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'.
Let three random variables form the Markov chain , implying that the conditional distribution of depends only on and is conditionally independent of . Specifically, we have such a Markov chain if the joint probability mass function can be written as
In this setting, no processing of Y , deterministic or random, can increase the information that Y contains about X. Using the mutual information, this can be written as :
With the equality if and only if , i.e. and contain the same information about , and also forms a Markov chain.
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