Data processing inequality

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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]


Let be a Markov chain; then,
if and only if
where is the mutual information.

See also[edit]


  1. ^ Beaudry, Normand (2012), "An intuitive proof of the data processing inequality", Quantum Information & Computation, 12 (5–6): 432–441, arXiv:1107.0740, Bibcode:2011arXiv1107.0740B
  2. ^ Kinney; Atwal (Mar 2014). "Equitability, mutual information, and the maximal information coefficient". Proc Natl Acad Sci U S A. 111 (9): 3354–9. arXiv:1301.7745. Bibcode:2014PNAS..111.3354K. doi:10.1073/pnas.1309933111. PMC 3948249. PMID 24550517.

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