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## On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit (2001)

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Venue: | IEEE COMMUNICATIONS LETTERS |

Citations: | 306 - 6 self |

### Citations

1776 | Near Shannon Limit Error-Correcting Coding and Decoding
- Berrou, Glavieux, et al.
- 1993
(Show Context)
Citation Context ...hen the block length of the code is large. This shows that LDPC codes|originally invented by Gallager [2], forgotten for decades, rediscovered by many [3], [4]|can now outperform powerful turbo codes =-=[5]-=- if designed properly. They also showed that for many interesting channels, including additive white Gaussian noise (AWGN) channels, one can use an algorithm called density evolution [6] to calculate ... |

1366 | Low-density parity-check codes,”
- Gallager
- 1962
(Show Context)
Citation Context ...ucted irregular lowdensity parity-check (LDPC) codes that easily beat the best known turbo codes when the block length of the code is large. This shows that LDPC codes|originally invented by Gallager =-=[2]-=-, forgotten for decades, rediscovered by many [3], [4]|can now outperform powerful turbo codes [5] if designed properly. They also showed that for many interesting channels, including additive white G... |

750 | Good error-correcting codes based on very sparse matrices,
- MacKay
- 1999
(Show Context)
Citation Context ...region asymptotically as the block length tends to innity. (Density evolution based on combinatorial or Monte Carlo approaches had been previously attempted by Gallager [2], Spielman [7], and MacKay [=-=8]-=-.) In this letter, we develop an improved implementation of density evolution called discretized density evolution [9]. We show that this improved algorithm models the exact behavior of discretized su... |

610 | Iterative Decoding of Binary Block and Convolutional Codes”,
- Hagenauer, Papke
- 1996
(Show Context)
Citation Context ...heck nodes can be obtained by observing the duality between variable and check nodes and the resulting Fourier transform relationship [10]. From this, we get the following well known \tanh rule" =-=(see [11]-=-): tanh u 2 = dc 1 Y j=1 tanh v j 2 ; (2) where v j ; i = 1; : : : ; d c 1, are the incoming LLRs from d c 1 neighbors of a degree-d c check node, and u is the output LLR message sent to the remaining... |

574 | Urbanke, “The capacity of low-density parity-check codes under message-passing decoding
- Richardson, L
- 2001
(Show Context)
Citation Context ...l turbo codes [5] if designed properly. They also showed that for many interesting channels, including additive white Gaussian noise (AWGN) channels, one can use an algorithm called density evolution =-=[6-=-] to calculate a threshold value for a randomly constructed irregular LDPC code which determines the boundary of the error-free region asymptotically as the block length tends to innity. (Density evol... |

500 | Near Shannon limit performance of low density parity check codes”,
- MacKay, Neal
- 1962
(Show Context)
Citation Context ...hat easily beat the best known turbo codes when the block length of the code is large. This shows that LDPC codes|originally invented by Gallager [2], forgotten for decades, rediscovered by many [3], =-=[4]-=-|can now outperform powerful turbo codes [5] if designed properly. They also showed that for many interesting channels, including additive white Gaussian noise (AWGN) channels, one can use an algorith... |

340 | Expander codes,”
- Sipser, Spielman
- 1996
(Show Context)
Citation Context ...des that easily beat the best known turbo codes when the block length of the code is large. This shows that LDPC codes|originally invented by Gallager [2], forgotten for decades, rediscovered by many =-=[3]-=-, [4]|can now outperform powerful turbo codes [5] if designed properly. They also showed that for many interesting channels, including additive white Gaussian noise (AWGN) channels, one can use an alg... |

244 | Analysis of sumproduct decoding of low-density parity-check codes using a Gaussian approximation,”
- Chung, Richardson, et al.
- 2001
(Show Context)
Citation Context ... )x j 1 + x j for some integer j 2. This restriction not only makes it easier to optimize (x), especially for large maximum variable degrees, but also is not too restrictive for the AWGN channel [12]. The average check degree av is used in Table II to parametrize (x) where av = (1 )(j 1) + j = j 1 + . TO APPEAR IN IEEE COMMUNICATIONS LETTERS 3 10 1 10 2 10 3 10 4 0 0.02 0.04 0.06 0.08 0.1... |

178 |
Codes on graphs: Normal realizations
- Forney
- 2001
(Show Context)
Citation Context ...t associated with the variable node. The message update rule for check nodes can be obtained by observing the duality between variable and check nodes and the resulting Fourier transform relationship =-=[10]. Fro-=-m this, we get the following well known \tanh rule" (see [11]): tanh u 2 = dc 1 Y j=1 tanh v j 2 ; (2) where v j ; i = 1; : : : ; d c 1, are the incoming LLRs from d c 1 neighbors of a degree-d c... |

84 | On the construction of some capacity-approaching coding schemes,”
- Chung
- 2000
(Show Context)
Citation Context ...pproaches had been previously attempted by Gallager [2], Spielman [7], and MacKay [8].) In this letter, we develop an improved implementation of density evolution called discretized density evolution =-=[9]-=-. We show that this improved algorithm models the exact behavior of discretized sum-product decoding. Using this algorithm and an improved optimization algorithm, we design good rate-1/2 irregular LDP... |

31 |
Design of capacity-approaching low-density parity-check codes
- Richardson, Shokrollahi, et al.
- 2001
(Show Context)
Citation Context ... limit at a bit error rate of 10 6 using a block length of 10 7 . Keywords| Density evolution, low-density parity-check codes, Shannon limit, sum-product algorithm. I. Introduction R ICHARDSON et al. =-=[1]-=- constructed irregular lowdensity parity-check (LDPC) codes that easily beat the best known turbo codes when the block length of the code is large. This shows that LDPC codes|originally invented by Ga... |

28 |
Codes on graphs: normal realizations
- Jr
- 2001
(Show Context)
Citation Context ...t associated with the variable node. The message update rule for check nodes can be obtained by observing the duality between variable and check nodes and the resulting Fourier transform relationship =-=[10]-=-. From this, we get the following well known “tanh rule” (see [11]): where are the incoming LLR’s from neighbors of a degree- check node, and is the output LLR message sent to the remaining neighbor. ... |

5 |
Finding good LDPC codes
- Spielman
- 1998
(Show Context)
Citation Context ... the error-free region asymptotically as the block length tends to innity. (Density evolution based on combinatorial or Monte Carlo approaches had been previously attempted by Gallager [2], Spielman [=-=7]-=-, and MacKay [8].) In this letter, we develop an improved implementation of density evolution called discretized density evolution [9]. We show that this improved algorithm models the exact behavior o... |