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List Decoding of Error-Correcting Codes

Winning Thesis of the 2002 ACM Doctoral Dissertation Competition

  • Book
  • © 2005

Overview

Authors:
  1. Venkatesan Guruswami

    1. Department of Comp. Sci. & Eng., University of Washington, Seattle, USA

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

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Table of contents (15 chapters)

  1. Front Matter

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  2. 1 Introduction

    1. 1 Introduction

      • Venkatesan Guruswami
      Pages 1-14

    2. 2 Preliminaries and Monograph Structure

      • Venkatesan Guruswami
      Pages 15-30

  3. Part I Combinatorial Bounds

    1. Front Matter

      Pages 31-31
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    2. 3 Johnson-Type Bounds and Applications to List Decoding

      • Venkatesan Guruswami
      Pages 33-44

    3. 4 Limits to List Decodability

      • Venkatesan Guruswami
      Pages 45-78

    4. 5 List Decodability Vs. Rate

      • Venkatesan Guruswami
      Pages 79-92

  4. Part II Code Constructions and Algorithms

    1. Front Matter

      Pages 93-93
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    2. 6 Reed-Solomon and Algebraic-Geometric Codes

      • Venkatesan Guruswami
      Pages 95-145

    3. 7 A Unified Framework for List Decoding of Algebraic Codes

      • Venkatesan Guruswami
      Pages 147-175

    4. 8 List Decoding of Concatenated Codes

      • Venkatesan Guruswami
      Pages 177-207

    5. 9 New, Expander-Based List Decodable Codes

      • Venkatesan Guruswami
      Pages 209-250

    6. 10 List Decoding from Erasures

      • Venkatesan Guruswami
      Pages 251-277

  5. Part III Applications

    1. Front Matter

      Pages 279-279
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    2. Interlude

      • Venkatesan Guruswami
      Pages 281-281

  6. Part III Applications

    1. 11 Linear-Time Codes for Unique Decoding

      • Venkatesan Guruswami
      Pages 283-298

    2. 12 Sample Applications Outside Coding Theory

      • Venkatesan Guruswami
      Pages 299-327

    3. 13 Concluding Remarks

      • Venkatesan Guruswami
      Pages 329-332

    4. A GMD Decoding of Concatenated Codes

      • Venkatesan Guruswami
      Pages 333-335

  7. Back Matter

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Keywords

About this book

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.

Authors and Affiliations

  • Department of Comp. Sci. & Eng., University of Washington, Seattle, USA

    Venkatesan Guruswami

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