) and the equivocation H (X | Y)

The mathematical definition of the information content is closely linked to the entropy function , with the random variable describing the set of all possible symbols in the transmission channel. An information source now sends, as shown in the figure on the right, via a channel to the information sink which receives it. can also be different as a result of incorrect information introduced at the canal or as a result of the equivocation occurring at the canal . The notation stands for the conditional entropy with the two random variables . ${\ displaystyle H (A)}$ ${\ displaystyle A}$ ${\ displaystyle H (X)}$ ${\ displaystyle H (Y)}$ ${\ displaystyle Y}$ ${\ displaystyle X}$ ${\ displaystyle H (Y | X)}$ ${\ displaystyle H (X | Y)}$ ${\ displaystyle H (A | B)}$ ${\ displaystyle A, B}$

As a conditional entropy function , the equivocation, with the transinformation between source and sink, can be expressed as: ${\ displaystyle H (X | Y)}$ ${\ displaystyle I (X; Y)}$

{\ displaystyle H (X | Y) = H (X) -I (X; Y)}

As a probability function , the equivocation with the logarithm to base 2 can be expressed as: ${\ displaystyle P (.)}$

{\ displaystyle - \ sum _ {i} \ sum _ {j} P (x_ {i}, y_ {i}) \ log _ {2} P (x_ {i} | y_ {j})}

swell

Jürgen Lindner: Information transfer . Springer Verlag, Berlin Heidelberg 2005, ISBN 3-540-21400-3 , pp. 313 .
Johann Blieberger, Bernd Burgstaller, Gerhard Helge Schildt: Computer science. Basics, 4th edition, Springer Verlag, Wien GmbH, Vienna 2002, ISBN 978-3-211-83710-8 , pp. 30–31.
Hermann Rohling: Introduction to information and coding theory. BG Teubner, Stuttgart 1995, ISBN 978-3-519-06174-8 , pp. 42-50.