IRWIN AND JOAN JACOBS CENTER FOR COMMUNICATION AND INFORMATION TECHNOLOGIES Average Redundancy of the Shannon Code for Markov Sources

IRWIN AND JOAN JACOBS CENTER FOR COMMUNICATION AND INFORMATION TECHNOLOGIES Relations Between Redundancy Patterns of the Shannon Code and Wave Diffraction Patterns of Partially Disordered Media

The average redundancy of the Shannon code, Rn, as a function of the block length n, is known to exhibit two very different types of behavior, depending on the rationality or irrationality of certain parameters of the source: It either converges to 1/2 as n grows without bound, or it may have a non–vanishing, oscillatory, (quasi–) periodic pattern around the value 1/2 for all large n. In this p...

IRWIN AND JOAN JACOBS CENTER FOR COMMUNICATION AND INFORMATION TECHNOLOGIES LDPC Codes for Two- Dimensional Arrays

IRWIN AND JOAN JACOBS CENTER FOR COMMUNICATION AND INFORMATION TECHNOLOGIES Burst-Erasure Correcting Codes with Optimal Average Delay

Irwin and Joan Jacobs Center for Communication and Information Technologies on the Classical – and Not so Classical – Shannon Sampling Theorem

We proceed with our recently-introduced geometric approach to sampling of manifolds and investigate the relationship that exists between the classical, i.e. Shannon type, and geometric sampling concepts and formalism. Some aspects of coding and the Gaussian channel problem are considered. A geometric version of Shannon’s Second Theorem is introduced. Applications to Pulse Code Modulation and Ve...

IRWIN AND JOAN JACOBS CENTER FOR COMMUNICATION AND INFORMATION TECHNOLOGIES On-Line Fountain Codes with Low Overhead

An on-line fountain code is defined as a fountain code for which an optimal encoding strategy can be found efficiently given any instantaneous decoding state. This property is important for data distribution in practical networks. In this paper we formalize the problem of on-line fountain code construction, and propose new on-line fountain codes that outperform known ones in having factor 3-5 l...