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Deterministic randomness extraction from generalized and distributed santha-vazirani sources

Beigi, S ; Sharif University of Technology | 2015

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  1. Type of Document: Article
  2. DOI: 10.1007/978-3-662-47672-7_12
  3. Publisher: Springer Verlag , 2015
  4. Abstract:
  5. A Santha-Vazirani (SV) source is a sequence of random bits where the conditional distribution of each bit, given the previous bits, can be partially controlled by an adversary. Santha and Vazirani show that deterministic randomness extraction from these sources is impossible. In this paper, we study the generalization of SV sources for nonbinary sequences. We show that unlike the binary case, deterministic randomness extraction in the generalized case is sometimes possible. We present a necessary condition and a sufficient condition for the possibility of deterministic randomness extraction. These two conditions coincide in “non-degenerate” cases. Next, we turn to a distributed setting. In this setting the SV source consists of a random sequence of pairs (a1, b1), (a2, b2),… distributed between two parties, where the first party receives ai’s and the second one receives bi’s. The goal of the two parties is to extract common randomness without communication. Using the notion of maximal correlation, we prove a necessary condition and a sufficient condition for the possibility of common randomness extraction from these sources. Based on these two conditions, the problem of common randomness extraction essentially reduces to the problem of randomness extraction from (non-distributed) SV sources. This result generalizes results of Gács and Körner, and Witsenhausen about common randomness extraction from i. i. d. sources to adversarial sources
  6. Keywords:
  7. Automata theory ; Computational linguistics ; Extraction ; Common randomness ; Conditional distribution ; Maximal correlation ; Nonbinary sequences ; Random bits ; Random sequence ; Randomness extractions ; Random processes
  8. Source: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 6 July 2015 through 10 July 2015 ; Volume 9134 , 2015 , Pages 143-154 ; 03029743 (ISSN) ; 9783662476710 (ISBN)
  9. URL: http://link.springer.com/chapter/10.1007/978-3-662-47672-7_12