UID:
almahu_9949972471702882
Umfang:
XX, 352 p.
,
online resource.
Ausgabe:
1st ed. 2005.
ISBN:
9783540301806
Serie:
Lecture Notes in Computer Science, 3282
Inhalt:
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.
Anmerkung:
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.
In:
Springer Nature eBook
Weitere Ausg.:
Printed edition: ISBN 9783540240518
Weitere Ausg.:
Printed edition: ISBN 9783540805915
Sprache:
Englisch
URL:
https://doi.org/10.1007/b104335
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