Data processing inequality

The Data processing inequality is an information theoretic concept which states that the information content of a signal cannot be increased via a local physical operation. This can be expressed concisely as 'post-processing cannot increase information'. As explained by Kinney and Atwal, the DPI means that information is generally lost (never gained) when transmitted through a noisy channel.

Example

Let $X\rightarrow Y\rightarrow Z$ be a Markov chain.
Then,
$I(x;y)\geqslant I(x;z)$ with
$I(x;y)=I(x;z)$ if and only if $X\rightarrow Z\rightarrow Y$
where $I(x;y)$ is the mutual information.

See also

• Garbage in, garbage out

External links

• http://www.scholarpedia.org/article/Mutual_information