Paper Abstract and Keywords |
Presentation |
2018-03-09 13:30
On the Generalization of Fano's Inequality for Countably Infinite Alphabets, List-Decoding, and General Conditional Information Measures Yuta Sakai (Univ. Fukui) IT2017-133 ISEC2017-121 WBS2017-114 |
Abstract |
(in Japanese) |
(See Japanese page) |
(in English) |
Analogues of Fano's inequality are investigated under the following settings:
Firstly, the alphabet $mathcal{X}$ of a discrete random variable $X$ is allowed to be countably infinite.
Secondly, instead of a fixed finite cardinality $|mathcal{X}|$, a fixed $X$-marginal distribution is given.
Thirdly, information measures are generalized from the conditional Shannon entropy $H(X mid Y)$ to a general type of conditional information measures without explicit form, which contains Arimoto's and Hayashi's conditional R'{e}nyi entropies.
And fourthly, the average probability of error is defined on list-decoding settings.
The main results of this study are tight upper bounds on the generalized conditional information measures for given (i) an $X$-marginal distribution; (ii) a size of list-decoding; and (iii) a tolerated probability of error.
Our Fano-type inequalities are formalized by specific discrete probability distributions.
Sufficient conditions of the sharpness of our Fano-type inequalities are then also clarified on the cardinality of the alphabet $mathcal{Y}$ of a side information $Y$ of $X$. |
Keyword |
(in Japanese) |
(See Japanese page) |
(in English) |
Fano's inequality / list-decoding / R'{e}nyi's information measures / majorization theory / Schur-concavity / / / |
Reference Info. |
IEICE Tech. Rep., vol. 117, no. 487, IT2017-133, pp. 179-184, March 2018. |
Paper # |
IT2017-133 |
Date of Issue |
2018-03-01 (IT, ISEC, WBS) |
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) |
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IT2017-133 ISEC2017-121 WBS2017-114 |
Conference Information |
Committee |
WBS IT ISEC |
Conference Date |
2018-03-08 - 2018-03-09 |
Place (in Japanese) |
(See Japanese page) |
Place (in English) |
Katsusika Campas, Tokyo University of Science |
Topics (in Japanese) |
(See Japanese page) |
Topics (in English) |
joint meeting of IT, ISEC, and WBS |
Paper Information |
Registration To |
IT |
Conference Code |
2018-03-WBS-IT-ISEC |
Language |
English |
Title (in Japanese) |
(See Japanese page) |
Sub Title (in Japanese) |
(See Japanese page) |
Title (in English) |
On the Generalization of Fano's Inequality for Countably Infinite Alphabets, List-Decoding, and General Conditional Information Measures |
Sub Title (in English) |
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Keyword(1) |
Fano's inequality |
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list-decoding |
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R'{e}nyi's information measures |
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majorization theory |
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Schur-concavity |
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1st Author's Name |
Yuta Sakai |
1st Author's Affiliation |
University of Fukui (Univ. Fukui) |
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Speaker |
Author-1 |
Date Time |
2018-03-09 13:30:00 |
Presentation Time |
25 minutes |
Registration for |
IT |
Paper # |
IT2017-133, ISEC2017-121, WBS2017-114 |
Volume (vol) |
vol.117 |
Number (no) |
no.487(IT), no.488(ISEC), no.489(WBS) |
Page |
pp.179-184 |
#Pages |
6 |
Date of Issue |
2018-03-01 (IT, ISEC, WBS) |
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