## A random linear network coding approach to multicast

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Citations: | 297 - 70 self |

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@MISC{Ho_arandom,

author = {Tracey Ho and Muriel Médard and Ralf Koetter and David R. Karger and Michelle Effros and Jun Shi and Ben Leong},

title = {A random linear network coding approach to multicast},

year = {}

}

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1942 | Randomized Algorithms
- Motwani, Raghavan
- 1995
(Show Context)
Citation Context ...rror-free transmission for independent or linearly correlated sources, which, owing to the particular form of transfer matrix determinant polynomials, is tighter than the Schwartz–Zippel bound (e.g., =-=[23]-=-) for general polynomials of the same total degree. This bound, which is exponentially dependent on the code length, holds for any feasible set of multicast connections over any network topology (incl... |

1228 | Network information flow
- Ahlswede, Cai, et al.
- 2000
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Citation Context ...orks. Index Terms—Distributed compression, distributed networking, multicast, network coding, random linear coding. I. INTRODUCTION THE capacity of multicast networks with network coding was given in =-=[1]-=-. We present an efficient distributed randomized approach that asymptotically achieves this capacity. We consider a general multicast framework—multisource multicast, possibly with correlated sources,... |

933 |
Noiseless coding for correlated information sources
- Slepian, Wolf
- 1973
(Show Context)
Citation Context ...rrelated sources. We next consider transmission of arbitrarily correlated sources, using random linear network coding, over networks where compression may be required. Analogously to Slepian and Wolf =-=[28]-=-, we consider the problem of distributed encoding and joint decoding of two sources whose output values in each unit time period are drawn independent and identically distributed (i.i.d.) from the sam... |

651 | Secure network coding
- Cai, Yeung
- 2002
(Show Context)
Citation Context ...] showed that with network coding, as symbol size approaches infinity, a source can multicast information at a rate approaching the smallest minimum cut between the source and any receiver. Li et al. =-=[19]-=- showed that linear coding with finite symbol size is sufficient for multicast. Koetter and Médard [17] presented an algebraic framework for network coding that extended previous results to arbitrary ... |

567 | An algebraic approach to network coding
- Koetter, Médard
- 2003
(Show Context)
Citation Context ...on at a rate approaching the smallest minimum cut between the source and any receiver. Li et al. [19] showed that linear coding with finite symbol size is sufficient for multicast. Koetter and Médard =-=[17]-=- presented an algebraic framework for network coding that extended previous results to arbitrary networks and robust networking, and proved the achievability with time-invariant solutions of the min-c... |

320 | Practical network coding
- Chou, Wu, et al.
- 2003
(Show Context)
Citation Context ...nmulticast problems was considered by Rasala Lehman and Lehman [18], Médard et al. [22], and Riis [25]. Various practical protocols for and experimental demonstrations of random linear network coding =-=[3]-=- and nonrandomized network coding [29], [24] have also been presented. II. MODEL AND PRELIMINARIES A. Basic Model Our basic network coding model is based on [1], [17]. A network is represented as a di... |

250 | The Benefits of Coding over Routing in a Randomized Setting
- Ho, Koetter, et al.
- 2003
(Show Context)
Citation Context ...ined in this new environment. For instance, if we allow for retrials to find successful codes, we in effect trade code length for some rudimentary coordination. Portions of this work have appeared in =-=[9]-=-, which introduced distributed random linear network coding; [8], which presented the Edmonds matrix formulation and a new bound on required field size for centralized network coding; [12], which gene... |

203 | Bimodal multicast - Birman, Hayden, et al. - 1999 |

164 | On randomized network coding
- Ho, Medard, et al.
- 1998
(Show Context)
Citation Context ... appeared in [9], which introduced distributed random linear network coding; [8], which presented the Edmonds matrix formulation and a new bound on required field size for centralized network coding; =-=[12]-=-, which generalized previous results to arbitrary networks and gave tighter bounds for acyclic networks; [11], on network coding for arbitrarily correlated sources; and [10], which considered random l... |

121 | Minimum-cost multicast over coded packet networks
- Lun, Ratnakar, et al.
- 2006
(Show Context)
Citation Context ...ources. Resource consumption can naturally be traded off against capacity and robustness, and across multiple communicating sessions; subsequent work on distributed resource optimization, e.g., [13], =-=[21]-=-, has used random linear network coding as a component of the solution. There are also many issues surrounding the adaptation of protocols, which generally assume routing, to random coding approaches.... |

105 | Polynomial time algorithms for network information flow
- Sander, Egner, et al.
- 2003
(Show Context)
Citation Context ... upper bound on the required field size than the previous bound of [17], and in our analysis of distributed randomized network coding, introduced in [9]. Concurrent independent work by Sanders et al. =-=[26]-=- and Jaggi et al. [14] considered single-source multicast on acyclic delay-free graphs, showing a similar bound on field size by different means, and giving centralized deterministic and randomized po... |

100 | Constrained random walks on random graphs; routing algorithms for large scale wireless sensor networks
- Servetto, Barrenechea
- 2002
(Show Context)
Citation Context ...arge numbers of nodes and/or changing topologies, it may be expensive or infeasible to reliably maintain routing state at network nodes. Distributed randomized routing schemes have been proposed [2], =-=[27]-=- which address this kind of issue. However, not allowing different signals to be combined can impose intrinsic penalties in efficiency compared to using network coding. Consider as a simple example th... |

92 | Achieving Minimum-cost Multicast: a Decentralized Approach Based on Network Coding
- Lun, Ratnakar, et al.
- 2005
(Show Context)
Citation Context ...er and still achieve the information rates of the optimized solution. Our distributed network coding approach has led to and enabled subsequent developments in distributed network optimization, e.g., =-=[20]-=-, [13]. The distributed nature of our approach also ties in well with considerations of robustness to changing network conditions. We show that our approach can take advantage of redundant network cap... |

82 | Complexity classification of network information flow problems,” manuscript - Rasala-Lehman, Lehman - 2003 |

73 |
codes for sources and source networks: Error exponents, universal coding
- Csiszár, “Linear
- 1982
(Show Context)
Citation Context ... a distributed source coding problem, we demonstrate that random linear coding also performs compression when necessary in a network, generalizing known error exponents for linear Slepian–Wolf coding =-=[4]-=- in a natural way. This approach not only recovers the capacity and achievable rates, but also offers a number of advantages. While capacity can be achieved by other deterministic or random approaches... |

54 | Multicast with network coding in application-layer overlay networks
- Zhu, Li, et al.
(Show Context)
Citation Context ... Rasala Lehman and Lehman [18], Médard et al. [22], and Riis [25]. Various practical protocols for and experimental demonstrations of random linear network coding [3] and nonrandomized network coding =-=[29]-=-, [24] have also been presented. II. MODEL AND PRELIMINARIES A. Basic Model Our basic network coding model is based on [1], [17]. A network is represented as a directed graph , where is the set of net... |

53 | Dynamic algorithms for multicast with intrasession network coding
- Ho, Viswanathan
- 2005
(Show Context)
Citation Context ... still achieve the information rates of the optimized solution. Our distributed network coding approach has led to and enabled subsequent developments in distributed network optimization, e.g., [20], =-=[13]-=-. The distributed nature of our approach also ties in well with considerations of robustness to changing network conditions. We show that our approach can take advantage of redundant network capacity ... |

49 | Network coding for correlated sources
- Ho, Medard, et al.
- 2004
(Show Context)
Citation Context ... matrix formulation and a new bound on required field size for centralized network coding; [12], which generalized previous results to arbitrary networks and gave tighter bounds for acyclic networks; =-=[11]-=-, on network coding for arbitrarily correlated sources; and [10], which considered random linear network coding for online network operation in dynamically varying environments. A. Overview A brief ov... |

48 |
Constructing a perfect matching is in random NC
- Karp, Upfal, et al.
- 1986
(Show Context)
Citation Context ...e graph has a perfect matching (e.g., [23]). The problem of determining whether a bipartite graph has a perfect matching is a classical reduction of the problem of checking the feasibility of an flow =-=[15]-=-. 4 This latter problem can be viewed as a degenerate case of network coding, restricted to the binary field and without any coding; it is interesting to find that the two formulations are equivalent ... |

47 | On coding for non-multicast networks
- Médard, Effros, et al.
- 2003
(Show Context)
Citation Context ...binary solvable multicast networks, and on nonfinite field alphabets. The need for vector coding solutions in some nonmulticast problems was considered by Rasala Lehman and Lehman [18], Médard et al. =-=[22]-=-, and Riis [25]. Various practical protocols for and experimental demonstrations of random linear network coding [3] and nonrandomized network coding [29], [24] have also been presented. II. MODEL AND... |

45 | Information flow decomposition for network coding
- Fragouli, Soljanin
(Show Context)
Citation Context ...ed deterministic and randomized polynomial-time algorithms for finding network coding solutions over a subgraph consisting of flow solutions to each receiver. Subsequent work by Fragouli and Soljanin =-=[7]-=- gave a tighter bound for the case of two sources and for some configurations with more than two sources. Lower bounds on coding field size were presented by Rasala Lehman and Lehman [18] and Feder et... |

40 | Network coding from a network flow perspective
- Ho, Karger, et al.
(Show Context)
Citation Context ...ials to find successful codes, we in effect trade code length for some rudimentary coordination. Portions of this work have appeared in [9], which introduced distributed random linear network coding; =-=[8]-=-, which presented the Edmonds matrix formulation and a new bound on required field size for centralized network coding; [12], which generalized previous results to arbitrary networks and gave tighter ... |

29 | Bounds on Linear Codes for Network Multicast
- Tavory, Feder, et al.
(Show Context)
Citation Context ... a tighter bound for the case of two sources and for some configurations with more than two sources. Lower bounds on coding field size were presented by Rasala Lehman and Lehman [18] and Feder et al. =-=[6]-=-. [6] also gave graph-specific upper bounds based on the number of “clashes” between flows from source to terminals.sHO et al.: A RANDOM LINEAR NETWORK CODING APPROACH TO MULTICAST 4415 Dougherty et a... |

25 |
versus Non-Linear Boolean functions in Network Flow
- Riis, “Linear
- 2004
(Show Context)
Citation Context ... multicast networks, and on nonfinite field alphabets. The need for vector coding solutions in some nonmulticast problems was considered by Rasala Lehman and Lehman [18], Médard et al. [22], and Riis =-=[25]-=-. Various practical protocols for and experimental demonstrations of random linear network coding [3] and nonrandomized network coding [29], [24] have also been presented. II. MODEL AND PRELIMINARIES ... |

20 | Performance evaluation of new multicast architecture with network coding
- Noguchi, Matsuda, et al.
- 2003
(Show Context)
Citation Context ...a Lehman and Lehman [18], Médard et al. [22], and Riis [25]. Various practical protocols for and experimental demonstrations of random linear network coding [3] and nonrandomized network coding [29], =-=[24]-=- have also been presented. II. MODEL AND PRELIMINARIES A. Basic Model Our basic network coding model is based on [1], [17]. A network is represented as a directed graph , where is the set of network n... |

17 | Online multicast routing with bandwidth guarantees: a new approach using multicast network flow
- Kodialam, Lakshman, et al.
(Show Context)
Citation Context ...work coding can be advantageous is for multisource multicast with dynamically varying connections. We compare distributed randomized coding to an approximate online Steiner tree routing approach from =-=[16]-=- in which, for each transmitter, a tree is selected in a centralized fashion. Since the complexity of setting up each connection is a significant consideration in the dynamic scenario we consider, we ... |

14 | On the utility of network coding in dynamic environments
- Ho, Leong, et al.
- 2004
(Show Context)
Citation Context ...entralized network coding; [12], which generalized previous results to arbitrary networks and gave tighter bounds for acyclic networks; [11], on network coding for arbitrarily correlated sources; and =-=[10]-=-, which considered random linear network coding for online network operation in dynamically varying environments. A. Overview A brief overview of related work is given in Section I-B. In Section II, w... |

14 |
Low complexity algebraic network codes
- Jaggi, Chou, et al.
- 2003
(Show Context)
Citation Context ...quired field size than the previous bound of [17], and in our analysis of distributed randomized network coding, introduced in [9]. Concurrent independent work by Sanders et al. [26] and Jaggi et al. =-=[14]-=- considered single-source multicast on acyclic delay-free graphs, showing a similar bound on field size by different means, and giving centralized deterministic and randomized polynomial-time algorith... |

13 | Linearity and Solvability in Multicast Networks - Dougherty, Freiling, et al. - 2004 |

6 | Linearity and Solvability in Multicast Networks,” submitted to the - Dougherty, Freiling, et al. |

3 | joined the faculty at the California Institute of Technology in - She - 1994 |

2 | Effros (S’93–M’95–SM’03) received the B.S. degree with distinction - Michelle - 1994 |

2 | received Stanford’s Frederick Emmons Terman Engineering Scholastic Award (for excellence in engineering) in 1989, the Hughes Masters Full-Study Fellowship in 1989, the National Science Foundation Graduate Fellowship - She - 1997 |

1 | Médard Muriel Médard (SM) is an Associate Professor in the Electrical Engineering and Computer Science at MIT and the Associate Director of the Laboratory for Information and Decision Systems. She was previously an Assistant Professor in the Electrical an - Muriel - 1995 |

1 | serves as an Associate Editor for the Optical Communications and Networking Series of the IEEE Journal on Selected Areas in Communications, as an Associate Editor in Communications for the IEEE Transactions on Information Theory and as a Guest Editor for - She - 2003 |

1 | Tracey Ho (M) is an Assistant Professor in Electrical Engineering and Computer Science at the California Institute of Technology. She received a - Ho - 1999 |

1 | SM’06) received a Diploma in Electrical Engineering from the Technical University Darmstadt, Germany in 1990 and a Ph.D. degree from the Department of Electrical Engineering at Linköping University, Sweden. From 1996/1998, he was a visiting scientist at t - Koetter |

1 | research interest include coding and information theory and their application to communication systems. In the years 1999-2001, he served as associate editor for coding theory - Koetter’s |

1 | received an IBM Invention Achievement Award in 1997, an NSF CAREER Award in 2000, and an IBM Partnership Award in 2001. He is co-recipient of the 2004 Paper Award of the Information Theory Society. Since 2003 he has been a member of the Board of Governers - He - 1989 |

1 | Jun Shi (S’97-M’05) received the B.S. and M.S. degrees in electrical engineering from Tsinghua University - Shi - 1997 |

1 | is a member of Tau Beta - She |