Madiman, M and Kontoyiannis, I (2010) *The entropies of the sum and the difference of two IID random variables are not too different.* In: UNSPECIFIED pp. 1369-1372..

## Abstract

Consider the entropy increase h(Y + Y′) - h(Y) of the sum of two continuous i.i.d. random variables Y,Y′, and the corresponding entropy increase h(Y - Y′) - h(Y) of their difference. We show that the ratio between these two quantities always lies between 1/2 and 2. This complements a recent result of Lapidoth and Pete, showing that the difference h(Y + Y′) -h(Y - Y′) may be arbitrarily large. Corresponding results are discussed for the discrete entropy, and connections are drawn with exciting recent mathematical work in the area of additive combinatorics. © 2010 IEEE.

Item Type: | Conference or Workshop Item (UNSPECIFIED) |
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Subjects: | UNSPECIFIED |

Divisions: | Div F > Signal Processing and Communications |

Depositing User: | Cron Job |

Date Deposited: | 08 Jan 2018 20:12 |

Last Modified: | 15 Apr 2021 05:28 |

DOI: | 10.1109/ISIT.2010.5513562 |