## Comparison of constructions of irregular Gallager codes (1999)

Venue: | IEEE Transactions on Communications |

Citations: | 44 - 5 self |

### BibTeX

@ARTICLE{Mackay99comparisonof,

author = {David J. C. Mackay and Simon T. Wilson and Matthew C. Davey},

title = {Comparison of constructions of irregular Gallager codes},

journal = {IEEE Transactions on Communications},

year = {1999},

volume = {47},

pages = {1449--1454}

}

### OpenURL

### Abstract

Abstract The low density parity check codes whose performance is closest to the Shannon limit are `Gallager codes ' based on irregular graphs. We compare alternative methods for constructing these graphs and present two results. First, we find a `super-Poisson ' construction which gives a small improvement in empirical performance over a random construction.

### Citations

566 | Good Error-Correcting Codes based on Very Sparse Matrices
- MacKay
- 1999
(Show Context)
Citation Context ...e weight 3 columns.] These codes are asymptotically good, and can be practically decoded with Gallager's sum--product algorithm giving near Shannon limit performance when large block lengths are used =-=[8, 9, 6]-=-. Regular Gallager codes have also been found to be competitive codes for short block-length CDMA applications [11]. Recent advances in the performance of Gallager codes are summarised in figure 1. Th... |

470 |
Low density parity check codes
- Gallager
- 1963
(Show Context)
Citation Context ...es which allow more rapid encoding and have smaller memory requirements in the encoder. We find that these `fast--encoding' Gallager codes have equally good performance. 1 Introduction Gallager codes =-=[3, 4]-=- are low density parity check codes constructed at random subject to constraints on the weight of each row and of each column. The original regular Gallager codes have very sparse random parity check ... |

359 | Near Shannon limit performance of low density parity check codes
- MacKay, Neal
- 1996
(Show Context)
Citation Context ...me weight 3 columns.] These codes are asymptotically good, and can be practically decoded with Gallager's sum-product algorithm giving near Shannon limit performance when large block lengths are used =-=[7, 8, 6]-=-. Regular Gallager codes have also been found to be competitive codes for short block-length CDMA applications [10]. Recent advances in the performance of Gallager codes are summarised in figure 1. Th... |

339 | Turbo decoding as an instance of Pearl’s ’belief propagation’ algorithm
- McEliece, MacKay, et al.
- 1998
(Show Context)
Citation Context ... whereas Turbo codes make undetected errors at high signal to noise ratio. This difference is not caused by a difference in the decoding algorithm: both codes are decoded by the sum-product algorithm =-=[9]-=-. Turbo Codes make undetected errors because they have low-weight codewords. For Gallager codes, the rate of occurrence of undetected errors is extremely small because they have good distance properti... |

176 | Improved low-density parity-check codes using irregular graphs
- Luby, Mitzenmacher, et al.
- 2001
(Show Context)
Citation Context ...ost curve shows the performance of a regular binary Gallager code with rate 1/4. The best known binary Gallager codes are irregular codes whose parity check matrices have nonuniform weight per column =-=[5]-=-; the performance of one such code is shown by the second curve from the right. The best known Gallager codes of all are Gallager codes defined over finite fields GF (q) [2, 1]. The remaining two soli... |

122 | Linear-time encodable and decodable error-correcting codes
- Spielman
- 1996
(Show Context)
Citation Context ...= 0:7dB the error rates are 0.035 and 0.097. 4 Fast-encoding Gallager codes One of the possible drawbacks of Gallager codes is that their encoding time generally scales as N 2. Inspired by Spielman's =-=[11]-=- work, we have investigated constructions of Gallager codes whose profiles are similar to or identical to the 3 and 93 profiles above, but which are fast-encoding. The general form of parity check mat... |

91 | Low Density Parity Check Codes over GF (q
- Davey, MacKay
- 1998
(Show Context)
Citation Context ...nuniform weight per column [5]; the performance of one such code is shown by the second curve from the right. The best known Gallager codes of all are Gallager codes defined over finite fields GF (q) =-=[2, 1]-=-. The remaining two solid curves in figure 1 show the performance of a regular Gallager code over GF (16) [2] and an irregular code over GF (8) with bit error probability of 10 \Gamma4 at E b =N 0 = \... |

83 | Good codes based on very sparse matrices
- MacKay, Neal
- 1995
(Show Context)
Citation Context ...e weight 3 columns.] These codes are asymptotically good, and can be practically decoded with Gallager's sum--product algorithm giving near Shannon limit performance when large block lengths are used =-=[8, 9, 6]-=-. Regular Gallager codes have also been found to be competitive codes for short block-length CDMA applications [11]. Recent advances in the performance of Gallager codes are summarised in figure 1. Th... |

25 |
Low Density Parity Check Codes. Number 21 in MIT Research monograph series
- Gallager
- 1963
(Show Context)
Citation Context ...es which allow more rapid encoding and have smaller memory requirements in the encoder. We find that these `fast--encoding' Gallager codes have equally good performance. 1 Introduction Gallager codes =-=[3, 4]-=- are low density parity check codes constructed at random subject to constraints on the weight of each row and of each column. The original regular Gallager codes have very sparse random parity check ... |

6 |
Improved low density parity-check codes using irregular graphs and belief propagation
- Luby, Mitzenmacher, et al.
- 1998
(Show Context)
Citation Context ...ost curve shows the performance of a regular binary Gallager code with rate 1/4. The best known binary Gallager codes are irregular codes whose parity check matrices have nonuniform weight per column =-=[5]-=-; the performance of one such code is shown by the second curve from the right. The best known Gallager codes of all are Gallager codes defined over finite fields GF (q) [2, 1]. The remaining two soli... |

1 | Codes from Cayley graphs - MacKay, Lafferty - 1997 |

1 |
Gallager codes for CDMA applications II: Implementations, complexity and system capacity
- Sorokine, Kschischang, et al.
- 1998
(Show Context)
Citation Context ...gorithm giving near Shannon limit performance when large block lengths are used [7, 8, 6]. Regular Gallager codes have also been found to be competitive codes for short block-length CDMA applications =-=[10]-=-. Recent advances in the performance of Gallager codes are summarised in figure 1. The rightmost curve shows the performance of a regular binary Gallager code with rate 1/4. The best known binary Gall... |