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244
On the design of lowdensity paritycheck codes within 0.0045 dB of the Shannon limit
 IEEE COMMUNICATIONS LETTERS
, 2001
"... We develop improved algorithms to construct good lowdensity paritycheck codes that approach the Shannon limit very closely. For rate 1/2, the best code found has a threshold within 0.0045 dB of the Shannon limit of the binaryinput additive white Gaussian noise channel. Simulation results with a ..."
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Cited by 306 (6 self)
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We develop improved algorithms to construct good lowdensity paritycheck codes that approach the Shannon limit very closely. For rate 1/2, the best code found has a threshold within 0.0045 dB of the Shannon limit of the binaryinput additive white Gaussian noise channel. Simulation results with a somewhat simpler code show that we can achieve within 0.04 dB of the Shannon limit at a bit error rate of 10 T using a block length of 10 U.
"Turbo equalization": principles and new results
, 2000
"... Since the invention of \turbo codes" by Berrou et al. in 1993, the \turbo principle" has been adapted to several communication problems such as \turbo equalization", \turbo trellis coded modulation", and iterative multi user detection. In this paper we study the \turbo equalizati ..."
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Cited by 274 (25 self)
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Since the invention of \turbo codes" by Berrou et al. in 1993, the \turbo principle" has been adapted to several communication problems such as \turbo equalization", \turbo trellis coded modulation", and iterative multi user detection. In this paper we study the \turbo equalization" approach, which can be applied to coded data transmission over channels with intersymbol interference (ISI). In the original system invented by Douillard et al., the data is protected by a convolutional code and a receiver consisting of two trellisbased detectors are used, one for the channel (the equalizer) and one for the code (the decoder). It has been shown that iterating equalization and decoding tasks can yield tremendous improvements in bit error rate (BER). We introduce new approaches to combining equalization based on linear ltering with the decoding. The result is a receiver that is capable of improving BER performance through iterations of equalization and decoding in a manner similar to turbo ...
Compression of binary sources with side information using lowdensity paritycheck codes
 in Proc. Global Telecommunications Conf
, 2002
"... Abstract—We show how lowdensity paritycheck (LDPC) codes can be used to compress close to the Slepian–Wolf limit for correlated binary sources. Focusing on the asymmetric case of compression of an equiprobable memoryless binary source with side information at the decoder, the approach is based o ..."
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Cited by 209 (6 self)
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Abstract—We show how lowdensity paritycheck (LDPC) codes can be used to compress close to the Slepian–Wolf limit for correlated binary sources. Focusing on the asymmetric case of compression of an equiprobable memoryless binary source with side information at the decoder, the approach is based on viewing the correlation as a channel and applying the syndrome concept. The encoding and decoding procedures are explained in detail. The performance achieved is seen to be better than recently published results using turbo codes and very close to the Slepian–Wolf limit. Index Terms—Channel coding, distributed source coding, LDPC codes, Slepian–Wolf theorem. I.
Extrinsic Information Transfer Functions: A Model and Two Properties,”
 in Proc. Conference on Information Sciences and Systems (CISS),
, 2002
"... ..."
Irregular RepeatAccumulate Codes
, 2000
"... In this paper we will introduce an ensemble of codes called irregular repeataccumulate (IRA) codes. IRA codes are a generalization of the repeataccumulate codes introduced in [1], and as such have a natural linear time encoding algorithm. We shall prove that on the binary erasure channel, IRA code ..."
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Cited by 151 (1 self)
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In this paper we will introduce an ensemble of codes called irregular repeataccumulate (IRA) codes. IRA codes are a generalization of the repeataccumulate codes introduced in [1], and as such have a natural linear time encoding algorithm. We shall prove that on the binary erasure channel, IRA codes can be decoded reliably in linear time, using iterative sumproduct decoding,a# ra#SJ a#SJ8T a#SJ8 close tocha#T36 ca pa#J464 Asimila# resulta#u ea#S to be true on the AWGN channel, although we have no proof of this. We illustrate our results with numerical and experimental examples.
Generalized Approximate Message Passing for Estimation with Random Linear Mixing
, 2012
"... We consider the estimation of an i.i.d. random vector observed through a linear transform followed by a componentwise, probabilistic (possibly nonlinear) measurement channel. A novel algorithm, called generalized approximate message passing (GAMP), is presented that provides computationally effici ..."
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Cited by 123 (18 self)
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We consider the estimation of an i.i.d. random vector observed through a linear transform followed by a componentwise, probabilistic (possibly nonlinear) measurement channel. A novel algorithm, called generalized approximate message passing (GAMP), is presented that provides computationally efficient approximate implementations of maxsum and sumproblem loopy belief propagation for such problems. The algorithm extends earlier approximate message passing methods to incorporate arbitrary distributions on both the input and output of the transform and can be applied to a wide range of problems in nonlinear compressed sensing and learning. Extending an analysis by Bayati and Montanari, we argue that the asymptotic componentwise behavior of the GAMP method under large, i.i.d. Gaussian transforms is described by a simple set of state evolution (SE) equations. From the SE equations, one can exactly predict the asymptotic value of virtually any componentwise performance metric including meansquared error or detection accuracy. Moreover, the analysis is valid for arbitrary input and output distributions, even when the corresponding optimization problems are nonconvex. The results match predictions by Guo and Wang for relaxed belief propagation on large sparse matrices and, in certain instances, also agree with the optimal performance predicted by the replica method. The GAMP methodology thus provides a computationally efficient methodology, applicable to a large class of nonGaussian estimation problems with precise asymptotic performance guarantees.
Iterative multiuser joint decoding: unified framework and asymptotic analysis
 IEEE TRANS. INFORM. THEORY
, 2002
"... We present a framework for iterative multiuser joint decoding of codedivision multipleaccess (CDMA) signals, based on the factorgraph representation and on the sumproduct algorithm. In this framework, known parallel and serial, hard and soft interference cancellation algorithms are derived in a ..."
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Cited by 116 (3 self)
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We present a framework for iterative multiuser joint decoding of codedivision multipleaccess (CDMA) signals, based on the factorgraph representation and on the sumproduct algorithm. In this framework, known parallel and serial, hard and soft interference cancellation algorithms are derived in a unified way. The asymptotic performance of these algorithms in the limit of large code block length can be rigorously analyzed by using density evolution. We show that, for random spreading in the largesystem limit, density evolution is considerably simplified. Moreover, by making a Gaussian approximation of the decoder soft output, we show that the behavior of iterative multiuser joint decoding is approximately characterized by the stable fixed points of a simple onedimensional nonlinear dynamical system.
Iterative turbo decoder analysis based on density evolution
 IEEE J. Select. Areas Commun
, 2001
"... We track the density of extrinsic information in iterative turbo decoders by actual ..."
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Cited by 99 (3 self)
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We track the density of extrinsic information in iterative turbo decoders by actual
LDPC block and convolutional codes based on circulant matrices
 IEEE TRANS. INFORM. THEORY
, 2004
"... A class of algebraically structured quasicyclic (QC) lowdensity paritycheck (LDPC) codes and their convolutional counterparts is presented. The QC codes are described by sparse paritycheck matrices comprised of blocks of circulant matrices. The sparse paritycheck representation allows for prac ..."
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Cited by 93 (8 self)
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A class of algebraically structured quasicyclic (QC) lowdensity paritycheck (LDPC) codes and their convolutional counterparts is presented. The QC codes are described by sparse paritycheck matrices comprised of blocks of circulant matrices. The sparse paritycheck representation allows for practical graphbased iterative messagepassing decoding. Based on the algebraic structure, bounds on the girth and minimum distance of the codes are found, and several possible encoding techniques are described. The performance of the QC LDPC block codes compares favorably with that of randomly constructed LDPC codes for short to moderate block lengths. The performance of the LDPC convolutional codes is superior to that of the QC codes on which they are based; this performance is the limiting performance obtained by increasing the circulant size of the base QC code. Finally, a continuous decoding procedure for the LDPC convolutional codes is described.
RateCompatible Puncturing of LowDensity ParityCheck Codes
 IEEE TRANS. INFORMATION THEORY
, 2004
"... In this correspondence, we consider puncturing of lowdensity paritycheck (LDPC) codes for additive white Gaussian noise (AWGN) channels. We show that good puncturing patterns exist and that the puncturing can be performed in a ratecompatible fashion. Furthermore, ratecompatible puncturing result ..."
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Cited by 84 (2 self)
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In this correspondence, we consider puncturing of lowdensity paritycheck (LDPC) codes for additive white Gaussian noise (AWGN) channels. We show that good puncturing patterns exist and that the puncturing can be performed in a ratecompatible fashion. Furthermore, ratecompatible puncturing results in a small loss of performance with respect to threshold, namely, the punctured code is good (in terms of threshold) across a range of rates when compared with the optimal codes for each rate. This allows one to implement a single “mother” encoder and decoder that is good across a wide range of rates.