4 research outputs found
Resolving Entanglements in Topological Interference Management with Alternating Connectivity
The sum-capacity of a three user interference wired network for time-varying
channels is considered. Due to the channel variations, it is assumed that the
transmitters are only able to track the connectivity between the individual
nodes, thus only the (alternating) state of the network is known. By
considering a special subset of all possible states, we show that state
splitting combined with joint encoding over the alternating states is required
to achieve the sum-capacity. Regarding upper bounds, we use a genie aided
approach to show the optimality of this scheme. This highlights that more
involved transmit strategies are required for characterizing the degrees of
freedom even if the transmitters have heavily restricted channel state
information
When Does an Ensemble of Matrices with Randomly Scaled Rows Lose Rank?
We consider the problem of determining rank loss conditions for a
concatenation of full-rank matrices, such that each row of the composing
matrices is scaled by a random coefficient. This problem has applications in
wireless interference management and recommendation systems. We determine
necessary and sufficient conditions for the design of each matrix, such that
the random ensemble will almost surely lose rank by a certain amount. The
result is proved by converting the problem to determining rank loss conditions
for the union of some specific matroids, and then using tools from matroid and
graph theories to derive the necessary and sufficient conditions. As an
application, we discuss how this result can be applied to the problem of
topological interference management, and characterize the linear symmetric
degrees of freedom for a class of network topologies.Comment: submitted to IEEE Transactions on Information Theory; shorter version
to appear at IEEE International Symposium on Information Theory (ISIT 2015