Explicit characterization and computation of the multi-source network coding capacity region (or even bounds) is long standing open problem. In fact, finding the capacity region requires determination of the set of all entropic vectors Γ * , which is known to be an extremely hard problem. On the other hand, calculating the explicitly known linear programming bound is very hard in practice due to an exponential growth in complexity as a function of network size. We give a new, easily computable outer bound, based on characterization of all functional dependencies in networks. We also show that the proposed bound is tighter than some known bounds.
Explicit characterization of the capacity region of communication networks is
a long standing problem. While it is known that network coding can outperform
routing and replication, the set of feasible rates is not known in general.
Characterizing the network coding capacity region requires determination of the
set of all entropic vectors. Furthermore, computing the explicitly known linear
programming bound is infeasible in practice due to an exponential growth in
complexity as a function of network size. This paper focuses on the fundamental
problems of characterization and computation of outer bounds for networks with
correlated sources. Starting from the known local functional dependencies
induced by the communications network, we introduce the notion of irreducible
sets, which characterize implied functional dependencies. We provide recursions
for computation of all maximal irreducible sets. These sets act as
information-theoretic bottlenecks, and provide an easily computable outer
bound. We extend the notion of irreducible sets (and resulting outer bound) for
networks with independent sources. We compare our bounds with existing bounds
in the literature. We find that our new bounds are the best among the known
graph theoretic bounds for networks with correlated sources and for networks
with independent sources.Comment: to appear in IEEE Transactions on Information Theor
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