Computer Science – Information Theory
Scientific paper
2011-02-12
Computer Science
Information Theory
Result from previous version was extended to characterize full degrees-of-freedom region. Submitted to IEEE Transactions on In
Scientific paper
We consider two-source two-destination (i.e., two-unicast) multi-hop wireless networks that have a layered structure with arbitrary connectivity. We show that, if the channel gains are chosen independently according to continuous distributions, then, with probability 1, two-unicast layered Gaussian networks can only have 1, 3/2 or 2 sum degrees-of-freedom. We provide sufficient and necessary conditions for each case based on network connectivity and a new notion of source-destination paths with manageable interference. Our achievability scheme is based on forwarding the received signals at all nodes, except for a small fraction of them in at most two key layers. Hence, we effectively create a "condensed network" that has at most four layers (including the sources layer and the destinations layer). We design the transmission strategies based on the structure of this condensed network. The converse results are obtained by developing information-theoretic inequalities that capture the structures of the network connectivity. Finally, we extend this result and characterize the full degrees-of-freedom region of two-unicast layered wireless networks.
Avestimehr Amir Salman
Shomorony Ilan
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