Algorithmic Results In List Decoding

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Algorithmic Results In List Decoding

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Author : Venkatesan Guruswami
language : en
Publisher: Now Publishers Inc
Release Date : 2007-01-24

Algorithmic Results In List Decoding written by Venkatesan Guruswami and has been published by Now Publishers Inc this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-24 with Computers categories.

Algorithmic Results in List Decoding introduces and motivates the problem of list decoding, and discusses the central algorithmic results of the subject, culminating with the recent results on achieving "list decoding capacity." The main technical focus is on giving a complete presentation of the recent algebraic results achieving list decoding capacity, while pointers or brief descriptions are provided for other works on list decoding. Algorithmic Results in List Decoding is intended for scholars and graduate students in the fields of theoretical computer science and information theory. The author concludes by posing some interesting open questions and suggests directions for future work.

List Decoding Of Error Correcting Codes

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Author : Venkatesan Guruswami
language : en
Publisher: Springer
Release Date : 2004-11-29

List Decoding Of Error Correcting Codes written by Venkatesan Guruswami and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-11-29 with Computers categories.

How can one exchange information e?ectively when the medium of com- nication introduces errors? This question has been investigated extensively starting with the seminal works of Shannon (1948) and Hamming (1950), and has led to the rich theory of “error-correcting codes”. This theory has traditionally gone hand in hand with the algorithmic theory of “decoding” that tackles the problem of recovering from the errors e?ciently. This thesis presents some spectacular new results in the area of decoding algorithms for error-correctingcodes. Speci?cally,itshowshowthenotionof“list-decoding” can be applied to recover from far more errors, for a wide variety of err- correcting codes, than achievable before. A brief bit of background: error-correcting codes are combinatorial str- tures that show how to represent (or “encode”) information so that it is - silient to a moderate number of errors. Speci?cally, an error-correcting code takes a short binary string, called the message, and shows how to transform it into a longer binary string, called the codeword, so that if a small number of bits of the codewordare ?ipped, the resulting string does not look like any other codeword. The maximum number of errorsthat the code is guaranteed to detect, denoted d, is a central parameter in its design. A basic property of such a code is that if the number of errors that occur is known to be smaller than d/2, the message is determined uniquely. This poses a computational problem,calledthedecodingproblem:computethemessagefromacorrupted codeword, when the number of errors is less than d/2.

List Decoding Of Error Correcting Codes

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Author : Venkatesan Guruswami
language : en
Publisher:
Release Date : 2001

List Decoding Of Error Correcting Codes written by Venkatesan Guruswami and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with categories.

(Cont.) We prove several combinatorial results that sharpen our understanding of the potential and limits of list decoding, and its relation to more classical parameters like the rate and minimum distance. The crux of the thesis is its algorithmic results, which were lacking in the early works on list decoding. Our algorithmic results include: * Efficient list decoding algorithms for classically studied codes such as Reed-Solomon codes and algebraic-geometric codes. In particular, building upon an earlier algorithm due to Sudan, we present the first polynomial time algorithm to decode Reed-Solomon codes beyond d/2 errors for every value of the rate. * A new soft list decoding algorithm for Reed-Solomon and algebraic-geometric codes, and novel decoding algorithms for concatenated codes based on it. * New code constructions using concatenation and/or expander graphs that have good (and sometimes near-optimal) rate and are efficiently list decodable from extremely large amounts of noise. * Expander-based constructions of linear time encodable and decodable codes that can correct up to the maximum possible fraction of errors, using unique (not list) decoding.

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Author :
language : en
Publisher: World Scientific
Release Date :

written by and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Proceedings Of The International Congress Of Mathematicians 2010 Icm 2010 In 4 Volumes Vol I Plenary Lectures And Ceremonies Vols Ii Iv Invited Lectures

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Author : Rajendra Bhatia
language : en
Publisher: World Scientific
Release Date : 2011-06-06

Proceedings Of The International Congress Of Mathematicians 2010 Icm 2010 In 4 Volumes Vol I Plenary Lectures And Ceremonies Vols Ii Iv Invited Lectures written by Rajendra Bhatia and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-06 with Mathematics categories.

ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.

Approximation Randomization And Combinatorial Optimization Algorithms And Techniques

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Author : Leslie Ann Goldberg
language : en
Publisher: Springer
Release Date : 2011-08-05

Approximation Randomization And Combinatorial Optimization Algorithms And Techniques written by Leslie Ann Goldberg and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-05 with Computers categories.

This book constitutes the joint refereed proceedings of the 14th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2011, and the 15th International Workshop on Randomization and Computation, RANDOM 2011, held in Princeton, New Jersey, USA, in August 2011. The volume presents 29 revised full papers of the APPROX 2011 workshop, selected from 66 submissions, and 29 revised full papers of the RANDOM 2011 workshop, selected from 64 submissions. They were carefully reviewed and selected for inclusion in the book. In addition two abstracts of invited talks are included. APPROX focuses on algorithmic and complexity issues surrounding the development of efficient approximate solutions to computationally difficult problems. RANDOM is concerned with applications of randomness to computational and combinatorial problems.

Algorithms And Theory Of Computation Handbook 2 Volume Set

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Author : Mikhail J. Atallah
language : en
Publisher: CRC Press
Release Date : 2022-05-29

Algorithms And Theory Of Computation Handbook 2 Volume Set written by Mikhail J. Atallah and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-29 with Computers categories.

Algorithms and Theory of Computation Handbook, Second Edition in a two volume set, provides an up-to-date compendium of fundamental computer science topics and techniques. It also illustrates how the topics and techniques come together to deliver efficient solutions to important practical problems. New to the Second Edition: Along with updating and revising many of the existing chapters, this second edition contains more than 20 new chapters. This edition now covers external memory, parameterized, self-stabilizing, and pricing algorithms as well as the theories of algorithmic coding, privacy and anonymity, databases, computational games, and communication networks. It also discusses computational topology, computational number theory, natural language processing, and grid computing and explores applications in intensity-modulated radiation therapy, voting, DNA research, systems biology, and financial derivatives. This best-selling handbook continues to help computer professionals and engineers find significant information on various algorithmic topics. The expert contributors clearly define the terminology, present basic results and techniques, and offer a number of current references to the in-depth literature. They also provide a glimpse of the major research issues concerning the relevant topics

Essays On Coding Theory

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Author : Ian F. Blake
language : en
Publisher: Cambridge University Press
Release Date : 2024-03-14

Essays On Coding Theory written by Ian F. Blake and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-14 with Mathematics categories.

Critical coding techniques have developed over the past few decades for data storage, retrieval and transmission systems, significantly mitigating costs for governments and corporations that maintain server systems containing large amounts of data. This book surveys the basic ideas of these coding techniques, which tend not to be covered in the graduate curricula, including pointers to further reading. Written in an informal style, it avoids detailed coverage of proofs, making it an ideal refresher or brief introduction for students and researchers in academia and industry who may not have the time to commit to understanding them deeply. Topics covered include fountain codes designed for large file downloads; LDPC and polar codes for error correction; network, rank metric, and subspace codes for the transmission of data through networks; post-quantum computing; and quantum error correction. Readers are assumed to have taken basic courses on algebraic coding and information theory.

Computing And Combinatorics

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Author : Hung Q. Ngo
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-07-11

Computing And Combinatorics written by Hung Q. Ngo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-11 with Computers categories.

The papers in this volume were selected for presentation at the 15th Annual InternationalComputing and CombinatoricsConference (COCOON 2009), held during July 13-15, 2009 in Niagara Falls, New York, USA. Previous meetings of this conference were held in Xian (1995), Hong Kong (1996), Shanghai (1997), Taipei(1998), Tokyo(1999), Sydney(2000), Guilin(2001), Singapore(2002), Big Sky (2003), Jeju Island (2004), Kunming (2005), Taipei (2006), Alberta (2007), and Dalian (2008). In response to the Call for Papers, 125 extended abstracts (not counting withdrawn papers) were submitted from 28 countries and regions, of which 51 were accepted. Authors of the submitted papers were from Cyprus (1), The Netherlands (1), Bulgaria (1), Israel (1), Vietnam (2), Finland (1), Puerto Rico (2), Australia (4), Norway (4), Portugal (1) Spain (2), France (16), Republic of Korea(3), Singapore(2), Italy(6), Iran, (4), Greece(7), Poland(4), Switzerland (8), Hong Kong (10), UK (12), India (7), Taiwan (18), Canada (23), China (19), Japan (39), Germany (44), and the USA (77). The submitted papers were evaluated by an international Technical P- gram Committee (TPC) consisting of Srinivas Aluru (Iowa State University, USA), Lars Arge (University of Aarhus, Denmark), Vikraman Arvind (Ins- tute of Mathematical Sciences, India), James Aspnes (Yale University, USA), Mikhail Atallah (Purdue University, USA), Gill Barequet (Technion - Israel - stitute of Technology, Israel), Michael Brudno (University of Toronto, Canada), Jianer Chen (Texas A & M, USA), Bhaskar DasGupta (University of Illinois at Chicago, USA), Anupam Gupta (Carnegie Mellon University, USA), Lane A.

Encyclopedia Of Algorithms

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Author : Ming-Yang Kao
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-08-06

Encyclopedia Of Algorithms written by Ming-Yang Kao and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-06 with Computers categories.

One of Springer’s renowned Major Reference Works, this awesome achievement provides a comprehensive set of solutions to important algorithmic problems for students and researchers interested in quickly locating useful information. This first edition of the reference focuses on high-impact solutions from the most recent decade, while later editions will widen the scope of the work. All entries have been written by experts, while links to Internet sites that outline their research work are provided. The entries have all been peer-reviewed. This defining reference is published both in print and on line.