List Decoding of Error-Correcting Codes

Winning Thesis of the 2002 ACM Doctoral Dissertation Competition

  • Venkatesan Guruswami

Part of the Lecture Notes in Computer Science book series (LNCS, volume 3282)

Table of contents

  1. Front Matter
  2. 1 Introduction

    1. Venkatesan Guruswami
      Pages 1-14
    2. Venkatesan Guruswami
      Pages 15-30
  3. Part I Combinatorial Bounds

    1. Front Matter
      Pages 31-31
    2. Venkatesan Guruswami
      Pages 45-78
    3. Venkatesan Guruswami
      Pages 79-92
  4. Part II Code Constructions and Algorithms

    1. Front Matter
      Pages 93-93
    2. Venkatesan Guruswami
      Pages 95-145
    3. Venkatesan Guruswami
      Pages 177-207
    4. Venkatesan Guruswami
      Pages 209-250
    5. Venkatesan Guruswami
      Pages 251-277
  5. Part III Applications

    1. Front Matter
      Pages 279-279
    2. Venkatesan Guruswami
      Pages 281-281
  6. Part III Applications

    1. Venkatesan Guruswami
      Pages 283-298
    2. Venkatesan Guruswami
      Pages 299-327
    3. Venkatesan Guruswami
      Pages 329-332
    4. Venkatesan Guruswami
      Pages 333-335
  7. Back Matter

About this book

Introduction

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.

Keywords

Code Error-correcting Code Information Shannon algorithms coding theory complexity theory concatenated codes decoding decoding algorithms encoding error-detecting codes information theory list decoding reed-solomon codes

Authors and affiliations

  • Venkatesan Guruswami
    • 1
  1. 1.Department of Comp. Sci. & Eng.University of WashingtonSeattleUSA

Bibliographic information

  • DOI https://doi.org/10.1007/b104335
  • Copyright Information Springer-Verlag Berlin Heidelberg 2005
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Computer Science
  • Print ISBN 978-3-540-24051-8
  • Online ISBN 978-3-540-30180-6
  • Series Print ISSN 0302-9743
  • Series Online ISSN 1611-3349
  • About this book