An algebraic approach to network coding

By Ralf Koetter, Muriel Médard. Proceedings. 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252), 2001

2,542 citations recorded by the source corpus.

We consider the problem of information flow in networks. In particular, we relate the question whether a set of desired connections can be accommodated in a network to the problem of finding a point on a variety defined over a suitable field. This approach lends itself to the derivation of a number of theorems concerning the feasibility of a communication scenario involving failures.

Subfields: Computational Theory and Mathematics, Computer Networks and Communications, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/05ee3c8db4cd44e36cc08a71d279c2aa1ed55b14

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Citations in the corpus

Capacity of wireless erasure networks (2006, neutral): “Table I summarizes our notation.”
A network coding approach to cooperative diversity (2007, background): “The proposed design is referred to as a network coding [9], [10] approach to cooperative diversity because it has the defining characteristic of network coding: the transmitting node constructs a linear combination (over a finite field) of the multiple data flows it wishes to convey and transmits th”
Growth codes: maximizing sensor network data persistence (2006, background): “, [29, 9], where it has been shown that simple linear codes are very efficient [24].”
Distributed space-time coded protocols for exploiting cooperative diversity in wireless networks (2002, positive): “There is a growing body of work focused on network coding for enhancing performance of wireless and other communication networks [5], [6], [ 7 ].”
Fading relay channels: performance limits and space-time signal design (2004, neutral): “into the framework of network coding [15]–[17].”
A Survey on Network Codes for Distributed Storage (2010, background): “Further work showed that linear network coding suffices [16], [18] and random linear combinations construct good network codes with high probability [19].”
XORs in the Air: Practical Wireless Network Coding (2006, background): “Koetter and Médard [24] presented polynomial time algorithms for encoding and decoding, and Ho et al. extended these results to random codes [17].”
Symbol-level network coding for wireless mesh networks (2008, methodology): “Checking for independence is straightforward using Gaussian elimination over these short vectors [13].”
Distributed Matrix Scaling and Application to Average Consensus in Directed Graphs (2013, neutral): “, [1], [2], [3], [4], [5], [6], [7], and references therein).”
Algebraic gossip: a network coding approach to optimal multiple rumor mongering (2006, background): “There is significant recent work on network coding [9], especially on the algorithmic aspects of construction of linear network codes [2], [14], [10], [19] for multicast connections.”
Network coding for efficient communication in extreme networks (2005, background): “Much work has been published on optimal centralized network coding algorithms [19, 13].”
Byzantine modification detection in multicast networks using randomized network coding (2004, background): “Interest in network coding has grown following demonstrations of its various advantages: in network capacity [1], robustness to nonergodic network failures [2] and ergodic packet erasures [3], [4], and distributed network operation [5].”
Homomorphic MACs: MAC-Based Integrity for Network Coding (2009, background): “Network coding [1,2] proposes to replace the traditional ‘store and forward’ paradigm in networks by more intelligent routing that allows intermediate nodes to transform the data in transit.”