## LT Codes (2002)

### Cached

### Download Links

- [people.cs.uchicago.edu]
- [www.cc.gatech.edu]
- [cs.wisc.edu]
- [www.cs.wisc.edu]
- DBLP

### Other Repositories/Bibliography

Citations: | 333 - 2 self |

### BibTeX

@MISC{Luby02ltcodes,

author = {Michael Luby},

title = {LT Codes},

year = {2002}

}

### Years of Citing Articles

### OpenURL

### Abstract

We introduce LT codes, the first rateless erasure codes that are very efficient as the data length grows.

### Citations

1950 |
Sloane The Theory of Error-Correcting Codes
- MacWilliams, A
- 1977
(Show Context)
Citation Context ...ss begins, see e.g. [21] [26] [2] [7] [6]. Ideally, as is the case with a ReedSolomon code [25], any k of the n encoding symbols is sufficient to recover the original k input symbols (see for example =-=[18]-=-). Sometimes, as is the case with a Tornado code [16] [17], slightly more than k of the n encoding symbols are needed to recover the original k input symbols. Reed-Solomon codes in practice are only e... |

995 | A Reliable Multicast Framework for Light-weight - Floyd, Jacobson, et al. - 1997 |

662 | Receiver-driven layered multicast
- McCanne, Jacobson, et al.
- 1996
(Show Context)
Citation Context ...reliability protocol that scalably delivers a different fraction of the packets generated to each receiver depending on current network conditions and the receivers bandwidth connection to the sender =-=[19]-=- [30] [4] [14]. Erasure codes can be used in conjunction with these congestion control protocols to help provide a complete reliable delivery transport. For many-to-one delivery it is useful for recei... |

590 | RMTP: A Reliable Multicast Transport Protocol for High Speed Networks - Paul, Sabnani, et al. |

453 | Ecient dispersal of information for security, load balancing and fault tolerance
- Rabin
- 1989
(Show Context)
Citation Context ...y of streaming content, delivery of content to mobile clients in wireless networks, peer-to-peer applications [3], delivery of content along multiple paths to ensure resiliency to network disruptions =-=[24]-=-, and a number of other applications too numerous to detail in this paper. 2. LT Codes Design The length ℓ of the encoding symbols can be chosen as desired. The overall encoding and decoding is more e... |

410 | Effective erasure codes for reliable computer communication protocols
- Rizzo
- 1997
(Show Context)
Citation Context ...ata distribution applications, and in these cases both k and n either are limited to fairly small values due to practical considerations or are fixed before the encoding process begins, see e.g. [21] =-=[26]-=- [2] [7] [6]. Ideally, as is the case with a ReedSolomon code [25], any k of the n encoding symbols is sufficient to recover the original k input symbols (see for example [18]). Sometimes, as is the c... |

384 | The performance of TCP/IP for networks with high bandwidth-delay products and random loss - Lakshman, Madhow - 1997 |

383 | A Digital Fountain Approach to Reliable Distribution of Bulk Data
- Byers, Luby, et al.
- 1998
(Show Context)
Citation Context ... the behavior of the LT process using first principles of probability theory, which precisely captures the behavior of the data recovery process. The “digital fountain approach” concept introduced in =-=[7]-=- [6] is similar to that of a universal erasure code, and LT codes are the first full realization of this concept. This paper describes some of the theoretical underpinnings of some portions of the wor... |

357 |
Polynomial codes over certain finite fields
- Reed, Solomon
- 1960
(Show Context)
Citation Context ...her are limited to fairly small values due to practical considerations or are fixed before the encoding process begins, see e.g. [21] [26] [2] [7] [6]. Ideally, as is the case with a ReedSolomon code =-=[25]-=-, any k of the n encoding symbols is sufficient to recover the original k input symbols (see for example [18]). Sometimes, as is the case with a Tornado code [16] [17], slightly more than k of the n e... |

346 | TCP-like congestion control for layered multicast data transfer
- Vicisano, Rizzo, et al.
- 1998
(Show Context)
Citation Context ...bility protocol that scalably delivers a different fraction of the packets generated to each receiver depending on current network conditions and the receivers bandwidth connection to the sender [19] =-=[30]-=- [4] [14]. Erasure codes can be used in conjunction with these congestion control protocols to help provide a complete reliable delivery transport. For many-to-one delivery it is useful for receivers ... |

291 | Parity-based loss recovery for reliable multicast transmission
- Nonnenmacher, Biersack, et al.
- 1997
(Show Context)
Citation Context ...der needs to be limited and sending packets that are redundant for some receivers is wasteful, reliability may be able to be provided using erasure codes as described in [21], [28], [26], [27], [22], =-=[23]-=-, [9] [7] [6]. The attractiveness of this approach is that if the erasure codes are powerful enough then a single sender can potentially be used to reliably deliver data efficiently to a large number ... |

250 | Efficient Erasure Correcting Codes
- Luby, Mitzenmacher, et al.
(Show Context)
Citation Context ...hey are simultaneously near optimal for every erasure channel and they are very efficient as the data length grows. The analysis of LT codes is quite different than the analysis of Tornado codes [16] =-=[17]-=- [15]. In particular, the Tornado codes analysis is only applicable to graphs with constant maximum degree, and LT codes use graphs of logarithmic density, and thus the Tornado codes analysis does not... |

227 | Practical loss-resilient codes
- Luby, Mitzenmacher, et al.
- 1997
(Show Context)
Citation Context ...hat they are simultaneously near optimal for every erasure channel and they are very efficient as the data length grows. The analysis of LT codes is quite different than the analysis of Tornado codes =-=[16]-=- [17] [15]. In particular, the Tornado codes analysis is only applicable to graphs with constant maximum degree, and LT codes use graphs of logarithmic density, and thus the Tornado codes analysis doe... |

226 | A Reliable Dissemination Protocol for Interactive Collaborative Applications - Yavatkar, Griffioen, et al. - 1995 |

205 | Informed content delivery across adaptive overlay networks
- Byers, Considine, et al.
- 2004
(Show Context)
Citation Context ...a variety of other applications of LT codes, including robust distributed storage, delivery of streaming content, delivery of content to mobile clients in wireless networks, peer-to-peer applications =-=[3]-=-, delivery of content along multiple paths to ensure resiliency to network disruptions [24], and a number of other applications too numerous to detail in this paper. 2. LT Codes Design The length ℓ of... |

160 | Accessing Multiple Mirror Sites in Parallel: Using Tornado Codes to Speed Up Downloads
- Byers, Luby, et al.
- 1999
(Show Context)
Citation Context ...s potentially at different locations. In this case receiving redundant packets is a concern, and erasure codes can be used to minimize delivery of redundant packets. This application is considered in =-=[5]-=-, and a partial solution is given based on Tornado codes [16] [17]. LT codes offers compelling advantages for all these different types of data delivery applications that no previous erasure codes pro... |

138 | Extending equation-based congestion control to multicast applications - Widmer, Handley - 2001 |

114 | A digital fountain approach to asynchronous reliable multicast
- Byers, Luby, et al.
- 2002
(Show Context)
Citation Context ... behavior of the LT process using first principles of probability theory, which precisely captures the behavior of the data recovery process. The “digital fountain approach” concept introduced in [7] =-=[6]-=- is similar to that of a universal erasure code, and LT codes are the first full realization of this concept. This paper describes some of the theoretical underpinnings of some portions of the work de... |

96 | An XOR-based erasure-resilient coding scheme
- Blomer, Kalfane, et al.
- 1995
(Show Context)
Citation Context ...istribution applications, and in these cases both k and n either are limited to fairly small values due to practical considerations or are fixed before the encoding process begins, see e.g. [21] [26] =-=[2]-=- [7] [6]. Ideally, as is the case with a ReedSolomon code [25], any k of the n encoding symbols is sufficient to recover the original k input symbols (see for example [18]). Sometimes, as is the case ... |

82 | FLID-DL: Congestion Control for Layered Multicast
- Byers, Frumin, et al.
- 2000
(Show Context)
Citation Context ...y protocol that scalably delivers a different fraction of the packets generated to each receiver depending on current network conditions and the receivers bandwidth connection to the sender [19] [30] =-=[4]-=- [14]. Erasure codes can be used in conjunction with these congestion control protocols to help provide a complete reliable delivery transport. For many-to-one delivery it is useful for receivers to b... |

74 | Analysis of Random Processes via And-Or Tree Evaluation
- Luby, Mitzenmacher, et al.
- 1998
(Show Context)
Citation Context ...re simultaneously near optimal for every erasure channel and they are very efficient as the data length grows. The analysis of LT codes is quite different than the analysis of Tornado codes [16] [17] =-=[15]-=-. In particular, the Tornado codes analysis is only applicable to graphs with constant maximum degree, and LT codes use graphs of logarithmic density, and thus the Tornado codes analysis does not appl... |

45 | Wave and Equation Based Rate Control Using Multicast Round Trip Time: Extended Report", Digital Fountain - Luby, Goyal |

34 |
Reliable Multicast: Where to Use Forward Error Correction
- Nonnenmacher, Biersack
- 1996
(Show Context)
Citation Context ...ble data distribution applications, and in these cases both k and n either are limited to fairly small values due to practical considerations or are fixed before the encoding process begins, see e.g. =-=[21]-=- [26] [2] [7] [6]. Ideally, as is the case with a ReedSolomon code [25], any k of the n encoding symbols is sufficient to recover the original k input symbols (see for example [18]). Sometimes, as is ... |

26 | Using multicast FEC to solve the midnight madness problem," Microsoft Research
- Schooler, Gemmell
- 1997
(Show Context)
Citation Context ...nce, feedback to the sender needs to be limited and sending packets that are redundant for some receivers is wasteful, reliability may be able to be provided using erasure codes as described in [21], =-=[28]-=-, [26], [27], [22], [23], [9] [7] [6]. The attractiveness of this approach is that if the erasure codes are powerful enough then a single sender can potentially be used to reliably deliver data effici... |

24 | Asynchronous Multicast Push: AMP
- Nonnenmacher, Biersack
- 1997
(Show Context)
Citation Context ...he sender needs to be limited and sending packets that are redundant for some receivers is wasteful, reliability may be able to be provided using erasure codes as described in [21], [28], [26], [27], =-=[22]-=-, [23], [9] [7] [6]. The attractiveness of this approach is that if the erasure codes are powerful enough then a single sender can potentially be used to reliably deliver data efficiently to a large n... |

19 |
Information additive code generator and decoder for communication systems
- Luby
(Show Context)
Citation Context ... to that of a universal erasure code, and LT codes are the first full realization of this concept. This paper describes some of the theoretical underpinnings of some portions of the work described in =-=[12]-=- [13]. 1.1 Some encoding details The process of generating an encoding symbol is conceptually very easy to describe: • Randomly choose the degree d of the encoding symbol from a degree distribution. T... |

13 | Reliable Multicast Protocols: A Practical View - Miller - 1997 |

13 |
A Reliable Multicast Data Distribution
- Rizzo, Vicisano
- 1997
(Show Context)
Citation Context ...k to the sender needs to be limited and sending packets that are redundant for some receivers is wasteful, reliability may be able to be provided using erasure codes as described in [21], [28], [26], =-=[27]-=-, [22], [23], [9] [7] [6]. The attractiveness of this approach is that if the erasure codes are powerful enough then a single sender can potentially be used to reliably deliver data efficiently to a l... |

9 | A modular analysis of network transmission protocols
- Adler, Bartal, et al.
- 1997
(Show Context)
Citation Context ...variety of data delivery applications. For one-toone delivery, there are advantages in designing the reliability mechanism independently from the flow and congestion control mechanism, as outlined in =-=[1]-=-. The advantage of using erasure codes in one-to-one data delivery is that it makes it easier to design the flow and congestion control mechanisms independently of reliability. For the one-to-many dat... |

6 |
ECRSM - Erasure Correcting Scalable Reliable Multicast. Microsoft Research
- Gemmell
- 1997
(Show Context)
Citation Context ...eds to be limited and sending packets that are redundant for some receivers is wasteful, reliability may be able to be provided using erasure codes as described in [21], [28], [26], [27], [22], [23], =-=[9]-=- [7] [6]. The attractiveness of this approach is that if the erasure codes are powerful enough then a single sender can potentially be used to reliably deliver data efficiently to a large number of co... |

3 |
Report on Waves. Report of the fourteenth meeting of the British Association for the
- Scott
(Show Context)
Citation Context ...added to the ripple at the same rate as they are processed. This property is the inspiration for the name Soliton distribution, as a soliton wave is one where dispersion balances refraction perfectly =-=[29]-=-. A desired effect is that as few released encoding symbols as possible cover a input symbol that is already in the ripple. This is because released encoding symbols that cover input symbols already i... |