Proof of replica formulas in the high noise regime for communication using LDGM codes
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In this thesis, quantum chemical methods have been applied to elucidate the thermodynamics and the kinetics of reactions involving reactive species in water. Due to their high reactivity in water, many transient species are difficult to study by experiment ...
Various aspects of the built environment have important effects on ecology. Providing suitable metrics for the built forms so as to quantify and model their internal relations and external ecological footprints, however, remains a challenge. Here we provid ...
The relative entropy is a principal measure of distinguishability in quantum information theory, with its most important property being that it is non-increasing with respect to noisy quantum operations. Here, we establish a remainder term for this inequal ...
The aim of this paper is to show that spatial coupling can be viewed not only as a means to build better graphical models, but also as a tool to better understand uncoupled models. The starting point is the observation that some asymptotic properties of gr ...
The main objective of this paper is to explore the precise relationship between the Bethe free energy (or entropy) and the Shannon conditional entropy of graphical error correcting codes. The main result shows that the Bethe free energy associated with a l ...
Investigations on spatially coupled codes have lead to the conjecture that, in the infinite size limit, the average input-output conditional entropy for spatially coupled low-density parity-check ensembles, over binary memoryless symmetric channels, equals ...
The loop series provides a formal way to write down corrections to the Bethe entropy (and/or free energy) of graphical models. We provide methods to rigorously control such expansions for low-density parity-check codes used over a highly noisy binary symme ...
Pressurized fluid-distribution networks are key strategic elements of infrastructure. Drinking water is a precious resource and will become more and more important with the depletion of reserves. With the growth of the human population, challenges related ...
The entropy power inequality (EPI) yields lower bounds on the differential entropy of the sum of two independent real-valued random variables in terms of the individual entropies. Versions of the EPI for discrete random variables have been obtained for spe ...
Institute of Electrical and Electronics Engineers2014
Investigations on spatially coupled codes have lead to the conjecture that, in the infinite size limit, the average input-output conditional entropy for spatially coupled low-density parity-check ensembles, over binary memoryless symmetric channels, equals ...