Redundancy (information theory)

Data compression is a way to reduce or eliminate unwanted redundancy, while checksums are a way of adding desired redundancy for purposes of error detection when communicating over a noisy channel of limited capacity.

Lossless compression reduces bits by identifying and eliminating statistical redundancy.

Data compression is a way to reduce or eliminate unwanted redundancy, while checksums are a way of adding desired redundancy for purposes of error detection when communicating over a noisy channel of limited capacity.

All error-detection and correction schemes add some redundancy (i.e., some extra data) to a message, which receivers can use to check consistency of the delivered message, and to recover data that has been determined to be corrupted.

In Information theory, redundancy measures the fractional difference between the entropy H(X) of an ensemble X, and its maximum possible value.

The rate of a source of information is related to its redundancy and how well it can be compressed, the subject of source coding.

In Information theory, redundancy measures the fractional difference between the entropy H(X) of an ensemble X, and its maximum possible value. In describing the redundancy of raw data, the rate of a source of information is the average entropy per symbol.

See also Redundancy (information theory).

Data compression is a way to reduce or eliminate unwanted redundancy, while checksums are a way of adding desired redundancy for purposes of error detection when communicating over a noisy channel of limited capacity.

A measure of redundancy between two variables is the mutual information or a normalized variant.

In some cases a symmetric measure may be desired, such as the following redundancy measure:

In Information theory, redundancy measures the fractional difference between the entropy H(X) of an ensemble X, and its maximum possible value.

Data compression is a way to reduce or eliminate unwanted redundancy, while checksums are a way of adding desired redundancy for purposes of error detection when communicating over a noisy channel of limited capacity.

Data compression is a way to reduce or eliminate unwanted redundancy, while checksums are a way of adding desired redundancy for purposes of error detection when communicating over a noisy channel of limited capacity.

In describing the redundancy of raw data, the rate of a source of information is the average entropy per symbol.

For memoryless sources, this is merely the entropy of each symbol, while, in the most general case of a stochastic process, it is

the limit, as n goes to infinity, of the joint entropy of the first n symbols divided by n.

the logarithm of the cardinality of the message space, or alphabet.

the logarithm of the cardinality of the message space, or alphabet.

(This formula is sometimes called the Hartley function.) This is the maximum possible rate of information that can be transmitted with that alphabet.

(The logarithm should be taken to a base appropriate for the unit of measurement in use.) The absolute rate is equal to the actual rate if the source is memoryless and has a uniform distribution.

The quantity \frac D R is called the relative redundancy and gives the maximum possible data compression ratio, when expressed as the percentage by which a file size can be decreased.

A measure of redundancy among many variables is given by the total correlation.

Redundancy of compressed data refers to the difference between the expected compressed data length of n messages L(M^n) \,\!

(Here we assume the data is ergodic and stationary, e.g., a memoryless source.) Although the rate difference can be arbitrarily small as n \,\!

(Here we assume the data is ergodic and stationary, e.g., a memoryless source.) Although the rate difference can be arbitrarily small as n \,\!