Kontoyiannis, I *Efficient sphere-covering and converse measure concentration via generalized coding theorems.* (Unpublished)

## Abstract

Suppose A is a finite set equipped with a probability measure P and let M be a ``mass'' function on A. We give a probabilistic characterization of the most efficient way in which A^n can be almost-covered using spheres of a fixed radius. An almost-covering is a subset C_n of A^n, such that the union of the spheres centered at the points of C_n has probability close to one with respect to the product measure P^n. An efficient covering is one with small mass M^n(C_n); n is typically large. With different choices for M and the geometry on A our results give various corollaries as special cases, including Shannon's data compression theorem, a version of Stein's lemma (in hypothesis testing), and a new converse to some measure concentration inequalities on discrete spaces. Under mild conditions, we generalize our results to abstract spaces and non-product measures.

Item Type: | Article |
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Uncontrolled Keywords: | math.PR math.PR cs.IT math.FA math.IT 60E15, 28A35 (primary), 94A15, 60F10 (secondary) |

Subjects: | UNSPECIFIED |

Divisions: | Div F > Signal Processing and Communications |

Depositing User: | Cron Job |

Date Deposited: | 08 Jan 2018 20:12 |

Last Modified: | 18 Aug 2020 12:42 |

DOI: |