Abstract
Topological interference management (TIM) can obtain degrees of freedom (DoF) gains with no channel state information at the transmitters (CSIT) except topological information of network in the interference channel. It was shown that TIM achieves symmetric DoF 1/2 when internal conflict does not exist among messages [7]. However, it is difficult to assure whether a specific topology can achieve symmetric DoF 1/2 without scrutinizing internal conflict. It is also hard to derive a specific topology directly from the conventional condition for symmetric DoF 1/2. Even except for the topology achieving symmetric DoF 1/2, topology achieving specific DoF less than 1/2 is not well known. With these problems in mind, we propose a method to derive all maximal topologies directly in TIM, named as alliance construction in K-user interference channel. That is, it is proved that a topology is maximal if and only if it is derived from alliance construction. Further we translate a topology design by alliance construction in the alignment-conflict graph into topology matrix and propose conditions for maximal topology matrix (MTM). Moreover, we propose a generalized alliance construction that derives topologies achieving DoF 1/n for n ≥ 3 by generalizing sub-alliances. A topology matrix can also be used to analyze topologies with DoF 1/n .
Highlights
There have been many advances in the wireless networks with interference and the most remarkable achievement is the idea of interference alignment (IA) [1]
In this paper, we introduced the alliance as a set of messages that follows no internal conflict and set conflict in the alignment-conflict graph
We proposed the alliance construction with MPH, which results in generating maximal topology
Summary
There have been many advances in the wireless networks with interference and the most remarkable achievement is the idea of interference alignment (IA) [1]. Since the study on TIM in [6] is based on index coding problems which mainly focus on each message, it is hard to design a specific topology achieving symmetric DoF 1/2 directly from Theorem 4 in [6], which is not suitable for dealing with actual network topologies. Compared to dealing with LRMC problem in [15], design of topology matrix in our work is based on index coding problem (i.e, graph theory) For this reason, our topology design covers only some cases, not the whole, of topology achieving symmetric DoF less than 1/2. The generalized alliance construction and the maximal topology with symmetric DoF 1/n are proposed in Section VI and Section VII concludes the paper
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