Publications de Rafah El-Khatib

Displacement Convexity in Spatially Coupled Scalar Recursions

Rüdiger Urbanke, Nicolas Macris, Rafah El-Khatib

We introduce a technique for the analysis of general spatially coupled systems that are governed by scalar recursions. Such systems can be expressed in variational form in terms of a potential function. We show, under mild conditions, that the potential fu ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2019

The Velocity of the Propagating Wave for Spatially Coupled Systems With Applications to LDPC Codes

Nicolas Macris, Rafah El-Khatib

We consider the dynamics of message passing for spatially coupled codes and, in particular, the set of density evolution equations that tracks the profile of decoding errors along the spatial direction of coupling. It is known that, for suitable boundary c ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2018

Analysis of Spatially Coupled Systems using the Potential Functional with Applications to Coding Theory

Rafah El-Khatib

For the past 70 years or so, coding theorists have been aiming at designing transmission schemes with efficient encoding and decoding algorithms that achieve the capacity of various noisy channels. It was not until the '90s that graph-based codes, such as ...

EPFL2016

The Velocity of the Propagating Wave for General Coupled Scalar Systems

Nicolas Macris, Rafah El-Khatib

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 ...

Ieee2016

Analysis of Coupled Scalar Systems by Displacement Convexity

Rüdiger Urbanke, Nicolas Macris, Rafah El-Khatib

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 displace ...

Ieee2014

Displacement Convexity - A Useful Framework for the Study of Spatially Coupled Codes

Rüdiger Urbanke, Nicolas Macris, Rafah El-Khatib

Spatial coupling has recently emerged as a powerful paradigm to construct graphical models that work well under low-complexity message-passing algorithms. Although much progress has been made on the analysis of spatially coupled models under message passin ...

Ieee2013