Abstract
The main result of this paper is that an orthogonal access scheme, such as time division multiple access achieves the all-unicast degrees of freedom (DoF) region of the topological interference management problem if and only if the network topology graph is chordal bipartite, i.e., every cycle that can contain a chord, does contain a chord. The all-unicast DoF region includes the DoF region for any arbitrary choice of a unicast message set, so e.g., the results of Maleki and Jafar on the optimality of orthogonal access for the sum-DoF of one-dimensional convex networks are recovered as a special case. The result is also established for the corresponding topological representation of the index coding problem.
Highlights
The topological interference management problem (TIM), introduced in [1], studies the degrees of freedom (DoF) of partially connected one-hop wireless networks with no channel state information at the transmitters except the network topology
Last but not the least, the focus on sum-DoF is restrictive as well. This brings us to the motivation of this work, which is to go beyond these limitations, to answer the question — what is the fundamental topological structure that determines the optimality of TDMA for the TIM problem, making other sophisticated schemes redundant?
In the rest of this paper, we identify the optimality of TDMA through the structural property of the bipartite network topology graphs, and characterize the DoF region via vertex coloring on the undirected message conflict graphs
Summary
The topological interference management problem (TIM), introduced in [1], studies the degrees of freedom (DoF) of partially connected one-hop wireless networks with no channel state information at the transmitters except the network topology. For the TIM problem, [19] shows that orthogonal access (such as time division multiple access — TDMA) achieves the sum-DoF of a one-dimensional cellular network (all nodes placed on a straight line) that satisfies (i) source convexity, (ii) destination convexity, and (iii) message convexity Even for physically motivated TIM topologies that satisfy all the convexity constraints, it is shown in [19] that going from one-dimensional settings to the much more realistic two-dimensional placements of sources and destinations, one immediately runs into examples where TDMA is no longer optimal and interference alignment solutions significantly outperform conventional baselines. This brings us to the motivation of this work, which is to go beyond these limitations, to answer the question — what is the fundamental topological structure that determines the optimality of TDMA (fractional coloring) for the TIM (index coding) problem, making other sophisticated schemes redundant?
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