212 citations · 1.4k across the 61 of their papers we have counts for
5 papers · 2 filters
The Bethe Free Energy Allows to Compute the Conditional Entropy of Graphical Code Instances. A Proof from the Polymer Expansion
Nicolas Macris, Marc Vuffray
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…
Threshold Saturation for Spatially-Coupled LDPC and LDGM Codes on BMS Channels
Santhosh Kumar, Andrew J. Young, Nicolas Macris +1
Spatially-coupled low-density parity-check (LDPC) codes, which were first introduced as LDPC convolutional codes, have been shown to exhibit excellent performance under low-complex…
Approaching the Rate-Distortion Limit with Spatial Coupling, Belief propagation and Decimation
Vahid Aref, Nicolas Macris, 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 n…
Displacement Convexity, A Useful Framework for the Study of Spatially Coupled Codes
Rafah El-Khatib, Nicolas Macris, Ruediger Urbanke
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 ha…
Spatial Coupling as a Proof Technique
Andrei Giurgiu, Nicolas Macris, Rüdiger Urbanke
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.…