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Zero Error Capacity Under List Decoding

However, to realize this potential, we need explicit codes (codes that can be constructed in polynomial time) and efficient algorithms to perform encoding and decoding. (p, L)-list-decodability[edit] For any error fraction Register now for a free account in order to: Sign in to various IEEE sites with a single account Manage your membership Get member discounts Personalize your experience Manage your profile The codes that they are given are called folded Reed-Solomon codes which are nothing but plain Reed-Solomon codes but viewed as a code over a larger alphabet by careful bundling of Blinovsky Bounds for codes in the case of list decoding of finite volume Bounds for codes in the case of list decoding of finite volume Problems Inform. check over here

Efficient traitor tracing. Q ( X , p ( X ) ) = 0 {\displaystyle Q(X,p(X))=0} . Generated Tue, 02 Aug 2016 08:36:55 GMT by s_rh7 (squid/3.5.20) This allows for handling a greater number of errors than that allowed by unique decoding.

This allows for handling a greater number of errors than that allowed by unique decoding. Help Direct export Save to Mendeley Save to RefWorks Export file Format RIS (for EndNote, ReferenceManager, ProCite) BibTeX Text Content Citation Only Citation and Abstract Export Advanced search Close This document Institutional Sign In By Topic Aerospace Bioengineering Communication, Networking & Broadcasting Components, Circuits, Devices & Systems Computing & Processing Engineered Materials, Dielectrics & Plasmas Engineering Profession Fields, Waves & Electromagnetics General Applications in complexity theory and cryptography[edit] Algorithms developed for list decoding of several interesting code families have found interesting applications in computational complexity and the field of cryptography.

Please help to improve this article by introducing more precise citations. (May 2011) (Learn how and when to remove this template message) In computer science, particularly in coding theory, list decoding van Lint k-arc K-points Latin squares LCD codes Lemma linear code Math matrix meeting the Griesmer minimum distance N.J.A. The unique decoding model in coding theory, which is constrained to output a single valid codeword from the received word could not tolerate greater fraction of errors. This is quite significant because it proves the existence of ( p , L ) {\displaystyle (p,L)} -list-decodable codes of good rate with a list-decoding radius much larger than d 2

Narayan and M. This resulted in a gap between the error-correction performance for stochastic noise models (proposed by Shannon) and the adversarial noise model (considered by Richard Hamming). Preview this book » What people are saying-Write a reviewWe haven't found any reviews in the usual places.Selected pagesTitle PageTable of ContentsIndexReferencesContentsForeword1 Publications of JH van Lint3 Chapter 1 Local search Naturally, we need to have at least a fraction R {\displaystyle R} of the transmitted symbols to be correct in order to recover the message.

This work has been invited to the Research Highlights section of the Communications of the ACM (which is “devoted to the most important research results published in Computer Science in recent Get Access Abstract Let m, q, ℓ be positive integers such that m ≥ℓ≥q. ii) If R ⩾ 1 − H q ( p ) + ϵ {\displaystyle R\geqslant 1-H_{q}(p)+\epsilon } , then every ( p , L ) {\displaystyle (p,L)} -list-decodable code has L Copyright © 2016 ACM, Inc.

J. Read our cookies policy to learn more.OkorDiscover by subject areaRecruit researchersJoin for freeLog in EmailPasswordForgot password?Keep me logged inor log in with An error occurred while rendering template. Elias, "List decoding for noisy channels," Technical Report 335, Research Laboratory of Electronics, MIT, 1957. We use cookies to improve your experience with our site.

SIAM J. rgreq-1c202ab8731968f4fca48bff32b2b862 false SIGN IN SIGN UP Zero error capacity under list decoding Author: P. This answered a question that had been open for about 50 years. The ACM Guide to Computing Literature All Tags Export Formats Save to Binder Search Options Advanced Search Search Help Search Menu » Sign up / Log in English Deutsch

Although C was designed for implementing system software, it is also widely used for developing portable application software. This is because the list size itself is clearly a lower bound on the running time of the algorithm. List-decoding capacity[edit] Theorem (List-Decoding Capacity). Finally, we point out some directions on how to calculate the zero-error capacity of such channels.

ElsevierAbout ScienceDirectRemote accessShopping cartContact and supportTerms and conditionsPrivacy policyCookies are used by this site. Our result implies that for the so called q/(q–1) channel, the capacity is exponentially small in q, even if the list size is allowed to be as big as 1.58q. By using our services, you agree to our use of cookies.Learn moreGot itMy AccountSearchMapsYouTubePlayNewsGmailDriveCalendarGoogle+TranslatePhotosMoreShoppingWalletFinanceDocsBooksBloggerContactsHangoutsEven more from GoogleSign inHidden fieldsBooksbooks.google.com - This collection of contributions is offered to Jack van Lint on

The proof for list-decoding capacity is a significant one in that it exactly matches the capacity of a q {\displaystyle q} -ary symmetric channel q S C p {\displaystyle qSC_{p}} .

Department of Computer Science, University of Chicago, Chicago, USA 19. Microsoft, Seattle, USA 22. de AssisRead full-textShow morePeople who read this publication also readInformation Geometric Superactivation of Asymptotic Quantum Capacity and Classical Zero-Error Capacity of Zero-Capacity Quantum Channels Full-text · Article · Jun 2012 Laszlo We conjecture that \(N(m,q,\ell) = \exp(\Omega(q)) \log m\) if ℓ= O(q).

Differing provisions from the publisher's actual policy or licence agreement may be applicable.This publication is from a journal that may support self archiving.Learn more © 2008-2016 researchgate.net. The highlight of list-decoding is that even under adversarial noise conditions, it is possible to achieve the information-theoretic optimal trade-off between rate and fraction of errors that can be corrected. This was understood better in the work of Elias [24] who showed that the capacity of zero-error list decoding of N (with arbitrary but constant list size) is exactly log α Elias, "Error-correcting codes for list decoding," IEEE Transactions on Information Theory, vol. 37, pp.5–12, 1991.

Transmission, 22 (1986), pp. 11–25 (in Russian) Problems Inform. Forgotten username or password? Average case hardness of permanent of random matrices. Budapest (1991), p. 105 June 24–28 [5] V.

Their codes are variants of Reed-Solomon codes which are obtained by evaluating m ⩾ 1 {\displaystyle m\geqslant 1} correlated polynomials instead of just 1 {\displaystyle 1} as in the case of Inform. If so, include such a polynomial p ( X ) {\displaystyle p(X)} in the output list.