List decoding of error-correcting codes : winning thesis of the 2002 ACM doctoral dissertation competition / Venkatesan Guruswami.
"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 trad...
I tiakina i:
| Kaituhi matua: | |
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| Hōputu: | iPukapuka |
| Reo: | English |
| I whakaputaina: |
Berlin ; New York :
Springer,
[2005]
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| Rangatū: | Lecture notes in computer science ;
3282. ACM distinguished theses. |
| Ngā marau: | |
| Urunga tuihono: | Springer eBooks Publisher description |
| Whakarāpopototanga: | "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."--Publisher's website. |
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| Whakaahutanga tūemi: | "Revised version of [the author's] doctoral dissertation, written under the supervision of Madhu Sudan and submitted to MIT in August 2001"--Page xi. |
| Whakaahuatanga ōkiko: | 1 online resource (xix, 350 pages) : illustrations. |
| Rārangi puna kōrero: | Includes bibliographical references and index. |
| ISBN: | 3540240519 9783540240518 3540805915 9783540805915 1281401994 9781281401991 3540301801 9783540301806 |
| ISSN: | 0302-9743 ; |