A quantitative subspace Balian-Low theorem

Let $\mathcal G\subset L^2(\mathbb R)$ be the subspace spanned by a Gabor Riesz sequence $(g,\Lambda)$ with $g\in L^2(\mathbb R)$ and a lattice $\Lambda\subset\mathbb R^2$ of rational density. It was shown recently that if $g$ is well-localized both in time and frequency, then $\mathcal G$ cannot contain any time-frequency shift $\pi(z) g$ of $g$ with $z\notin\Lambda$. In this paper, we improve the result to the quantitative statement that the $L^2$-distance of $\pi(z)g$ to the space $\mathcal G$ is equivalent to the Euclidean distance of $z$ to the lattice $\Lambda$, in the sense that the ratio between those two distances is uniformly bounded above and below by positive constants. On the way, we prove several results of independent interest, one of them being closely related to the so-called weak Balian-Low theorem for subspaces.Comment: 37 page

Self-optimized Coverage Coordination in Femtocell Networks

This paper proposes a self-optimized coverage coordination scheme for two-tier femtocell networks, in which a femtocell base station adjusts the transmit power based on the statistics of the signal and the interference power that is measured at a femtocell downlink. Furthermore, an analytic expression is derived for the coverage leakage probability that a femtocell coverage area leaks into an outdoor macrocell. The coverage analysis is verified by simulation, which shows that the proposed scheme provides sufficient indoor femtocell coverage and that the femtocell coverage does not leak into an outdoor macrocell.Comment: 16 pages, 5 figure

XJ-BP: Express Journey Belief Propagation Decoding for Polar Codes

This paper presents a novel propagation (BP) based decoding algorithm for polar codes. The proposed algorithm facilitates belief propagation by utilizing the specific constituent codes that exist in the factor graph, which results in an express journey (XJ) for belief information to propagate in each decoding iteration. In addition, this XJ-BP decoder employs a novel round-trip message passing scheduling method for the increased efficiency. The proposed method simplifies min-sum (MS) BP decoder by 40.6%. Along with the round-trip scheduling, the XJ-BP algorithm reduces the computational complexity of MS BP decoding by 90.4%; this enables an energy-efficient hardware implementation of BP decoding in practice.Comment: submitted to GLOBECOMM 201