Network Coherence Time Matters - Aligned Image Sets and the Degrees of Freedom of Interference Networks with Finite Precision CSIT and Perfect CSIR

This work obtains the first bound that is provably sensitive to network coherence time, i.e., coherence time in an interference network where all channels experience the same coherence patterns. This is accomplished by a novel adaptation of the aligned image sets bound, and settles various open problems noted previously by Naderi and Avestimehr and by Gou et al. For example, a necessary and sufficient condition is obtained for the optimality of 1/2 DoF per user in a partially connected interference network where the channel state information at the receivers (CSIR) is perfect, the channel state information at the transmitters (CSIT) is instantaneous but limited to finite precision, and the network coherence time is T_c= 1. The surprising insight that emerges is that even with perfect CSIR and instantaneous finite precision CSIT, network coherence time matters, i.e., it has a DoF impact.Comment: 19 pages, 4 figure

Sum-set inequalities from aligned image sets: Instruments for robust GDoF bounds

We present sum-set inequalities specialized to the generalized degrees of freedom (GDoF) framework. These are information theoretic lower bounds on the entropy of bounded density linear combinations of discrete, power-limited dependent random variables in terms of the joint entropies of arbitrary linear combinations of new random variables that are obtained by power level partitioning of the original random variables. The bounds are useful instruments to obtain GDoF characterizations for wireless interference networks, especially with multiple antenna nodes, subject to arbitrary channel strength and channel uncertainty levels