Cost-Effective Cache Deployment in Mobile Heterogeneous Networks

This paper investigates one of the fundamental issues in cache-enabled heterogeneous networks (HetNets): how many cache instances should be deployed at different base stations, in order to provide guaranteed service in a cost-effective manner. Specifically, we consider two-tier HetNets with hierarchical caching, where the most popular files are cached at small cell base stations (SBSs) while the less popular ones are cached at macro base stations (MBSs). For a given network cache deployment budget, the cache sizes for MBSs and SBSs are optimized to maximize network capacity while satisfying the file transmission rate requirements. As cache sizes of MBSs and SBSs affect the traffic load distribution, inter-tier traffic steering is also employed for load balancing. Based on stochastic geometry analysis, the optimal cache sizes for MBSs and SBSs are obtained, which are threshold-based with respect to cache budget in the networks constrained by SBS backhauls. Simulation results are provided to evaluate the proposed schemes and demonstrate the applications in cost-effective network deployment

Caveats for information bottleneck in deterministic scenarios

Information bottleneck (IB) is a method for extracting information from one random variable $X$ that is relevant for predicting another random variable $Y$. To do so, IB identifies an intermediate "bottleneck" variable $T$ that has low mutual information $I(X;T)$ and high mutual information $I(Y;T)$. The "IB curve" characterizes the set of bottleneck variables that achieve maximal $I(Y;T)$ for a given $I(X;T)$, and is typically explored by maximizing the "IB Lagrangian", $I(Y;T) - \beta I(X;T)$. In some cases, $Y$ is a deterministic function of $X$, including many classification problems in supervised learning where the output class $Y$ is a deterministic function of the input $X$. We demonstrate three caveats when using IB in any situation where $Y$ is a deterministic function of $X$: (1) the IB curve cannot be recovered by maximizing the IB Lagrangian for different values of $\beta$; (2) there are "uninteresting" trivial solutions at all points of the IB curve; and (3) for multi-layer classifiers that achieve low prediction error, different layers cannot exhibit a strict trade-off between compression and prediction, contrary to a recent proposal. We also show that when $Y$ is a small perturbation away from being a deterministic function of $X$, these three caveats arise in an approximate way. To address problem (1), we propose a functional that, unlike the IB Lagrangian, can recover the IB curve in all cases. We demonstrate the three caveats on the MNIST dataset