Paper Abstract and Keywords |
Presentation |
2015-01-30 13:00
The second order asymptotic rates in intrinsic randomness problem in terms of smooth Renyi entropy Eiichi Namekawa, Tomohiko Uyematsu (Tokyo Tech) IT2014-54 |
Abstract |
(in Japanese) |
(See Japanese page) |
(in English) |
The intrinsic randomness problem is to approximately generate uniform random numbers from output sequences of a general source by using a mapping. In this problem, the rate of mapping for generating random numbers is defined by the ratio of the logarithm of the size of generated random numbers to the length of output sequence of the source, and the approximation error is defined by the variational distance between the probability distribution of random numbers obtained by the mapping and the uniform distributuion. In memoryless sources, whenever the rate of mapping is smaller than the entropy of the source, there exists a sequence of mappings such that the approximation error vanishes as the length of sequences becomes longer. On the other hands, when the rate is greater than the entropy, the approximation error converges to one as the length of sequences becomes longer. However the value of the approximation error is unknown when the rate is equal to the entropy. Hence, we need to investigate the second order asymptotic rate of the intrinsic randomness to know the infimum value of the approximation error. In this paper, we clarify the second order asymptotic rate for a given approximation error in terms of the smooth R'{e}nyi entropy instead of the information spectrum. |
Keyword |
(in Japanese) |
(See Japanese page) |
(in English) |
Intrinsic randomness / $delta$-intrinsic randomness / smooth R'{e}nyi entropy / second order asymptotic rate / / / / |
Reference Info. |
IEICE Tech. Rep., vol. 114, no. 438, IT2014-54, pp. 1-6, Jan. 2015. |
Paper # |
IT2014-54 |
Date of Issue |
2015-01-23 (IT) |
ISSN |
Print edition: ISSN 0913-5685 Online edition: ISSN 2432-6380 |
Copyright and reproduction |
All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034) |
Download PDF |
IT2014-54 |
Conference Information |
Committee |
IT |
Conference Date |
2015-01-30 - 2015-01-30 |
Place (in Japanese) |
(See Japanese page) |
Place (in English) |
|
Topics (in Japanese) |
(See Japanese page) |
Topics (in English) |
general |
Paper Information |
Registration To |
IT |
Conference Code |
2015-01-IT |
Language |
Japanese |
Title (in Japanese) |
(See Japanese page) |
Sub Title (in Japanese) |
(See Japanese page) |
Title (in English) |
The second order asymptotic rates in intrinsic randomness problem in terms of smooth Renyi entropy |
Sub Title (in English) |
|
Keyword(1) |
Intrinsic randomness |
Keyword(2) |
$delta$-intrinsic randomness |
Keyword(3) |
smooth R'{e}nyi entropy |
Keyword(4) |
second order asymptotic rate |
Keyword(5) |
|
Keyword(6) |
|
Keyword(7) |
|
Keyword(8) |
|
1st Author's Name |
Eiichi Namekawa |
1st Author's Affiliation |
Tokyo Institute of Technology (Tokyo Tech) |
2nd Author's Name |
Tomohiko Uyematsu |
2nd Author's Affiliation |
Tokyo Institute of Technology (Tokyo Tech) |
3rd Author's Name |
|
3rd Author's Affiliation |
() |
4th Author's Name |
|
4th Author's Affiliation |
() |
5th Author's Name |
|
5th Author's Affiliation |
() |
6th Author's Name |
|
6th Author's Affiliation |
() |
7th Author's Name |
|
7th Author's Affiliation |
() |
8th Author's Name |
|
8th Author's Affiliation |
() |
9th Author's Name |
|
9th Author's Affiliation |
() |
10th Author's Name |
|
10th Author's Affiliation |
() |
11th Author's Name |
|
11th Author's Affiliation |
() |
12th Author's Name |
|
12th Author's Affiliation |
() |
13th Author's Name |
|
13th Author's Affiliation |
() |
14th Author's Name |
|
14th Author's Affiliation |
() |
15th Author's Name |
|
15th Author's Affiliation |
() |
16th Author's Name |
|
16th Author's Affiliation |
() |
17th Author's Name |
|
17th Author's Affiliation |
() |
18th Author's Name |
|
18th Author's Affiliation |
() |
19th Author's Name |
|
19th Author's Affiliation |
() |
20th Author's Name |
|
20th Author's Affiliation |
() |
Speaker |
Author-1 |
Date Time |
2015-01-30 13:00:00 |
Presentation Time |
25 minutes |
Registration for |
IT |
Paper # |
IT2014-54 |
Volume (vol) |
vol.114 |
Number (no) |
no.438 |
Page |
pp.1-6 |
#Pages |
6 |
Date of Issue |
2015-01-23 (IT) |
|