Rate–distortion theory

The rate-distortion theory ( German: Rate - distortion theory ) is a theoretical basis for calculations in information theory. With their help, can mathematically be determined a lower bound of the data transfer rate for a news source in which a reconstruction of the message at the receiver while maintaining a predefined quality criterion, the so-called distortion, can be ensured. It was developed by Claude E. Shannon, who is considered the founder of information theory.

Use

By the rate -distortion theory, it is possible to find the theoretical limits for the maximum compression in the use of Irrelevanzreduzierender coding. In many processes the audio, speech, image and video coding, the theory is therefore applied.

It also enables the evaluation of the effectiveness of different source coding procedures by the respective data rate of the lossy compression method with the lower limit is compared.

Calculation

To calculate the rate-distortion function to each possible representation of a transmitted symbol, k associated with a received symbol j is a numerical value as a measure of distortion. This is the so-called distortion measure D (k; j). A large D (k; j) thus represents a major distortion of the signal. As a distortion of the simple case of the mean square error is often used. The maximum distortion is referred to as D *. The rate-distortion function R (D *) can now be calculated as the minimum of the average mutual information.

The course of the rate-distortion function corresponds to a convex U function that * falls with increasing D. The maximum of R ( D *) is equal to the entropy H ( U) and occurs at D * = 0, ie with no allowable distortion.