# 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'.[1] As explained by Kinney and Atwal, the DPI means that information is generally lost (never gained) when transmitted through a noisy channel.[2]

## Example

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