### Abstract

The entropy power inequality (EPI) provides lower bounds on the differential entropy of the sum of two independent real-valued random variables in terms of the individual entropies. Versions of the EPI for discrete random variables have been obtained for special families of distributions with the differential entropy replaced by the discrete entropy, but no universal inequality is known (beyond trivial ones). More recently, the sumset theory for the entropy function yields a sharp inequality H(X + X') - H(X) ≥ 1/2 - o(l) when Χ,Χ' are i.i.d. with high entropy. This paper provides the inequality H(X + X') - H(X) ≥ g(H(X)), where X, X' are arbitrary i.i.d. integer-valued random variables and where g is a universal strictly positive function on R_{+} satisfying g(0) = 0. Extensions to non identically distributed random variables and to conditional entropies are also obtained.

Original language | English (US) |
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Title of host publication | 2013 IEEE International Symposium on Information Theory, ISIT 2013 |

Pages | 589-593 |

Number of pages | 5 |

DOIs | |

State | Published - Dec 19 2013 |

Event | 2013 IEEE International Symposium on Information Theory, ISIT 2013 - Istanbul, Turkey Duration: Jul 7 2013 → Jul 12 2013 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
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ISSN (Print) | 2157-8095 |

### Other

Other | 2013 IEEE International Symposium on Information Theory, ISIT 2013 |
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Country | Turkey |

City | Istanbul |

Period | 7/7/13 → 7/12/13 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Information Systems
- Modeling and Simulation
- Applied Mathematics

### Keywords

- Entropic inequalities
- Entropy power inequality
- Mrs. Gerber's lemma
- Shannon sumset theory

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## Cite this

*2013 IEEE International Symposium on Information Theory, ISIT 2013*(pp. 589-593). [6620294] (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2013.6620294