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List decoding

In coding theory, list decoding is an alternative to unique decoding of error-correcting codes for large error rates. The notion was proposed by Elias in the 1950s. The main idea behind list decoding is that the decoding algorithm instead of outputting a single possible message outputs a list of possibilities one of which is correct. This allows for…

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Applications in complexity theory and cryptography

Computational complexityCryptographyHard-core predicatesOne-way permutationsPermanent
7 related topics

List-decoding algorithms

Madhu SudanGuruswami–Sudan '98Venkatesan GuruswamiAlexander VardyCommunications of the ACM
6 related topics

List-decoding capacity

Binary symmetric channelUnion boundProbabilistic method
3 related topics

Mathematical formulation

Error boundHamming distance
2 related topics

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Overview

Mathematical formulation

Motivation for list decoding

Combinatorics of list decoding

List-decoding capacity

List-decoding algorithms

Applications in complexity theory and cryptography

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List decoding

Nodes36
Edges35
Triples75
Avg. degree1.94
Density0.055556
Components1

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List decoding

Top relations

related to List-decoding algorithms · 30
List decoding → ACM, Alexander Vardy, Algorithms, An, Atri Rudra, Coding, Communications, Computer Science, Computing Join Forces, Farzad Parvaresh, Guruswami, However, In, Johnson, Madhu Sudan, Parvaresh, Reed, Reed-Solomon, Research Highlights, Rudra
related to References · 12
List decoding → Electronics, Elias, Historical, IRE WESCON Convention Record, List, MIT, PDF, Peter, Pt, Quarterly Progress Report, Research Laboratory, Wozencraft
has application · 11
List decoding → Algorithms, Amplifying, Average, Boolean, Construction, Efficient, Extractors, Following, NP-search, Predicting, Pseudorandom
related to List-decoding potential · 9
List decoding → For, Hamming, Hence, However, It, List, Naturally, The, This
related to Combinatorics of list decoding · 6
List decoding → Hamming, In, It, Johnson, The, This
related to List-decoding capacity · 4
List decoding → Also, In, The, What
is a · 1
List decoding → alternative to unique decoding of error-correcting codes for large error rates

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Important terminology

displaystyle list decoding codes list-decoding errors hamming codeword code received word model capacity theory codewords rate distance possible bound output

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
List decodingis aalternative to unique decoding of error-correcting codes for large error rates0.90text
minimum distanceinstance ofCombinatorics of list decodingThe relation between list decodability of a code and other fundamental parameters0.80text
rate have been fairly well studiedinstance ofCombinatorics of list decodingThe relation between list decodability of a code and other fundamental parameters0.80text
List decodinghas applicationAlgorithms0.60section
List decodinghas applicationFollowing0.60section
List decodinghas applicationConstruction0.60section
List decodinghas applicationPredicting0.60section
List decodinghas applicationNP-search0.60section
List decodinghas applicationAmplifying0.60section
List decodinghas applicationBoolean0.60section
List decodinghas applicationAverage0.60section
List decodinghas applicationExtractors0.60section

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