List Decoding of Error-Correcting Codes

Venkatesan Guruswami

ISBN 10: 3540240519 / ISBN 13: 9783540240518

Editore: Springer Berlin Heidelberg, Springer Berlin Heidelberg Nov 2004, 2004

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This item is printed on demand - Print on Demand Titel. Neuware -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. 376 pp. Englisch.

Codice articolo 9783540240518

Dati bibliografici

• Titolo: List Decoding of Error-Correcting Codes
• Editore: Springer Berlin Heidelberg, Springer Berlin Heidelberg Nov 2004
• Data di pubblicazione: 2004
• Lingua: Inglese
• ISBN 10: 3540240519
• ISBN 13: 9783540240518
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 235 L x 155 A x 21 P (millimetri) 235 millimetri di larghezza per 155 millimetri di altezza per 21 millimetri di profondità
• Peso: 569 grammi

Descrizione articolo

Riassunto

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.

Contenuti

1 Introduction.- 1 Introduction.- 2 Preliminaries and Monograph Structure.- I Combinatorial Bounds.- 3 Johnson-Type Bounds and Applications to List Decoding.- 4 Limits to List Decodability.- 5 List Decodability Vs. Rate.- II Code Constructions and Algorithms.- 6 Reed-Solomon and Algebraic-Geometric Codes.- 7 A Unified Framework for List Decoding of Algebraic Codes.- 8 List Decoding of Concatenated Codes.- 9 New, Expander-Based List Decodable Codes.- 10 List Decoding from Erasures.- III Applications.- Interlude.- III Applications.- 11 Linear-Time Codes for Unique Decoding.- 12 Sample Applications Outside Coding Theory.- 13 Concluding Remarks.- A GMD Decoding of Concatenated Codes.