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544
ListDecodable Codes
"... The field of coding theory is motivated by the problem of communicating reliably over noisy channels — where the data sent over the channel may come out corrupted on the other end, but we nevertheless want the receiver to be able to correct the errors and recover the original message. There is a vas ..."
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. ” In particular, a generalization of the notion of an errorcorrecting code yields a framework that we will use to unify all of the main pseudorandom objects covered in this survey (averaging samplers, expander graphs, randomness extractors, listdecodable codes, pseudorandom generators).
5 ListDecodable Codes
"... The field of coding theory is motivated by the problem of communicating reliably over noisy channels — where the data sent over the channel may come out corrupted on the other end, but we nevertheless want the receiver to be able to correct the errors and recover the original message. There is a vas ..."
Abstract
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. ” In particular, a generalization of the notion of an errorcorrecting code yields a framework that we will use to unify all of the main pseudorandom objects covered in this survey (averaging samplers, expander graphs, randomness extractors, listdecodable codes, pseudorandom generators).
5 ListDecodable Codes
"... The field of coding theory is motivated by the problem of communicating reliably over noisy channels — where the data sent over the channel may come out corrupted on the other end, but we nevertheless want the receiver to be able to correct the errors and recover the original message. There is a va ..."
Abstract
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. ” In particular, a generalization of the notion of an errorcorrecting code yields a framework that we will use to unify all of the main pseudorandom objects covered in this survey (averaging samplers, expander graphs, randomness extractors, listdecodable codes, pseudorandom generators).
Symmetric Disjunctive ListDecoding Codes
"... Abstract. A binary code is said to be a disjunctive listdecoding sLcode, s ≥ 2, L ≥ 1, if the code is identified by the incidence matrix of a family of finite sets in which the union (or disjunctive sum) of any s sets can cover not more than L − 1 other sets of the family. In this paper, we consid ..."
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Abstract. A binary code is said to be a disjunctive listdecoding sLcode, s ≥ 2, L ≥ 1, if the code is identified by the incidence matrix of a family of finite sets in which the union (or disjunctive sum) of any s sets can cover not more than L − 1 other sets of the family. In this paper, we
A listdecodable code with local encoding and decoding
"... For arbitrary constants ɛ> 0 and λ> 0 we present a code E: {0, 1} n → {0, 1} n such that n = n O(log(1/ɛ)) and every ball in {0, 1} n of radius ( 1 2 − ɛ)n (in the Hammingdistance sense) contains at most 2 λn strings. Furthermore, the code E has encoding and listdecoding algorithms that prod ..."
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For arbitrary constants ɛ> 0 and λ> 0 we present a code E: {0, 1} n → {0, 1} n such that n = n O(log(1/ɛ)) and every ball in {0, 1} n of radius ( 1 2 − ɛ)n (in the Hammingdistance sense) contains at most 2 λn strings. Furthermore, the code E has encoding and listdecoding algorithms
Explicit CapacityAchieving ListDecodable Codes
 In Proceedings of the 38th Annual ACM Symposium on Theory of Computing (STOC
, 2006
"... For every 0 < R < 1 and ε> 0, we present an explicit construction of errorcorrecting codes of rate R that can be list decoded in polynomial time up to a fraction (1 − R − ε) of errors. These codes achieve the “capacity ” for decoding from adversarial errors, i.e., achieve the optimal trade ..."
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Cited by 26 (9 self)
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For every 0 < R < 1 and ε> 0, we present an explicit construction of errorcorrecting codes of rate R that can be list decoded in polynomial time up to a fraction (1 − R − ε) of errors. These codes achieve the “capacity ” for decoding from adversarial errors, i.e., achieve the optimal
Linear time encodable and list decodable codes
 In Proceedings of the 35th ACM Symposium on Theory of Computing
, 2003
"... We present the first construction of errorcorrecting codes which can be (list) decoded from a noise fraction arbitrarily close to 1 in linear time. Specifically, we present an explicit construction of codes which can be encoded in linear time as well as list decoded in linear time from a fraction ( ..."
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Cited by 10 (0 self)
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We present the first construction of errorcorrecting codes which can be (list) decoded from a noise fraction arbitrarily close to 1 in linear time. Specifically, we present an explicit construction of codes which can be encoded in linear time as well as list decoded in linear time from a fraction
Better binary listdecodable codes via multilevel concatenation
 In Proceedings of the 11th International Workshop on Randomization and Computation (RANDOM
, 2007
"... Abstract. We give a polynomial time construction of binary codes with the best currently known tradeoff between rate and errorcorrection radius. Specifically, we obtain linear codes over fixed alphabets that can be list decoded in polynomial time up to the so called BlokhZyablov bound. Our work b ..."
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Cited by 7 (6 self)
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Abstract. We give a polynomial time construction of binary codes with the best currently known tradeoff between rate and errorcorrection radius. Specifically, we obtain linear codes over fixed alphabets that can be list decoded in polynomial time up to the so called BlokhZyablov bound. Our work
Results 1  10
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544