Publications by Marc Vuffray | EPFL Graph Search

The Bethe Free Energy Allows to Compute the Conditional Entropy of Graphical Code Instances: A Proof From the Polymer Expansion

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 ...

Ieee-Inst Electrical Electronics Engineers Inc2016

Approaching the Rate-Distortion Limit With Spatial Coupling, Belief Propagation, and Decimation

Nicolas Macris, Vahid Aref, Marc Vuffray

We investigate an encoding scheme for lossy compression of a binary symmetric source based on simple spatially coupled low-density generator-matrix codes. The degree of the check nodes is regular and the one of code-bits is Poisson distributed with an aver ...

Institute of Electrical and Electronics Engineers2015

The Cavity Method in Coding Theory

Marc Vuffray

EPFL2014

Approaching the Rate-Distortion Limit by spatial Coupling with Belief Propagation and Decimation

Nicolas Macris, Vahid Aref, Marc Vuffray

We investigate an encoding scheme for lossy compression based on spatially coupled Low-Density Generator-Matrix codes. The degree distributions are regular, or are Poisson on the code-bit side and check-regular which allows use for any compression rate. Th ...

2013

Beyond the Bethe Free Energy of LDPC Codes via Polymer Expansions

Nicolas Macris, Marc Vuffray

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 ...

Ieee2012

Lossy source coding via spatially coupled LDGM ensembles

Rüdiger Urbanke, Nicolas Macris, Vahid Aref, Marc Vuffray

We study a new encoding scheme for lossy source compression based on spatially coupled low-density generatormatrix codes. We develop a belief-propagation guided-decimation algorithm, and show that this algorithm allows to approach the optimal distortion of ...

Ieee2012

Bound states of the Schrödinger-Newton model in low dimensions

Joachim Stubbe, Marc Vuffray

We prove the existence of quasi-stationary symmetric solutions with exactly n >= 0 zeros and uniqueness for n = 0 for the Schrodinger-Newton model in one dimension and in two dimensions along with an angular momentum m >= 0. Our result is based on an analy ...

2010