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Weakly Secure MDS Codes for Simple Multiple Access Networks
We consider a simple multiple access network (SMAN), where sources of
unit rates transmit their data to a common sink via relays. Each relay is
connected to the sink and to certain sources. A coding scheme (for the relays)
is weakly secure if a passive adversary who eavesdrops on less than
relay-sink links cannot reconstruct the data from each source. We show that
there exists a weakly secure maximum distance separable (MDS) coding scheme for
the relays if and only if every subset of relays must be collectively
connected to at least sources, for all . Moreover, we
prove that this condition can be verified in polynomial time in and .
Finally, given a SMAN satisfying the aforementioned condition, we provide
another polynomial time algorithm to trim the network until it has a sparsest
set of source-relay links that still supports a weakly secure MDS coding
scheme.Comment: Accepted at ISIT'1
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