Related papers: The Sphere Packing Bound via Augustin's Method

Feedback control actively dissipates uncertainty from a dynamical system by means of actuation. We develop a notion of "control capacity" that gives a fundamental limit (in bits) on the rate at which a controller can dissipate the…

We present the first systematic algorithm to estimate the maximum packing density of spheres when the grain sizes are drawn from an arbitrary size distribution. With an Apollonian filling rule, we implement our technique for disks in 2d and…

We derive bounds on the noncoherent capacity of a very general class of multiple-input multiple-output channels that allow for selectivity in time and frequency as well as for spatial correlation. The bounds apply to peak-constrained…

A lower bound on the minimum required code length of binary codes is obtained. The bound is obtained based on observing a close relation between the Ulam's liar game and channel coding. In fact, Spencer's optimal solution to the game is…

This work considers a Poisson noise channel with an amplitude constraint. It is well-known that the capacity-achieving input distribution for this channel is discrete with finitely many points. We sharpen this result by introducing upper…

We consider an additive Gaussian channel with additive Gaussian noise feedback. We derive an upper bound on the n-block capacity (defined by Cover [1]). It is shown that this upper bound can be obtained by solving a convex optimization…

We derive a new upper bound on the reliability function for channel coding over discrete memoryless channels. Our bounding technique relies on two main elements: (i) adding an auxiliary genie-receiver that reveals to the original receiver a…

This work considers a binomial noise channel. The paper can be roughly divided into two parts. The first part is concerned with the properties of the capacity-achieving distribution. In particular, for the binomial channel, it is not known…

The R\'enyi and Shannon entropies are information-theoretic measures which have enabled to formulate the position-momentum uncertainty principle in a much more adequate and stringent way than the (variance-based) Heisenberg-like relation.…

We obtain an upper bound to the packing density of regular tetrahedra. The bound is obtained by showing the existence, in any packing of regular tetrahedra, of a set of disjoint spheres centered on tetrahedron edges, so that each sphere is…

A fundamental quantity of interest in Shannon theory, classical or quantum, is the optimal error exponent of a given channel W and rate R: the constant E(W,R) which governs the exponential decay of decoding error when using ever larger…

We study the spherical cap packing problem with a probabilistic approach. Such probabilistic considerations result in an asymptotic sharp universal uniform bound on the maximal inner product between any set of unit vectors and a…

We derive lower bounds on the maximal rates for multiple packings in high-dimensional Euclidean spaces. Multiple packing is a natural generalization of the sphere packing problem. For any $ N>0 $ and $ L\in\mathbb{Z}_{\ge2} $, a multiple…

We describe a program to prove the Kepler conjecture on sphere packings. We then carry out the first step of this program. Each packing determines a decomposition of space into Delaunay simplices, which are grouped together into finite…

Questions surrounding the spatial disposition of particles in various condensed-matter systems continue to pose many theoretical challenges. This paper explores the geometric availability of amorphous many-particle configurations that…

In this paper we prove a theorem that provides an upper bound for the density of packings of congruent copies of a given convex body in $\mathbb{R}^n$; this theorem is a generalization of the linear programming bound for sphere packings. We…

A new approach for upper bounding the channel reliability function using the code spectrum is described. It allows to treat both low and high rate cases in a unified way. In particular, the earlier known upper bounds are improved, and a new…

In this paper, the capacity of wireless channels is characterized based on electromagnetic and antenna theories with only minimal assumptions. We assume the transmitter can generate an arbitrary current distribution inside a spherical…

We establish a new outer bound for the capacity region of product broadcast channels. This outer bound matches Marton's inner bound for a variety of classes of product broadcast channels whose capacity regions were previously unknown. These…

We obtain an asymptotic formula for the number of circles of curvature at most T in any given bounded Apollonian circle packing. For an integral packing, we obtain the upper bounds for the number of circles with prime curvature as well as…