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Combinatorial Limitations of Averageradius List Decoding
"... We study certain combinatorial aspects of listdecoding, motivated by the exponential gap between the known upper bound (of O(1/γ)) and lower bound (of Ωp(log(1/γ))) for the listsize needed to list decode up to error fraction p with rate γ away from capacity, i.e., 1−h(p)−γ (here p ∈ (0, 1 2) and ..."
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) codewords with low “average radius. ” The standard notion of listdecoding corresponds to working with the maximum distance of a collection of codewords from a center instead of average distance. The averageradius form is in itself quite natural; for instance, the classical Johnson bound in fact implies
Improved Decoding of ReedSolomon and AlgebraicGeometry Codes
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1999
"... Given an errorcorrecting code over strings of length n and an arbitrary input string also of length n, the list decoding problem is that of finding all codewords within a specified Hamming distance from the input string. We present an improved list decoding algorithm for decoding ReedSolomon codes ..."
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Cited by 345 (44 self)
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Given an errorcorrecting code over strings of length n and an arbitrary input string also of length n, the list decoding problem is that of finding all codewords within a specified Hamming distance from the input string. We present an improved list decoding algorithm for decoding Reed
Achieving nearcapacity on a multipleantenna channel
 IEEE Trans. Commun
, 2003
"... Recent advancements in iterative processing of channel codes and the development of turbo codes have allowed the communications industry to achieve nearcapacity on a singleantenna Gaussian or fading channel with low complexity. We show how these iterative techniques can also be used to achieve nea ..."
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Cited by 402 (2 self)
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nearcapacity on a multipleantenna system where the receiver knows the channel. Combining iterative processing with multipleantenna channels is particularly challenging because the channel capacities can be a factor of ten or more higher than their singleantenna counterparts. Using a “list ” version
Decoding Reed Solomon Codes beyond the ErrorCorrection Bound
, 1997
"... We present a randomized algorithm which takes as input n distinct points f(xi; yi)g n i=1 from F \Theta F (where F is a field) and integer parameters t and d and returns a list of all univariate polynomials f over F in the variable x of degree at most d which agree with the given set of points in a ..."
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Cited by 274 (18 self)
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We present a randomized algorithm which takes as input n distinct points f(xi; yi)g n i=1 from F \Theta F (where F is a field) and integer parameters t and d and returns a list of all univariate polynomials f over F in the variable x of degree at most d which agree with the given set of points
The Complexity of Local List Decoding
"... We study the complexity of locally listdecoding binary error correcting codes with good parameters (that are polynomially related to information theoretic bounds). We show that computing majority over Θ(1/ǫ) bits is essentially equivalent to locally listdecoding binary codes from relative distance ..."
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Cited by 4 (1 self)
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to subexponential list sizes). This shows that the listdecoding radius of the constantdepth locallistdecoders of Goldwasser et al. [STOC07] is essentially optimal. Using the tight connection between locallylistdecodable codes and hardness amplification, we obtain similar limitations
Combinatorial limitations of a strong form of list decoding
 Electronic Colloquium on Computational Complexity (ECCC
, 2012
"... We prove the following results concerning the combinatorics of list decoding, motivated by the exponential gap between the known upper bound (of O(1/γ)) and lower bound (of Ωp(log(1/γ))) for the listsize needed to decode up to radius p with rate γ away from capacity, i.e., 1 − h(p) − γ (here p ∈ (0 ..."
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Cited by 3 (2 self)
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radius”. The motivation for this result is that it gives a listsize lower bound for a strong notion of list decoding; this strong form has been implicitly been used in the previous negative results for list decoding. (The usual notion of list decoding corresponds to replacing average radius
Combinatorial Bounds for List Decoding
 IEEE Transactions on Information Theory
, 2000
"... Informally, an errorcorrecting code has "nice" listdecodability properties if every Hamming ball of "large" radius has a "small" number of codewords in it. Here, we report linear codes with nontrivial listdecodability: i.e., codes of large rate that are nicely listde ..."
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Cited by 42 (24 self)
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Informally, an errorcorrecting code has "nice" listdecodability properties if every Hamming ball of "large" radius has a "small" number of codewords in it. Here, we report linear codes with nontrivial listdecodability: i.e., codes of large rate that are nicely
Decoding
, 2012
"... ses multivariate pattern analysis (MVPA). To what extent do these featureselective activity patterns depend on he sensory input, and might the reliability of these activity patterns be predicted NeuroImage 63 (2012) 1212–1222 Contents lists available at SciVerse ScienceDirect ..."
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ses multivariate pattern analysis (MVPA). To what extent do these featureselective activity patterns depend on he sensory input, and might the reliability of these activity patterns be predicted NeuroImage 63 (2012) 1212–1222 Contents lists available at SciVerse ScienceDirect
List Decoding: Algorithms and Applications
 SIGACT News
, 2000
"... Over the years coding theory and complexity theory have benefited from a number of mutually enriching connections. This article focuses on a new connection that has emerged between the two topics in the recent years. This connection is centered around the notion of "listdecoding" for ..."
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Cited by 36 (0 self)
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Over the years coding theory and complexity theory have benefited from a number of mutually enriching connections. This article focuses on a new connection that has emerged between the two topics in the recent years. This connection is centered around the notion of "listdecoding
Results 1  10
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