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914
An exponential number of generalized Kerdock codes
 Inform. Control
, 1982
"... If n 1 is an odd composite integer then there are at least 2 tl/2)~f ~ pairwise inequivalent binary errorcorrecting codes of length 2 n, size 22n, and minimum distance 2 n 12(1/2)n 1. 1. ..."
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Cited by 10 (6 self)
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If n 1 is an odd composite integer then there are at least 2 tl/2)~f ~ pairwise inequivalent binary errorcorrecting codes of length 2 n, size 22n, and minimum distance 2 n 12(1/2)n 1. 1.
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
Reducing Multiclass to Binary: A Unifying Approach for Margin Classifiers
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2000
"... We present a unifying framework for studying the solution of multiclass categorization problems by reducing them to multiple binary problems that are then solved using a marginbased binary learning algorithm. The proposed framework unifies some of the most popular approaches in which each class ..."
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Cited by 561 (20 self)
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is compared against all others, or in which all pairs of classes are compared to each other, or in which output codes with errorcorrecting properties are used. We propose a general method for combining the classifiers generated on the binary problems, and we prove a general empirical multiclass loss bound
Loopy belief propagation for approximate inference: An empirical study. In:
 Proceedings of Uncertainty in AI,
, 1999
"... Abstract Recently, researchers have demonstrated that "loopy belief propagation" the use of Pearl's polytree algorithm in a Bayesian network with loops can perform well in the context of errorcorrecting codes. The most dramatic instance of this is the near Shannonlimit performanc ..."
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Cited by 676 (15 self)
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Abstract Recently, researchers have demonstrated that "loopy belief propagation" the use of Pearl's polytree algorithm in a Bayesian network with loops can perform well in the context of errorcorrecting codes. The most dramatic instance of this is the near Shannon
Good quantum error correcting codes exist
 REV. A
, 1996
"... A quantum errorcorrecting code is defined to be a unitary mapping (encoding) of k qubits (2state quantum systems) into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not necessarily independently, the resulting n qubits can be used ..."
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Cited by 349 (9 self)
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be used to faithfully reconstruct the original quantum state of the k encoded qubits. Quantum errorcorrecting codes are shown to exist with asymptotic rate k/n = 1 − 2H2(2t/n) where H2(p) is the binary entropy function −p log2 p − (1 − p)log2(1 − p). Upper bounds on this asymptotic rate are given.
ErrorCorrecting Output Coding Corrects Bias and Variance
 In Proceedings of the Twelfth International Conference on Machine Learning
, 1995
"... Previous research has shown that a technique called errorcorrecting output coding (ECOC) can dramatically improve the classification accuracy of supervised learning algorithms that learn to classify data points into one of k AE 2 classes. This paper presents an investigation of why the ECOC techniq ..."
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Cited by 170 (5 self)
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ECOC can correct for errors caused by the bias of the learning algorithm. Experiments show that this bias correction ability relies on the nonlocal behavior of C4.5. 1 Introduction Errorcorrecting output coding (ECOC) is a method for applying binary (twoclass) learning algorithms to solve k
Recoding ErrorCorrecting Output Codes
"... Abstract. One of the most widely applied techniques to deal with multiclass categorization problems is the pairwise voting procedure. Recently, this classical approach has been embedded in the ErrorCorrecting Output Codes framework (ECOC). This framework is based on a coding step, where a set of bi ..."
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Cited by 2 (0 self)
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Abstract. One of the most widely applied techniques to deal with multiclass categorization problems is the pairwise voting procedure. Recently, this classical approach has been embedded in the ErrorCorrecting Output Codes framework (ECOC). This framework is based on a coding step, where a set
Learning ErrorCorrecting Output Codes from Data
 In ICANN'99
, 1999
"... A polychotomizer which assigns the input to one of K 3 classes is constructed using a set of dichotomizers which assign the input to one of two classes. Defining classes in terms of the dichotomizers is the binary decomposition matrix of size K \Theta L where each of the K 3 classes is written as ..."
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Cited by 14 (0 self)
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as errorcorrecting output codes (ECOC), i.e., an array of the responses of binary decisions made by L dichotomizers. We use linear dichotomizers and by combining them suitably, we build nonlinear polychotomizers, thereby reducing complex decisions into a group of simpler decisions. We propose a new
Results 1  10
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914