Results 1  10
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102
Approximate listdecoding of direct product . . .
"... Given a message msg ∈ {0, 1} N, its kwise direct product encoding is the sequence of ktuples (msg(i1),..., msg(ik)) over all possible ktuples of indices (i1,..., ik) ∈ {1,..., N} k. We give an efficient randomized algorithm for approximate local listdecoding of direct product codes. That is, gi ..."
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Cited by 33 (8 self)
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Given a message msg ∈ {0, 1} N, its kwise direct product encoding is the sequence of ktuples (msg(i1),..., msg(ik)) over all possible ktuples of indices (i1,..., ik) ∈ {1,..., N} k. We give an efficient randomized algorithm for approximate local listdecoding of direct product codes. That is
Sparse Approximation, List Decoding, and Uncertainty Principles∗
"... We consider list versions of sparse approximation problems, where unlike the existing results in sparse approximation that consider situations with unique solutions, we are interested in multiple solutions. We introduce these problems and present the first combinatorial results on the output list s ..."
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size. These generalize/enhance some of the existing results on threshold phenomenon and uncertainty principles in sparse approximations. Our definitions and results are inspired by similar results in list decoding. We also present lower bound examples that show that our results are in the correct
ListDecoding of VariableLength Codes
"... The residual redundancy that remains, intentionally or unintentionally, in source coded streams can be exploited by joint sourcechannel coding. This principle has been recently applied to variablelength encoded sequences via iterative decoding. This work improves on past results by proposing list ..."
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for variablelength codes (VLC's) with the help of a nonbinary outer CRC code. We show that the list Viterbi decoding of VLC's is beneficial, particularly for the redundant ones used in stateofart video coding standards. For a concatenated VLC and channel code, we propose an approximated listdecoder
List decoding for binary Goppa codes
, 2008
"... This paper presents a listdecoding algorithm for classical irreducible binary Goppa codes. The algorithm corrects, in polynomial time, approximately n − p n(n − 2t − 2) errors in a lengthn classical irreducible degreet binary Goppa code. Compared to the best previous polynomialtime listdecoding ..."
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Cited by 15 (4 self)
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This paper presents a listdecoding algorithm for classical irreducible binary Goppa codes. The algorithm corrects, in polynomial time, approximately n − p n(n − 2t − 2) errors in a lengthn classical irreducible degreet binary Goppa code. Compared to the best previous polynomialtime listdecoding
List decoding of ReedMuller codes
 in &quot;Proceedings of ACCT’9
, 2004
"... We construct list decoding algorithms for first order ReedMuller codes RM[1, m] of length n = 2m correcting up to n ( 1 2 − ɛ) errors with complexity O(nɛ−3). Considering probabilistic approximation of these algorithms leads to randomized list decoding algorithms with characteristics similar to Gol ..."
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Cited by 2 (0 self)
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We construct list decoding algorithms for first order ReedMuller codes RM[1, m] of length n = 2m correcting up to n ( 1 2 − ɛ) errors with complexity O(nɛ−3). Considering probabilistic approximation of these algorithms leads to randomized list decoding algorithms with characteristics similar
Proving hardcore predicates using list decoding.
 FOCS,
, 2003
"... ABSTRACT We introduce a unifying framework for proving that predicate P is hardcore for a oneway function f, and apply it to a broad family of functions and predicates, reproving old results in an entirely different way as well as showing new hardcore predicates for well known oneway function c ..."
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Cited by 41 (5 self)
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candidates. Our framework extends the listdecoding method of Goldreich and Levin for showing hardcore predicates. Namely, a predicate will correspond to some error correcting code, predicting a predicate will correspond to access to a corrupted code word, and the task of inverting oneway functions
ReedMuller codes List Decoding Algorithm Complexity
"... 2 Application to cryptanalysis Approximation of a bloc cipher 3 Power Analysis attacks overview ..."
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2 Application to cryptanalysis Approximation of a bloc cipher 3 Power Analysis attacks overview
On the complexity of approximating the vc dimension
 J. Comput. Syst. Sci
, 2001
"... We study the complexity of approximating the VC dimension of a collection of sets, when the sets are encoded succinctly by a small circuit. We show that this problem is • Σ p 3hard to approximate to within a factor 2 − ɛ for any ɛ> 0, • approximable in AM to within a factor 2, and • AMhard to a ..."
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Cited by 20 (3 self)
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hard to approximate to within a factor N ɛ for some constant ɛ> 0. To obtain the Σ p 3hardness result we solve a randomness extraction problem using listdecodable binary codes; for the positive result we utilize the SauerShelah(Perles) Lemma. The exact value of ɛ in the AMhardness result depends on the degree
Efficiently decodable compressed sensing by listrecoverable codes and recursion
 In STACS
, 2012
"... We present two recursive techniques to construct compressed sensing schemes that can be “decoded" in sublinear time. The first technique is based on the well studied code composition method called code concatenation where the “outer " code has strong list recoverability properties. This t ..."
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Cited by 5 (4 self)
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We present two recursive techniques to construct compressed sensing schemes that can be “decoded" in sublinear time. The first technique is based on the well studied code composition method called code concatenation where the “outer " code has strong list recoverability properties
Block Error Probability using List Viterbi Decoding with Hard Decisions
, 2000
"... We consider the List Viterbi Algorithm (LVA) for block decoding of a concatenated channel coding system. The inner code is either convolutional or rate compatible punctured convolutional (RCPC), and the outer code is a cyclic redundancy check (CRC). The block error probability is defined as the prob ..."
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Cited by 1 (0 self)
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We consider the List Viterbi Algorithm (LVA) for block decoding of a concatenated channel coding system. The inner code is either convolutional or rate compatible punctured convolutional (RCPC), and the outer code is a cyclic redundancy check (CRC). The block error probability is defined
Results 1  10
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102