Necessary Conditions for K/2 Degrees of Freedom

Stotz et al., 2016, reported a sufficient (injectivity) condition for each user in a K-user single-antenna constant interference channel to achieve 1/2 degree of freedom. The present paper proves that this condition is necessary as well and hence provides an equivalence characterization of interference channel matrices allowing full degrees of freedom

Entropy bounds on abelian groups and the ruzsa divergence

Over the past few years, a family of interesting new inequalities for the entropies of sums and differences of random variables has been developed by Ruzsa, Tao and others, motivated by analogous results in additive combinatorics. The present work extends these earlier results to the case of random variables taking values in $\mathbb{R}^n$ or, more generally, in arbitrary locally compact and Polish abelian groups. We isolate and study a key quantity, the Ruzsa divergence between two probability distributions, and we show that its properties can be used to extend the earlier inequalities to the present general setting. The new results established include several variations on the theme that the entropies of the sum and the difference of two independent random variables severely constrain each other. Although the setting is quite general, the result are already of interest (and new) for random vectors in $\mathbb{R}^n$. In that special case, quantitative bounds are provided for the stability of the equality conditions in the entropy power inequality; a reverse entropy power inequality for log-concave random vectors is proved; an information-theoretic analog of the Rogers-Shephard inequality for convex bodies is established; and it is observed that some of these results lead to new inequalities for the determinants of positive-definite matrices. Moreover, by considering the multiplicative subgroups of the complex plane, one obtains new inequalities for the differential entropies of products and ratios of nonzero, complex-valued random variables

Interference alignment: capacity bounds and practical algorithms for time-varying channels

Wireless communication systems are becoming essential to everyday life. Modern network deployments and protocols are struggling to keep up with these growing demands, due to interference between devices. The recent discovery of interference alignment has shown that, in principle, it may be possible to overcome this interference bottleneck in dense networks. However, most theoretical results are limited to very high signal-to-noise ratios (SNRs) and practical algorithms have only developed for interference alignment via multiple antennas. In this thesis, we develop new capacity bounds for the finite SNR regime by taking advantage of time-varying channel gains. We also explore practical algorithms for parallel single-antenna interference channels, which could arise due to orthogonal frequency-division multiplexing (OFDM). From the theoretical side, we study the phase-fading Gaussian interference channel. We approximate the capacity region in the very strong interference regime to within a constant gap. Our coding schemes combines ideas from ergodic and lattice interference alignment. On the practical side, we develop a matching algorithm for pairing together sub-channels for alignment. This algorithm relies on the concept of maximum weight matching from graph theory. Simulations demonstrate that this algorithm outperforms classical techniques when the network is interference limited