Lecture Notes in Computer Science

# List Decoding of Error-Correcting Codes

## Winning Thesis of the 2002 ACM Doctoral Dissertation Competition

Authors: Guruswami, Venkatesan

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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.

• 12 Sample Applications Outside Coding Theory

Venkatesan Guruswami

Pages 299-327

30,19 €

eBook 67,82 €
price for Spain (gross)
• ISBN 978-3-540-30180-6
• Digitally watermarked, DRM-free
• Included format: PDF
• ebooks can be used on all reading devices
Softcover 83,19 €
price for Spain (gross)
• ISBN 978-3-540-24051-8
• Free shipping for individuals worldwide
• Usually dispatched within 3 to 5 business days.
• The final prices may differ from the prices shown due to specifics of VAT rules

## Bibliographic Information

Bibliographic Information
Book Title
List Decoding of Error-Correcting Codes
Book Subtitle
Winning Thesis of the 2002 ACM Doctoral Dissertation Competition
Authors
Series Title
Lecture Notes in Computer Science
Series Volume
3282
2005
Publisher
Springer-Verlag Berlin Heidelberg
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-30180-6
DOI
10.1007/b104335
Softcover ISBN
978-3-540-24051-8
Series ISSN
0302-9743
Edition Number
1
Number of Pages
XX, 352
Topics