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Oversampled filter banks as error correction codes: Theory and impulse noise correction
 IEEE TRANSACTIONS ON SIGNAL PROCESSING
, 2005
"... Oversampled filter banks (OFBs) provide an overcomplete representation of their input signal. This paper describes how OFBs can be considered as errorcorrecting codes acting on real or complex sequences, very much like classical binary convolutional codes act on binary sequences. The structured red ..."
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Cited by 20 (6 self)
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Oversampled filter banks (OFBs) provide an overcomplete representation of their input signal. This paper describes how OFBs can be considered as errorcorrecting codes acting on real or complex sequences, very much like classical binary convolutional codes act on binary sequences. The structured
Constructing Free Energy Approximations and Generalized Belief Propagation Algorithms
 IEEE Transactions on Information Theory
, 2005
"... Important inference problems in statistical physics, computer vision, errorcorrecting coding theory, and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs. The belief propagation (BP) algorithm is an efficient way to solve these problems t ..."
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Cited by 585 (13 self)
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Important inference problems in statistical physics, computer vision, errorcorrecting coding theory, and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs. The belief propagation (BP) algorithm is an efficient way to solve these problems
Near Shannon limit errorcorrecting coding and decoding
, 1993
"... Abstract This paper deals with a new class of convolutional codes called Turbocodes, whose performances in terms of Bit Error Rate (BER) are close to the SHANNON limit. The TurboCode encoder is built using a parallel concatenation of two Recursive Systematic Convolutional codes and the associated ..."
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Cited by 1776 (6 self)
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Abstract This paper deals with a new class of convolutional codes called Turbocodes, whose performances in terms of Bit Error Rate (BER) are close to the SHANNON limit. The TurboCode encoder is built using a parallel concatenation of two Recursive Systematic Convolutional codes
Good ErrorCorrecting Codes based on Very Sparse Matrices
, 1999
"... We study two families of errorcorrecting codes defined in terms of very sparse matrices. "MN" (MacKayNeal) codes are recently invented, and "Gallager codes" were first investigated in 1962, but appear to have been largely forgotten, in spite of their excellent properties. The ..."
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Cited by 750 (23 self)
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We study two families of errorcorrecting codes defined in terms of very sparse matrices. "MN" (MacKayNeal) codes are recently invented, and "Gallager codes" were first investigated in 1962, but appear to have been largely forgotten, in spite of their excellent properties
Solving multiclass learning problems via errorcorrecting output codes
 JOURNAL OF ARTIFICIAL INTELLIGENCE RESEARCH
, 1995
"... Multiclass learning problems involve nding a de nition for an unknown function f(x) whose range is a discrete set containing k>2values (i.e., k \classes"). The de nition is acquired by studying collections of training examples of the form hx i;f(x i)i. Existing approaches to multiclass l ..."
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Cited by 726 (8 self)
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output representations. This paper compares these three approaches to a new technique in which errorcorrecting codes are employed as a distributed output representation. We show that these output representations improve the generalization performance of both C4.5 and backpropagation on a wide range
The Theory of ErrorCorrecting Codes
, 1998
"... The brachistochrone problem is to nd the curve between two points down which a bead will slide in the shortest amount of time, neglecting friction and assuming conservation of energy. To solve the problem, an integral is derived that computes the amount of time it would take a bead to slide down a g ..."
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The brachistochrone problem is to nd the curve between two points down which a bead will slide in the shortest amount of time, neglecting friction and assuming conservation of energy. To solve the problem, an integral is derived that computes the amount of time it would take a bead to slide down a given curve y(x). This integral is minimized over all possible curves and yields the di erential equation y(1+(y 0) 2) = k 2 asaconstraint for the minimizing function y(x). Solving this di erential equation shows that a cycloid (the path traced out by a point on the rim ofarolling wheel) is the solution to the brachistochrone problem. First proposed in 1696 by Johann Bernoulli, this problem is credited with having led to the development of the calculus of variations. The solution presented assumes knowledge of onedimensional calculus and elementary di erential equations.
ErrorCorrecting Codes for Multipermutations
"... PAPER AWARD. Multipermutations appear in various applications in information theory. New applications such as rank modulation for flash memories and voting have suggested the need to consider errorcorrecting codes for multipermutations. The construction of codes is challenging when permutations are ..."
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Cited by 4 (0 self)
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PAPER AWARD. Multipermutations appear in various applications in information theory. New applications such as rank modulation for flash memories and voting have suggested the need to consider errorcorrecting codes for multipermutations. The construction of codes is challenging when permutations
Errorcorrecting codes and genetics
"... Abstract: The conservation of genetic information through the ages can not be explained unless one assumes the existence of genomic errorcorrecting codes, our main hypothesis. Shielding by phenotypic membranes does not protect the genomes against radiations and their own quantum indeterminism. The ..."
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. The cumulated errors then make the genomic memory ephemeral at the time scale of geology. Only means intrinsic to the genome itself, taking the form of errorcorrecting codes, can ensure the genome permanency. According to information theory, they can achieve reliable communication over unreliable channels, so
A Theory of Quantum ErrorCorrecting Codes
, 1996
"... Quantum Error Correction will be necessary for preserving coherent states against noise and other unwanted interactions in quantum computation and communication. We develop a general theory of quantum error correction based on encoding states into larger Hilbert spaces subject to known interactions. ..."
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Cited by 101 (11 self)
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. We obtain necessary and sufficient conditions for the perfect recovery of an encoded state after its degradation by an interaction. The conditions depend only on the behavior of the logical states. We use them to give a recovery operator independent definition of errorcorrecting codes. We relate
on BLOCK ERRORCORRECTING CODES
, 2003
"... There is a unique way to teach: to lead the other person through the same experience with which you learned. Óscar Villarroya, cognitive scientist. 1 In this book, the mathematical aspects in our presentation of the basic theory of block errorcorrecting codes go together, in mutual reinforcement, w ..."
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There is a unique way to teach: to lead the other person through the same experience with which you learned. Óscar Villarroya, cognitive scientist. 1 In this book, the mathematical aspects in our presentation of the basic theory of block errorcorrecting codes go together, in mutual reinforcement
Results 1  10
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