Abstract
Conference Title: 2015 IEEE International Symposium on Information Theory (ISIT) Conference Start Date: 2015, June 14 Conference End Date: 2015, June 19 Conference Location: Hong Kong, Hong Kong We consider a simple multiple access network (SMAN), where k sources of unit rates transmit their data to a common sink via n 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 k 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 [cursive l] relays must be collectively connected to at least [cursive l]+1 sources, for all 0 < [cursive l] < k. Moreover, we prove that this condition can be verified in polynomial time in n and k. 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.