Results 1 - 10 of 102

Approximate list-decoding of direct product . . .

by Russell Impagliazzo, Ragesh Jaiswal, Valentine Kabanets
"... Given a message msg ∈ {0, 1} N, its k-wise direct product encoding is the sequence of k-tuples (msg(i1),..., msg(ik)) over all possible k-tuples of indices (i1,..., ik) ∈ {1,..., N} k. We give an efficient randomized algorithm for approximate local list-decoding of direct product codes. That is, gi ..."
Abstract - Cited by 33 (8 self) - Add to MetaCart
Given a message msg ∈ {0, 1} N, its k-wise direct product encoding is the sequence of k-tuples (msg(i1),..., msg(ik)) over all possible k-tuples of indices (i1,..., ik) ∈ {1,..., N} k. We give an efficient randomized algorithm for approximate local list-decoding of direct product codes. That is

Sparse Approximation, List Decoding, and Uncertainty Principles∗

by Mahmoud Abo, Khamis Anna, C. Gilbert, Hung Q. Ngo, Atri Rudra
"... 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 solu-tions. 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 princi-ples 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

List-Decoding of Variable-Length Codes

by With Application In, Ahmadreza Hedayat, Aria Nosratinia
"... The residual redundancy that remains, intentionally or unintentionally, in source coded streams can be exploited by joint source-channel coding. This principle has been recently applied to variable-length encoded sequences via iterative decoding. This work improves on past results by proposing list- ..."
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for variable-length codes (VLC's) with the help of a non-binary outer CRC code. We show that the list Viterbi decoding of VLC's is beneficial, particularly for the redundant ones used in state-of-art video coding standards. For a concatenated VLC and channel code, we propose an approximated list-decoder

List decoding for binary Goppa codes

by Daniel J. Bernstein , 2008
"... This paper presents a list-decoding algorithm for classical irreducible binary Goppa codes. The algorithm corrects, in polynomial time, approximately n − p n(n − 2t − 2) errors in a length-n classical irreducible degree-t binary Goppa code. Compared to the best previous polynomialtime list-decoding ..."
Abstract - Cited by 15 (4 self) - Add to MetaCart
This paper presents a list-decoding algorithm for classical irreducible binary Goppa codes. The algorithm corrects, in polynomial time, approximately n − p n(n − 2t − 2) errors in a length-n classical irreducible degree-t binary Goppa code. Compared to the best previous polynomialtime list-decoding

List decoding of Reed-Muller codes

by Grigory Kabatiansky, Cédric Tavernier - in "Proceedings of ACCT’9 , 2004
"... We construct list decoding algorithms for first order Reed-Muller 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 ..."
Abstract - Cited by 2 (0 self) - Add to MetaCart
We construct list decoding algorithms for first order Reed-Muller 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 hard-core predicates using list decoding.

by Adi Akavia , Shafi Goldwasser , Samuel Safra - FOCS, , 2003
"... ABSTRACT We introduce a unifying framework for proving that predicate P is hard-core for a one-way 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 hard-core predicates for well known one-way function c ..."
Abstract - Cited by 41 (5 self) - Add to MetaCart
candidates. Our framework extends the list-decoding method of Goldreich and Levin for showing hard-core 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 one-way functions

Reed-Muller codes List Decoding Algorithm Complexity

by Ilya Dumer, Rafael Fourquet, Grigory Kabatiansky, Pierre Loidreau, Thomas Roche
"... 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

by Elchanan Mossel - 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 3-hard to approximate to within a factor 2 − ɛ for any ɛ> 0, • approximable in AM to within a factor 2, and • AM-hard to a ..."
Abstract - Cited by 20 (3 self) - Add to MetaCart
-hard to approximate to within a factor N ɛ for some constant ɛ> 0. To obtain the Σ p 3-hardness result we solve a randomness extraction problem using list-decodable binary codes; for the positive result we utilize the Sauer-Shelah(-Perles) Lemma. The exact value of ɛ in the AM-hardness result depends on the degree

Efficiently decodable compressed sensing by list-recoverable codes and recursion

by Hung Q. Ngo, Ely Porat, Atri Rudra - In STACS , 2012
"... We present two recursive techniques to construct compressed sensing schemes that can be “decoded" in sub-linear 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 ..."
Abstract - Cited by 5 (4 self) - Add to MetaCart
We present two recursive techniques to construct compressed sensing schemes that can be “decoded" in sub-linear 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

by Salim Manji, Narayan B. Mandayam , 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 ..."
Abstract - Cited by 1 (0 self) - Add to MetaCart
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 of 102