### Abstract

The paper establishes the equality condition in the I-MMSE proof of the entropy power inequality (EPI). This is done by establishing an exact expression for the deficit between the two sides of the EPI. Interestingly, a necessary condition for the equality is established by making a connection to the famous Cauchy functional equation.

Original language | English (US) |
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Title of host publication | 55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 1034-1039 |

Number of pages | 6 |

ISBN (Electronic) | 9781538632666 |

DOIs | |

State | Published - Jan 17 2018 |

Event | 55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017 - Monticello, United States Duration: Oct 3 2017 → Oct 6 2017 |

### Publication series

Name | 55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017 |
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Volume | 2018-January |

### Other

Other | 55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017 |
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Country | United States |

City | Monticello |

Period | 10/3/17 → 10/6/17 |

### All Science Journal Classification (ASJC) codes

- Computer Networks and Communications
- Hardware and Architecture
- Signal Processing
- Energy Engineering and Power Technology
- Control and Optimization

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## Cite this

Dytso, A., Bustin, R., Poor, H. V., & Shitz, S. S. (2018). On the equality condition for the i-mmse proof of the entropy power inequality. In

*55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017*(pp. 1034-1039). (55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017; Vol. 2018-January). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ALLERTON.2017.8262851