List Decoding Of Error Correcting Codes
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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.
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.
Algebraic List Decoding Of Error Correcting Codes
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Author : Farzad Parvaresh
language : en
Publisher:
Release Date : 2007
Algebraic List Decoding Of Error Correcting Codes written by Farzad Parvaresh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.
This dissertation is concerned with algebraic list-decoding of error-correcting codes. During the past decade, significant advances in this are were achieved. The breakthrough papers of Sudan, Guruswami & Sudan, and Koetter & Vardy showed that the well-known Reed-Solomon (and other algebraic) codes can correct many more errors---in the list-decoding sense---than previously thought possible. Herein, we extend the theory developed in these seminal papers, and improve upon the results reported therein.
Theoretical Computer Science
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Author :
language : en
Publisher:
Release Date : 2000
Theoretical Computer Science written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Computer science categories.
Fundamentals Of Error Correcting Codes
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Author : W. Cary Huffman
language : en
Publisher: Cambridge University Press
Release Date : 2010-02-18
Fundamentals Of Error Correcting Codes written by W. Cary Huffman 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 2010-02-18 with Technology & Engineering categories.
Fundamentals of Error Correcting Codes is an in-depth introduction to coding theory from both an engineering and mathematical viewpoint. As well as covering classical topics, there is much coverage of techniques which could only be found in specialist journals and book publications. Numerous exercises and examples and an accessible writing style make this a lucid and effective introduction to coding theory for advanced undergraduate and graduate students, researchers and engineers, whether approaching the subject from a mathematical, engineering or computer science background.
Applied Algebra Algebraic Algorithms And Error Correcting Codes
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Author : Serdar Boztas
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-30
Applied Algebra Algebraic Algorithms And Error Correcting Codes written by Serdar Boztas 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 2007-11-30 with Computers categories.
This book constitutes the refereed proceedings of the 17th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-17, held in Bangalore, India, in December 2007. The 33 revised full papers presented together with 8 invited papers were carefully reviewed and selected from 61 submissions. Among the subjects addressed are block codes, including list-decoding algorithms; algebra and codes: rings, fields, algebraic geometry codes; algebra: rings and fields, polynomials, permutations, lattices; cryptography: cryptanalysis and complexity; computational algebra: algebraic algorithms and transforms; sequences and boolean functions.
Error Correction Coding
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Author : Todd K. Moon
language : en
Publisher: John Wiley & Sons
Release Date : 2005-06-06
Error Correction Coding written by Todd K. Moon and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-06 with Computers categories.
An unparalleled learning tool and guide to error correction coding Error correction coding techniques allow the detection and correction of errors occurring during the transmission of data in digital communication systems. These techniques are nearly universally employed in modern communication systems, and are thus an important component of the modern information economy. Error Correction Coding: Mathematical Methods and Algorithms provides a comprehensive introduction to both the theoretical and practical aspects of error correction coding, with a presentation suitable for a wide variety of audiences, including graduate students in electrical engineering, mathematics, or computer science. The pedagogy is arranged so that the mathematical concepts are presented incrementally, followed immediately by applications to coding. A large number of exercises expand and deepen students' understanding. A unique feature of the book is a set of programming laboratories, supplemented with over 250 programs and functions on an associated Web site, which provides hands-on experience and a better understanding of the material. These laboratories lead students through the implementation and evaluation of Hamming codes, CRC codes, BCH and R-S codes, convolutional codes, turbo codes, and LDPC codes. This text offers both "classical" coding theory-such as Hamming, BCH, Reed-Solomon, Reed-Muller, and convolutional codes-as well as modern codes and decoding methods, including turbo codes, LDPC codes, repeat-accumulate codes, space time codes, factor graphs, soft-decision decoding, Guruswami-Sudan decoding, EXIT charts, and iterative decoding. Theoretical complements on performance and bounds are presented. Coding is also put into its communications and information theoretic context and connections are drawn to public key cryptosystems. Ideal as a classroom resource and a professional reference, this thorough guide will benefit electrical and computer engineers, mathematicians, students, researchers, and scientists.
An Introduction To Error Correcting Codes With Applications
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Author : Scott A. Vanstone
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-18
An Introduction To Error Correcting Codes With Applications written by Scott A. Vanstone 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 2013-04-18 with Technology & Engineering categories.
5. 2 Rings and Ideals 148 5. 3 Ideals and Cyclic Subspaces 152 5. 4 Generator Matrices and Parity-Check Matrices 159 5. 5 Encoding Cyclic Codest 163 5. 6 Syndromes and Simple Decoding Procedures 168 5. 7 Burst Error Correcting 175 5. 8 Finite Fields and Factoring xn-l over GF(q) 181 5. 9 Another Method for Factoring xn-l over GF(q)t 187 5. 10 Exercises 193 Chapter 6 BCH Codes and Bounds for Cyclic Codes 6. 1 Introduction 201 6. 2 BCH Codes and the BCH Bound 205 6. 3 Bounds for Cyclic Codest 210 6. 4 Decoding BCH Codes 215 6. 5 Linearized Polynomials and Finding Roots of Polynomialst 224 6. 6 Exercises 231 Chapter 7 Error Correction Techniques and Digital Audio Recording 7. 1 Introduction 237 7. 2 Reed-Solomon Codes 237 7. 3 Channel Erasures 240 7. 4 BCH Decoding with Erasures 244 7. 5 Interleaving 250 7. 6 Error Correction and Digital Audio Recording 256 7.
Introduction To Coding Theory
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Author : Ron Roth
language : en
Publisher: Cambridge University Press
Release Date : 2006-02-23
Introduction To Coding Theory written by Ron Roth 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 2006-02-23 with Computers categories.
This 2006 book introduces the theoretical foundations of error-correcting codes for senior-undergraduate to graduate students.