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Paper Abstract and Keywords
Presentation 2021-07-08 16:40
[Invited Talk] RIP matrices breaking the square-root bottleneck and related combinatorics
Shohei Satake (Kumamoto Univ.) IT2021-22
Abstract (in Japanese) (See Japanese page) 
(in English) Compressed sensing theory has various applications to information theory and signal processing.
As one of challenging problems, deterministic constructions of matrices with the restricted isometry property (RIP) have been extensively studied.
In most of known construction of RIP matrices, their certified RIP face the barrier called the square-root bottleneck, and thus it has been desired to beat this barrier.
At present, there are only few known constructions of RIP matrices breaking the square-root bottleneck, and even in these matrices, their RIP exceeds the bottleneck very slightly.
On the other hand, some known works and our recent study found relationships between constructions of RIP matrices breaking the square-root bottleneck and several topics in combinatorics such as Ramsey theory and pseudo-randomness.

In this article, we briefly review these backgrounds and then introduce a (conditional) construction of RIP matrices breaking the square-root bottleneck due to Bandeira, Mixon and Moreira (2017) and the present author.
We also explain some relationships to the combinatorial topics mentioned above.
Keyword (in Japanese) (See Japanese page) 
(in English) Pseudo-randomness / Ramsey graph/tournament / restricted isometry property / / / / /  
Reference Info. IEICE Tech. Rep., vol. 121, no. 96, IT2021-22, pp. 40-44, July 2021.
Paper # IT2021-22 
Date of Issue 2021-07-01 (IT) 
ISSN Online edition: ISSN 2432-6380
Copyright
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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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Conference Information
Committee IT  
Conference Date 2021-07-08 - 2021-07-09 
Place (in Japanese) (See Japanese page) 
Place (in English) Online 
Topics (in Japanese) (See Japanese page) 
Topics (in English) Freshman session, General 
Paper Information
Registration To IT 
Conference Code 2021-07-IT 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) RIP matrices breaking the square-root bottleneck and related combinatorics 
Sub Title (in English)  
Keyword(1) Pseudo-randomness  
Keyword(2) Ramsey graph/tournament  
Keyword(3) restricted isometry property  
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1st Author's Name Shohei Satake  
1st Author's Affiliation Kumamoto University (Kumamoto Univ.)
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Date Time 2021-07-08 16:40:00 
Presentation Time 50 minutes 
Registration for IT 
Paper # IT2021-22 
Volume (vol) vol.121 
Number (no) no.96 
Page pp.40-44 
#Pages
Date of Issue 2021-07-01 (IT) 


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