Analysis of Coupled Scalar Systems by Displacement Convexity
Information Theory
2017-01-16 v1 math.IT
Abstract
Potential functionals have been introduced recently as an important tool for the analysis of coupled scalar systems (e.g. density evolution equations). In this contribution, we investigate interesting properties of this potential. Using the tool of displacement convexity, we show that, under mild assumptions on the system, the potential functional is displacement convex. Furthermore, we give the conditions on the system such that the potential is strictly displacement convex, in which case the minimizer is unique.
Keywords
Cite
@article{arxiv.1701.03767,
title = {Analysis of Coupled Scalar Systems by Displacement Convexity},
author = {Rafah El-Khatib and Nicolas Macris and Tom Richardson and Rüdiger Urbanke},
journal= {arXiv preprint arXiv:1701.03767},
year = {2017}
}
Comments
5 pages, 1 figure, submitted to the IEEE International Symposium on Information Theory (ISIT) 2014