Network coding with single arc failures
Résumé
Given a telecommunication network, modelled by a capacitated digraph,
we are interested in comparing the behaviour and usefulness of two
information propagation schemes, namely multicast and network coding,
when the aforementioned network is subject to simple arc failure.
We consider the case with a single source node and a set of terminal
nodes. The problem of studying the maximum quantity of information
that can be routed from the source to each terminal, using either
multicast replication alone or combined with network coding, has been
extensively studied. Multicast protocols allow an intermediate
node to replicate its input data towards several output interfaces,
and network coding refers to the ability for an intermediary node
to perform coding operations on its inputs, for example linear combinations, releasing a coded information flow on its outputs. We consider the survivability extension of the
throughput maximization problem where any single arc
can fail. Our aim is to design models and algorithms to compute the
survivable maximum throughput in multicast network and compare the
results obtained with and without network coding. The
coding advantage is defined as the quotient of the optimal throughput
obtained using network coding over the multicast optimal throughput. When no arc can fail, it has been shown that the
coding advantage can be strictly greater than one, but this holds
only on some particular network topologies (the so-called "butterfly
network"). However, when instances are randomly generated,
the coding advantage almost always vanishes. We investigated
the network's evolution when we remove a single arc to model the failure.
We define an analoguous quantity to the coding advantage which takes into
account
single arc failures. Our first experiments seem to show that, even when considering the possibility
of a single arc failure, the throughput gain offered by network coding remains
relatively moderate.