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Low-Density Parity-Check Codes

by Robert G. Gallager , 1963
"... Preface The Noisy Channel Coding Theorem discovered by C. E. Shannon in 1948 offered communication engineers the possibility of reducing error rates on noisy channels to negligible levels without sacrificing data rates. The primary obstacle to the practical use of this theorem has been the equipment ..."
Abstract - Cited by 1366 (1 self) - Add to MetaCart
Preface The Noisy Channel Coding Theorem discovered by C. E. Shannon in 1948 offered communication engineers the possibility of reducing error rates on noisy channels to negligible levels without sacrificing data rates. The primary obstacle to the practical use of this theorem has been

The Capacity of Low-Density Parity-Check Codes Under Message-Passing Decoding

by Thomas J. Richardson, Rüdiger L. Urbanke , 2001
"... In this paper, we present a general method for determining the capacity of low-density parity-check (LDPC) codes under message-passing decoding when used over any binary-input memoryless channel with discrete or continuous output alphabets. Transmitting at rates below this capacity, a randomly chos ..."
Abstract - Cited by 574 (9 self) - Add to MetaCart
In this paper, we present a general method for determining the capacity of low-density parity-check (LDPC) codes under message-passing decoding when used over any binary-input memoryless channel with discrete or continuous output alphabets. Transmitting at rates below this capacity, a randomly

Design of capacity-approaching irregular low-density parity-check codes

by Thomas J. Richardson, M. Amin Shokrollahi, Rüdiger L. Urbanke - IEEE TRANS. INFORM. THEORY , 2001
"... We design low-density parity-check (LDPC) codes that perform at rates extremely close to the Shannon capacity. The codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides. Our theoretical analysis of the codes is based on [1]. Assuming that the unde ..."
Abstract - Cited by 588 (6 self) - Add to MetaCart
We design low-density parity-check (LDPC) codes that perform at rates extremely close to the Shannon capacity. The codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides. Our theoretical analysis of the codes is based on [1]. Assuming

Unveiling Turbo Codes: Some Results on Parallel Concatenated Coding Schemes

by Sergio Benedetto, Guido Montorsi , 1995
"... A parallel concatenated coding scheme consists of two simple constituent systematic encoders linked by an interleaver. The input bits to the first encoder are scrambled by the interleaver before entering the second encoder. The codeword of the parallel concatenated code consists of the input bits to ..."
Abstract - Cited by 314 (6 self) - Add to MetaCart
to the first encoder followed by the parity check bits of both encoders. This construction can be generalized to any number of constituent codes. Parallel concatenated schemes employing two convolutional codes as constituent codes, in connection with an iterative decoding algorithm of complexity comparable

On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit

by Sae-young Chung, G. David Forney, Jr., Thomas J. Richardson, Rüdiger Urbanke - IEEE COMMUNICATIONS LETTERS , 2001
"... We develop improved algorithms to construct good low-density parity-check 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 binary-input additive white Gaussian noise channel. Simulation results with a ..."
Abstract - Cited by 306 (6 self) - Add to MetaCart
We develop improved algorithms to construct good low-density parity-check 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 binary-input additive white Gaussian noise channel. Simulation results with a

Nested Linear/Lattice Codes for Structured Multiterminal Binning

by Ram Zamir, Shlomo Shamai (Shitz), Uri Erez , 2002
"... Network information theory promises high gains over simple point-to-point communication techniques, at the cost of higher complexity. However, lack of structured coding schemes limited the practical application of these concepts so far. One of the basic elements of a network code is the binning sch ..."
Abstract - Cited by 345 (14 self) - Add to MetaCart
proposed the idea of nested codes, or more specifically, nested parity-check codes for the binary case and nested lattices in the continuous case. These ideas connect network information theory with the rich areas of linear codes and lattice codes, and have strong potential for practical applications. We

Improved low-density parity-check codes using irregular graphs

by Michael G. Luby, Michael Mitzenmacher, M. Amin Shokrollahi, Daniel A. Spielman - IEEE Trans. Inform. Theory , 2001
"... Abstract—We construct new families of error-correcting codes based on Gallager’s low-density parity-check codes. We improve on Gallager’s results by introducing irregular parity-check matrices and a new rigorous analysis of hard-decision decoding of these codes. We also provide efficient methods for ..."
Abstract - Cited by 223 (15 self) - Add to MetaCart
Abstract—We construct new families of error-correcting codes based on Gallager’s low-density parity-check codes. We improve on Gallager’s results by introducing irregular parity-check matrices and a new rigorous analysis of hard-decision decoding of these codes. We also provide efficient methods

Analysis of sum-product decoding of low-density parity-check codes using a Gaussian approximation

by Sae-Young Chung, Thomas J. Richardson, Rüdiger L. Urbanke - IEEE TRANS. INFORM. THEORY , 2001
"... Density evolution is an algorithm for computing the capacity of low-density parity-check (LDPC) codes under messagepassing decoding. For memoryless binary-input continuous-output additive white Gaussian noise (AWGN) channels and sum-product decoders, we use a Gaussian approximation for message densi ..."
Abstract - Cited by 244 (2 self) - Add to MetaCart
Density evolution is an algorithm for computing the capacity of low-density parity-check (LDPC) codes under messagepassing decoding. For memoryless binary-input continuous-output additive white Gaussian noise (AWGN) channels and sum-product decoders, we use a Gaussian approximation for message

Efficient Encoding of Low-Density Parity-Check Codes

by Thomas J. Richardson, Rüdiger L. Urbanke , 2001
"... Low-density parity-check (LDPC) codes can be considered serious competitors to turbo codes in terms of performance and complexity and they are based on a similar philosophy: constrained random code ensembles and iterative decoding algorithms. In this paper, we consider the encoding problem for LDPC ..."
Abstract - Cited by 183 (3 self) - Add to MetaCart
Low-density parity-check (LDPC) codes can be considered serious competitors to turbo codes in terms of performance and complexity and they are based on a similar philosophy: constrained random code ensembles and iterative decoding algorithms. In this paper, we consider the encoding problem

Compression of binary sources with side information using low-density parity-check codes

by Angelos D. Liveris, Student Member, Zixiang Xiong, Senior Member, Costas N. Georghiades - in Proc. Global Telecommunications Conf , 2002
"... Abstract—We show how low-density parity-check (LDPC) codes can be used to compress close to the Slepian–Wolf limit for cor-related binary sources. Focusing on the asymmetric case of com-pression of an equiprobable memoryless binary source with side information at the decoder, the approach is based o ..."
Abstract - Cited by 209 (6 self) - Add to MetaCart
Abstract—We show how low-density parity-check (LDPC) codes can be used to compress close to the Slepian–Wolf limit for cor-related binary sources. Focusing on the asymmetric case of com-pression of an equiprobable memoryless binary source with side information at the decoder, the approach is based
Results 1 - 10 of 3,321