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Low-Density Parity-Check Codes

The purpose of this work is to study how to communicate reliably through a noisy communication channel. In particular, we focus on the low-density parity-check error-correcting codes, which were introduced by Robert Gallager in his PhD thesis in 1963.
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Multilevel coding with low-density parity-check component codes

GLOBECOM'01. IEEE Global Telecommunications Conference (Cat. No.01CH37270), 2002
We design multilevel coding (MLC) schemes with low-density parity-check (LDPC) codes as component codes at each level. We develop a method to analyze the performance of an LDPC code at any level as the codeword length goes to infinity, even if the equivalent binary-input component channels are not symmetric.
Jilei Hou, Paul H. Siegel, Laurence B. Milstein, Henry D. Pfister   +3 more
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Low Density Parity Check Codes

2016
Besides the turbo codes, there is one more class of linear block codes that makes possible to approach to the Shannon bound. These are Low Density Parity Check (LDPC) codes. They were proposed by Gallager [83]. In principle they have a sparse parity - check matrix.
Predrag Ivaniš, Dušan Drajić
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Low-Density Parity-Check Codes

2000
Gallager first proposed low-density parity-check (LDPC) codes and their iterative detection algorithm in 1962 [Gallager, 1962]. They have been almost forgotten for thirty years. Recently, with the extensive research on “turbo-like” codes and on iterative detection, LDPC codes re-emerge as another category of random codes approaching the Shannon ...
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The semi-algebra low-density parity-check codes

2004 IEEE International Conference on Communications (IEEE Cat. No.04CH37577), 2004
In this paper, the construction of semi-algebra Low-density parity-check (LDPC) code with an arbitrary block length is presented. The encoding circuit is based on the original semi-algebra design and users can have the choice of using the matrix pattern and various code rates to design for different communication applications. Especially, a novel girth
Yu Yi, Gi Yean Hwang, Moon Ho Lee
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Low Density Parity Check Codes

2020
A linear code with a check matrix in which each column has few non-zero entries is called a low density parity check code or, for brevity, an LDPC code. These codes were introduced in the 1960s by Gallager who proved that probabilistic constructions of such matrices produce asymptotically good linear codes. Moreover, he observed that LDPC codes perform
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Low density parity check codes for the relay channel

IEEE Journal on Selected Areas in Communications, 2007
We propose Low Density Parity Check (LDPC) code designs for the half-duplex relay channel. Our designs are based on the information theoretic random coding scheme for decode-and-forward relaying. The source transmission is decoded with the help of side information in the form of additional parity bits from the relay.
Arnab Chakrabarti, Alexandre de Baynast, Ashutosh Sabharwal, Behnaam Aazhang   +3 more
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Low Density Parity Check Codes

2015
Low density parity check (LDPC) codes are forward error-correction codes, invented by Robert Gallager in his MIT Ph.D. dissertation, 1960. The LDPC codes are ignored for long time due to their high computational complexity and domination of highly structured algebraic block and convolutional codes for forward error correction.
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Rate-compatible low-density parity-check codes

International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings., 2004
Rate-compatible coding is appropriate for communication systems that experience a range of operating SNRs but seek to adhere to a single underlying codec structure. This paper constructs rate-compatible low-density parity-check (LDPC) codes by carefully selecting degree distributions, followed by a combination of information nulling and parity ...
Tao Tian, Chris Jones, John D. Villasenor   +2 more
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Low-Density Parity-Check Codes

2013
Low-density parity-check (LDPC) codes were introduced in 1960 by R. Gallager [1] in his Phd thesis. He already introduced the iterative method for decoding LDPC codes. However, also due to their computational and implementation complexity the iterative decoding was largely ignored.
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