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Low-Density Parity-Check Codes
2009AbstractLow-density parity-check (LDPC) codes are among the most efficient error correcting codes in use. This chapter introduces an important family of LDPC ensembles, based on random factor graphs, and studies some of their basic properties. It focuses on performances under optimal decoding, when no constraint is imposed on the computational ...
Marc Mézard, Andrea Montanari
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Low-density parity-check codes
IEEE Transactions on Information Theory, 1962openaire +4 more sources
Structured Low-Density Parity-Check Codes
IEEE Signal Processing Magazine, 2004This article describes the different methods to design regular low density parity-check (LDPC) codes with large girth. In graph terms, this corresponds to designing bipartite undirected regular graphs with large girth. Large girth speeds the convergence of iterative decoding and improves the performance at least in the high SNR range, by slowing down ...
Alexander Kuznetsov +3 more
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GRAPHICAL QUANTUM LOW-DENSITY PARITY-CHECK CODES
International Journal of Modern Physics B, 2012Graphical approach provides a direct way to construct error correction codes. Motivated by its good properties, associating low-density parity-check (LDPC) codes, in this paper we present families of graphical quantum LDPC codes which contain no girth of four.
Li, Yuan +3 more
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Low Density Parity Check Codes
2020A 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
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.+5 more sources
Low Density Parity Check Codes
2016Besides 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
2014The Tanner graph is described. A girth in the Tanner graph is equivalent to a short cycle of 1- symbols in the parity check matrix. The condition called row-column constraint is introduced, in order to allow practical decoding procedures. They are based on the sum-product algorithm, which is briefly outlined.
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Low-Density Parity-Check Codes
2000Gallager 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
1963This is a complete presentation of all important theoretical and experimental work done on low-density codes. Low-density coding is one of the three techniques thus far developed for efficient communication over noisy channels with an arbitrarily low probability of error. A principal result of information theory is that if properly coded information is
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