Two-Unicast Wireless Networks: Characterizing the Degrees of Freedom

DOI10.1109/TIT.2012.2214024zbMATH Open1364.94793arXiv1102.2498MaRDI QIDQ2989465

Ilan Shomorony, Amir Salman Avestimehr

Publication date: 8 June 2017

Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)

Abstract: 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 (unless both source-destination pairs are disconnected, in which case no degrees-of-freedom can be achieved). 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.

Full work available at URL: https://arxiv.org/abs/1102.2498

Mathematics Subject Classification ID

Analytic circuit theory (94C05) Information theory (general) (94A15) Applications of graph theory to circuits and networks (94C15)