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TR04-034 | 12th April 2004 00:00

Network Coding: Does the Model Need Tuning?


Authors: April Rasala Lehman, Eric Lehman
Publication: 13th April 2004 17:31
Downloads: 3013


We consider the general network information flow problem, which was
introduced by Ahlswede et. al. We show a periodicity effect: for
every integer m greater than 1, there exists an instance of the
network information flow problem that admits a solution if and only if
the alphabet size is a perfect mth power. Building on this result, we
construct an instance with O(m) messages and O(m) nodes that admits a
solution if and only if the alphabet size is doubly exponential in m.
In other words, if we regard each message as a length-k bit string,
then k must be exponential in the size of the network. For this same
instance, we show that if edge capacities are slightly increased, then
there is a solution with a modest alphabet that has size only
exponential in m. In light of these results, we suggest that a more
appropriate model would assume that the network operates at slightly
under capacity.

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