The Velocity of the Propagating Wave for General Coupled Scalar Systems
Information Theory
2017-01-16 v1 math.IT
Abstract
We consider spatially coupled systems governed by a set of scalar density evolution equations. Such equations track the behavior of message-passing algorithms used, for example, in coding, sparse sensing, or constraint-satisfaction problems. Assuming that the "profile" describing the average state of the algorithm exhibits a solitonic wave-like behavior after initial transient iterations, we derive a formula for the propagation velocity of the wave. We illustrate the formula with two applications, namely Generalized LDPC codes and compressive sensing.
Keywords
Cite
@article{arxiv.1701.03759,
title = {The Velocity of the Propagating Wave for General Coupled Scalar Systems},
author = {Rafah El-Khatib and Nicolas Macris},
journal= {arXiv preprint arXiv:1701.03759},
year = {2017}
}
Comments
5 pages, 5 figures, submitted to the Information Theory Workshop (ITW) 2016 in Cambridge, UK