A Generalization of Peres's Algorithm for Generating Random Bits From Loaded Dice
- Authors
- Pae, Sung-il
- Issue Date
- Feb-2015
- Publisher
- IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
- Keywords
- Random number generation; Peres algorithm; extracting function; coin flipping; loaded dice
- Citation
- IEEE TRANSACTIONS ON INFORMATION THEORY, v.61, no.2, pp.751 - 757
- Journal Title
- IEEE TRANSACTIONS ON INFORMATION THEORY
- Volume
- 61
- Number
- 2
- Start Page
- 751
- End Page
- 757
- URI
- https://scholarworks.bwise.kr/hongik/handle/2020.sw.hongik/13676
- DOI
- 10.1109/TIT.2014.2381223
- ISSN
- 0018-9448
- Abstract
- Peres's algorithm produces unbiased random bits from biased coin tosses, recursively, using the famous von Neumann's method as its base. The algorithm is simple and elegant, but, at first glance, appears to work almost like magic and its generalization is elusive. We generalize the method to generate unbiased random bits from loaded dice, i.e., many-valued Bernoulli source. The generalization is asymptotically optimal in its output rate as is the original Peres's algorithm. Three-valued case is discussed in detail, and then other many-faced cases are considered.
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