article

Lossless Condensers, Unbalanced Expanders, And Extractors

Authors:

Amnon Ta-Shma,

Christopher Umans†,

David Zuckerman‡Authors Info & Claims

Combinatorica, Volume 27, Issue 2

Pages 213 - 240

https://doi.org/10.1007/s00493-007-0053-2

Published: 01 March 2007 Publication History

Abstract

Trevisan showed that many pseudorandom generator constructions give rise to constructions of explicit extractors. We show how to use such constructions to obtain explicit lossless condensers. A lossless condenser is a probabilistic map using only O(logn) additional random bits that maps n bits strings to poly(logK) bit strings, such that any source with support size K is mapped almost injectively to the smaller domain. Our construction remains the best lossless condenser to date.

By composing our condenser with previous extractors, we obtain new, improved extractors. For small enough min-entropies our extractors can output all of the randomness with only O(logn) bits. We also obtain a new disperser that works for every entropy loss, uses an O(logn) bit seed, and has only O(logn) entropy loss. This is the best disperser construction to date, and yields other applications. Finally, our lossless condenser can be viewed as an unbalanced bipartite graph with strong expansion properties.

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Hsieh JMcKenzie TMohanty SParedes PMohar BShinkar IO'Donnell R(2024)Explicit Two-Sided Unique-Neighbor ExpandersProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649705(788-799)Online publication date: 10-Jun-2024
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Chionas GChlebus BKowalski DKrysta PElkind E(2023)Adversarial contention resolution gamesProceedings of the Thirty-Second International Joint Conference on Artificial Intelligence10.24963/ijcai.2023/289(2598-2606)Online publication date: 19-Aug-2023
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Bauwens* BZimand M(2023)Universal almost Optimal Compression and Slepian-wolf Coding in Probabilistic Polynomial TimeJournal of the ACM10.1145/357580770:2(1-33)Online publication date: 21-Mar-2023
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Index Terms

Lossless Condensers, Unbalanced Expanders, And Extractors
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
      1. Generating functions
    2. Graph theory
      1. Graph algorithms
  2. Mathematical analysis
    1. Numerical analysis
      1. Computations in finite fields
2. Theory of computation
  1. Models of computation
    1. Probabilistic computation

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Published In

Combinatorica Volume 27, Issue 2

March 2007

112 pages

ISSN:0209-9683

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Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 March 2007

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Hsieh JMcKenzie TMohanty SParedes PMohar BShinkar IO'Donnell R(2024)Explicit Two-Sided Unique-Neighbor ExpandersProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649705(788-799)Online publication date: 10-Jun-2024
https://dl.acm.org/doi/10.1145/3618260.3649705
Chionas GChlebus BKowalski DKrysta PElkind E(2023)Adversarial contention resolution gamesProceedings of the Thirty-Second International Joint Conference on Artificial Intelligence10.24963/ijcai.2023/289(2598-2606)Online publication date: 19-Aug-2023
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