Fairness Comparison of Uplink NOMA and OMA

In this paper, we compare the resource allocation fairness of uplink communications between non-orthogonal multiple access (NOMA) schemes and orthogonal multiple access (OMA) schemes. Through characterizing the contribution of the individual user data rate to the system sum rate, we analyze the fundamental reasons that NOMA offers a more fair resource allocation than that of OMA in asymmetric channels. Furthermore, a fairness indicator metric based on Jain's index is proposed to measure the asymmetry of multiuser channels. More importantly, the proposed metric provides a selection criterion for choosing between NOMA and OMA for fair resource allocation. Based on this discussion, we propose a hybrid NOMA-OMA scheme to further enhance the users fairness. Simulation results confirm the accuracy of the proposed metric and demonstrate the fairness enhancement of the proposed hybrid NOMA-OMA scheme compared to the conventional OMA and NOMA schemes.Comment: 6 pages, accepted for publication, VTC 2017, Spring, Sydne

A Monotone, Second Order Accurate Scheme for Curvature Motion

We present a second order accurate in time numerical scheme for curve shortening flow in the plane that is unconditionally monotone. It is a variant of threshold dynamics, a class of algorithms in the spirit of the level set method that represent interfaces implicitly. The novelty is monotonicity: it is possible to preserve the comparison principle of the exact evolution while achieving second order in time consistency. As a consequence of monotonicity, convergence to the viscosity solution of curve shortening is ensured by existing theory

On Median Filters for Motion by Mean Curvature

The median filter scheme is an elegant, monotone discretization of the level set formulation of motion by mean curvature. It turns out to evolve every level set of the initial condition precisely by another class of methods known as threshold dynamics. Median filters are, in other words, the natural level set versions of threshold dynamics algorithms. Exploiting this connection, we revisit median filters in light of recent progress on the threshold dynamics method. In particular, we give a variational formulation of, and exhibit a Lyapunov function for, median filters, resulting in energy based unconditional stability properties. The connection also yields analogues of median filters in the multiphase setting of mean curvature flow of networks. These new multiphase level set methods do not require frequent redistancing, and can accommodate a wide range of surface tensions.Comment: 41 pages, 8 figure