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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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The renaissance of gallager's low-density parity-check codes

IEEE Communications Magazine, 2003
LDPC codes were invented in 1960 by R. Gallager. They were largely ignored until the discovery of turbo codes in 1993. Since then, LDPC codes have experienced a renaissance and are now one of the most intensely studied areas in coding. In this article we review the basic structure of LDPC codes and the iterative algorithms that are used to decode them.
Tom Richardson 0001, Rüdiger L. Urbanke
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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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Low-Density Parity-Check codes [PDF]

, 2010
Transmition of data over various communication systems is lossy, because of all the noise affecting the communication channel. One of the most useful ways to achieve reliable transmision are error correcting codes. Recently, low-density parity-check codes became very popular.
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Low-density parity-check codes

IEEE Transactions on Information Theory, 1962
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Near Shannon limit performance of low density parity check codes

Electronics Letters, 1997
D J C Mackay
exaly