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

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

Generalized Degrees of Freedom of the Symmetric Cache-Aided MISO Broadcast Channel with Partial CSIT

We consider the cache-aided MISO broadcast channel (BC) in which a multi-antenna transmitter serves $K$ single-antenna receivers, each equipped with a cache memory. The transmitter has access to partial knowledge of the channel state information. For a symmetric setting, in terms of channel strength levels, partial channel knowledge levels and cache sizes, we characterize the generalized degrees of freedom (GDoF) up to a constant multiplicative factor. The achievability scheme exploits the interplay between spatial multiplexing gains and coded-multicasting gain. On the other hand, a cut-set-based argument in conjunction with a GDoF outer bound for a parallel MISO BC under channel uncertainty are used for the converse. We further show that the characterized order-optimal GDoF is also attained in a decentralized setting, where no coordination is required for content placement in the caches.Comment: first revisio

Secure GDoF of the Z-channel with Finite Precision CSIT: How Robust are Structured Codes?

Under the assumption of perfect channel state information at the transmitters (CSIT), it is known that structured codes offer significant advantages for secure communication in an interference network, e.g., structured jamming signals based on lattice codes may allow a receiver to decode the sum of the jamming signal and the signal being jammed, even though they cannot be separately resolved due to secrecy constraints, subtract the aggregate jammed signal, and then proceed to decode desired codewords at lower power levels. To what extent are such benefits of structured codes fundamentally limited by uncertainty in CSIT? To answer this question, we explore what is perhaps the simplest setting where the question presents itself -- a Z interference channel with secure communication. Using sum-set inequalities based on Aligned Images bounds we prove that the GDoF benefits of structured codes are lost completely under finite precision CSIT. The secure GDoF region of the Z interference channel is obtained as a byproduct of the analysis.Comment: 34 pages, 10 figure