Skip to main content
Top

2009 | OriginalPaper | Chapter

List Decoding of Binary Codes–A Brief Survey of Some Recent Results

Author : Venkatesan Guruswami

Published in: Coding and Cryptology

Publisher: Springer Berlin Heidelberg

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

We briefly survey some recent progress on list decoding algorithms for

binary

codes. The results discussed include:

Algorithms to list decode binary Reed-Muller codes of any order up to the minimum distance, generalizing the classical Goldreich-Levin algorithm for RM codes of order 1 (Hadamard codes). These algorithms are “local” and run in time polynomial in the

message

length.

Construction of binary codes efficiently list-decodable up to the Zyablov (and Blokh-Zyablov) radius. This gives a factor two improvement over the error-correction radius of traditional “unique decoding” algorithms.

The existence of binary linear

concatenated

codes that achieve list decoding capacity, i.e., the optimal trade-off between rate and fraction of worst-case errors one can hope to correct.

Explicit binary codes mapping

k

bits to

n

 ≤ poly(

k

/

ε

) bits that can be list decoded from a fraction (1/2 − 

ε

) of errors (even for

ε

= 

o

(1)) in poly(

k

/

ε

) time. A construction based on concatenating a variant of the Reed-Solomon code with dual BCH codes achieves the best known (cubic) dependence on 1/

ε

, whereas the existential bound is

n

 = 

O

(

k

/

ε

2

). (The above-mentioned result decoding up to Zyablov radius achieves a rate of

Ω

(

ε

3

) for the case of

constant

ε

.)

We will only sketch the high level ideas behind these developments, pointing to the original papers for technical details and precise theorem statements.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Metadata
Title
List Decoding of Binary Codes–A Brief Survey of Some Recent Results
Author
Venkatesan Guruswami
Copyright Year
2009
Publisher
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-642-01877-0_10

Premium Partner