Robust Network Coding [chapter]

Lana Iwaza, Marco Di Renzo, Michel Kieffer
2013 Network Coding  
Network coding [2, 42] , and more specifically random linear network coding [39, 13, 26, 28] , is a powerful tool for delivering information across a network. Random coding techniques may be implemented in a distributed way within network elements, independently of the structure of the network. In [28] , it has been shown that the max-flow capacity of the network can be reached with probability exponentionally approaching one with the size of the Galois field in which the random coding
more » ... dom coding operations are performed. This work has led to a number of practical schemes such as COPE, ANC, MIXIT, and MORE, etc. [35, 34, 33] . Nevertheless, network coding is very sensitive to transmission errors, packet losses, and corrupted packets which are intentionally injected by malicious nodes. Recombinations carried out by each node lead to a progressive contamination of the set of clean packets by the erroneous ones, which makes the decoding impossible at the receiver side. On the other hand, even in the absence of errors, losses of packets lead to an insufficient number of packets at the receiver side, making the use of the already received packets impossible. Error correcting network coding techniques aim at protecting packets from transmission errors, form erreneous packets, and/or losses. Error correcting network coding techniques introduce a certain level of redundancy and are similar in principle to classical error correcting codes. We can distinguish between two families of codes. The codes introduced in [8, 62] both focus on network coding and the introduction of redundancy. These codes require an a priori knowledge of the architecture of the network and the way in which network coding is carried out, see Section 1 for further details. These results are extended to the framework of random network coding in [28, 4] , see Section 2. The techniques introduced in [31, 38, 51, 1] exploit the fact that, in the absence of errors, random network coding preserves the space vector spanned by the transmitted packets. The proposed robust network codes have properties that are relatively independent from the way the network coding is carried out, see Section
doi:10.1002/9781118562819.ch8 fatcat:faw7uqseynfepnvgijaa2fkmg4