# (Solved) Zero Error Capacity Under List Decoding Tutorial

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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 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 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.

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 Theorem (List-Decoding Capacity). Finally, we point out some directions on how to calculate the zero-error capacity of such channels.

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).