On the Structure of the Capacity Region of Asynchronous Memoryless Multiple-Access Channels

The asynchronous capacity region of memoryless multiple-access channels is the union of certain polytopes. It is well-known that vertices of such polytopes may be approached via a technique called successive decoding. It is also known that an extension of successive decoding applies to the dominant face of such polytopes. The extension consists of forming groups of users in such a way that users within a group are decoded jointly whereas groups are decoded successively. This paper goes one step further. It is shown that successive decoding extends to every face of the above mentioned polytopes. The group composition as well as the decoding order for all rates on a face of interest are obtained from a label assigned to that face. From the label one can extract a number of structural properties, such as the dimension of the corresponding face and whether or not two faces intersect. Expressions for the the number of faces of any given dimension are also derived from the labels.Comment: 21 pages, 5 figures and 1 table. Submitted to IEEE Transactions on Information Theor

Rigidity results and topology at infinity of translating solitons of the mean curvature flow

In this paper we obtain rigidity results and obstructions on the topology at infinity of translating solitons of the mean curvature flow in the Euclidean space. Our approach relies on the theory of f-minimal hypersurfaces.Comment: 18 pages. Minor corrections. Final version: to appear on Commun. Contemp. Mat

A Tight Bound on the Performance of a Minimal-Delay Joint Source-Channel Coding Scheme

An analog source is to be transmitted across a Gaussian channel in more than one channel use per source symbol. This paper derives a lower bound on the asymptotic mean squared error for a strategy that consists of repeatedly quantizing the source, transmitting the quantizer outputs in the first channel uses, and sending the remaining quantization error uncoded in the last channel use. The bound coincides with the performance achieved by a suboptimal decoder studied by the authors in a previous paper, thereby establishing that the bound is tight.Comment: 5 pages, submitted to IEEE International Symposium on Information Theory (ISIT) 201

Asymptotically Optimal Joint Source-Channel Coding with Minimal Delay

We present and analyze a joint source-channel coding strategy for the transmission of a Gaussian source across a Gaussian channel in n channel uses per source symbol. Among all such strategies, our scheme has the following properties: i) the resulting mean-squared error scales optimally with the signal-to-noise ratio, and ii) the scheme is easy to implement and the incurred delay is minimal, in the sense that a single source symbol is encoded at a time.Comment: 5 pages, 1 figure, final version accepted at IEEE Globecom 2009 (Communication Theory Symposium

Stability properties and topology at infinity of f-minimal hypersurfaces

We study stability properties of $f$-minimal hypersurfaces isometrically immersed in weighted manifolds with non-negative Bakry-Emery Ricci curvature under volume growth conditions. Moreover, exploiting a weighted version of a finiteness result and the adaptation to this setting of Li-Tam theory, we investigate the topology at infinity of $f$-minimal hypersurfaces. On the way, we prove a new comparison result in weighted geometry and we provide a general weighted $L^1$-Sobolev inequality for hypersurfaces in Cartan-Hadamard weighted manifolds, satisfying suitable restrictions on the weight function.Comment: 30 pages. Final version: to appear on Geom. Dedicat

A remark on Einstein warped products

We prove triviality results for Einstein warped products with non-compact bases. These extend previous work by D.-S. Kim and Y.-H. Kim. The proof, from the viewpoint of "quasi-Einstein manifolds" introduced by J. Case, Y.-S. Shu and G. Wei, rely on maximum principles at infinity and Liouville-type theorems.Comment: 12 pages. Corrected typos. Final version: to appear on Pacific J. Mat