Binarization Trees and Random Number Generation
DC Field | Value | Language |
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dc.contributor.author | Pae, Sung-Il | - |
dc.date.available | 2021-03-17T06:54:31Z | - |
dc.date.created | 2021-02-26 | - |
dc.date.issued | 2020-04 | - |
dc.identifier.issn | 0018-9448 | - |
dc.identifier.uri | https://scholarworks.bwise.kr/hongik/handle/2020.sw.hongik/11771 | - |
dc.description.abstract | An $m$ -extracting procedure produces unbiased random bits from a loaded dice with $m$ faces, and its output rate, the average number of output per input is bounded by the Shannon entropy of the source. This information-theoretic upper bound can be achieved only asymptotically as the input size increases, by certain extracting procedures that we call asymptotically optimal. Although a computationally efficient asymptotically optimal 2-extracting procedure has been known for a while, its counterparts for $m$ -ary input, $m>2$ , was found only recently, and they are still relatively complicated to describe. A binarization takes inputs from an $m$ -faced dice and produce bit sequences to be fed into a binary extracting procedure to obtain random bits. Thus, binary extracting procedures give rise to an $m$ -extracting procedure via a binarization. A binarization is to be called complete, if it preserves the asymptotic optimality, and such a procedure has been proposed by Zhou and Bruck. We show that a complete binarization naturally arises from a binary tree with $m$ leaves. Therefore, there exist complete binarizations in abundance and Zhou-Bruck scheme is an instance of them. We now have a relatively simple way to obtain an asymptotically optimal and computationally efficient $m$ -extracting procedure, from a binary one, because these binarizations are both conceptually and computationally simple. The well-known leaf entropy theorem and a closely related structure lemma play important roles in the arguments. | - |
dc.publisher | IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC | - |
dc.title | Binarization Trees and Random Number Generation | - |
dc.type | Article | - |
dc.contributor.affiliatedAuthor | Pae, Sung-Il | - |
dc.identifier.doi | 10.1109/TIT.2019.2962480 | - |
dc.identifier.scopusid | 2-s2.0-85077264702 | - |
dc.identifier.wosid | 000522202300038 | - |
dc.identifier.bibliographicCitation | IEEE TRANSACTIONS ON INFORMATION THEORY, v.66, no.4, pp.2581 - 2587 | - |
dc.relation.isPartOf | IEEE TRANSACTIONS ON INFORMATION THEORY | - |
dc.citation.title | IEEE TRANSACTIONS ON INFORMATION THEORY | - |
dc.citation.volume | 66 | - |
dc.citation.number | 4 | - |
dc.citation.startPage | 2581 | - |
dc.citation.endPage | 2587 | - |
dc.type.rims | ART | - |
dc.type.docType | Article | - |
dc.description.journalClass | 1 | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalResearchArea | Computer Science | - |
dc.relation.journalResearchArea | Engineering | - |
dc.relation.journalWebOfScienceCategory | Computer Science, Information Systems | - |
dc.relation.journalWebOfScienceCategory | Engineering, Electrical & Electronic | - |
dc.subject.keywordAuthor | Random number generation | - |
dc.subject.keywordAuthor | binarization | - |
dc.subject.keywordAuthor | extracting procedures | - |
dc.subject.keywordAuthor | coin flipping | - |
dc.subject.keywordAuthor | loaded dice | - |
dc.subject.keywordAuthor | Peres algorithm | - |
dc.subject.keywordAuthor | leaf entropy theorem | - |
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