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Nicolas Macris

Cette personne a quitté l’EPFL

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Publications associées (64)

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High-dimensional rank-one nonsymmetric matrix decomposition: the spherical case

Nicolas Macris, Jean François Emmanuel Barbier, Clément Dominique Luneau

We consider the problem of estimating a rank-one nonsymmetric matrix under additive white Gaussian noise. The matrix to estimate can be written as the outer product of two vectors and we look at the special case in which both vectors are uniformly distribu ...

IEEE2020

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

Nicolas Macris, Marc Vuffray, Vahid Aref

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

Concentration of Magnetization for Linear Block Codes

Nicolas Macris, Shrinivas Kudekar

We consider communication over the binary erasure and the binary additive white gaussian noise channels using fixed linear block codes and also appropriate ensembles of such codes. We show concentration of the magnetization over the channel realizations an ...

2008

On the Capacity of a Code Division Multiple Access System

Nicolas Macris

We consider multiuser communication on a binary input additive white Gaussian noise channel using Randomly Spread-Code Division Multiple Access. We show concentration of various quantities of the system including the capacity and the free energy. We also o ...

2007

Threshold Saturation in Spatially Coupled Constraint Satisfaction Problems

Rüdiger Urbanke, Nicolas Macris, Seyed Hamed Hassani

We consider chains of random constraint satisfaction models that are spatially coupled across a finite window along the chain direction. We investigate their phase diagram at zero temperature using the survey propagation formalism and the interpolation met ...

Springer Verlag2013

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

Threshold Saturation for Spatially Coupled LDPC and LDGM Codes on BMS Channels

Nicolas Macris

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-complexity belief-propagation decoding. This phenomenon is now termed threshold sat ...

Institute of Electrical and Electronics Engineers2014

Tight Bounds on the Capacity of Binary Input random CDMA Systems

Nicolas Macris

We consider multiple access communication on a binary input additive white Gaussian noise channel using randomly spread code division. For a general class of symmetric distributions for spreading coefficients, in the limit of a large number of users, we pr ...

2010

Concentration of Multi-overlaps for Random Dilute Ferromagnetic Spin Models

Nicolas Macris, Jean François Emmanuel Barbier, Chun Lam Chan

We consider mean field ferromagnetic spin models on dilute random graphs and prove that, with suitable one-body infinitesimal perturbations added to the Hamiltonian, the multi-overlaps concentrate for all temperatures, both with respect to the thermal Gibb ...

SPRINGER2020

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 codes. The main result shows that the Bethe free energy associated with a l ...

Ieee-Inst Electrical Electronics Engineers Inc2016

Entropy and mutual information in models of deep neural networks

Nicolas Macris, Florent Gérard Krzakala, Lenka Zdeborová, Jean François Emmanuel Barbier, Clément Dominique Luneau

We examine a class of stochastic deep learning models with a tractable method to compute information-theoretic quantities. Our contributions are three-fold: (i) We show how entropies and mutual informations can be derived from heuristic statistical physics ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2018

Mutual information for low-rank even-order symmetric tensor estimation

Nicolas Macris, Jean François Emmanuel Barbier, Clément Dominique Luneau

We consider a statistical model for finite-rank symmetric tensor factorization and prove a single-letter variational expression for its asymptotic mutual information when the tensor is of even order. The proof applies the adaptive interpolation method orig ...

Oxford University Press2021

The adaptive interpolation method for proving replica formulas. Applications to the Curie-Weiss and Wigner spike models

Nicolas Macris, Jean François Emmanuel Barbier

In this contribution we give a pedagogic introduction to the newly introduced adaptive interpolation method to prove in a simple and unified way replica formulas for Bayesian optimal inference problems. Many aspects of this method can already be explained ...

IOP PUBLISHING LTD2019

On the concentration of the capacity for a code division multiple access system

Nicolas Macris

We prove the concentration of the capacity, in the large system limit, for a code division multiple access system over an additive white Gaussian noise channel, with Gaussian signature sequences and {\it binary input} symbols. The probabilistic tools that ...

2007

Correlation inequalities: a useful tool in the theory of LDPC codes

Nicolas Macris

2005

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

On the relation between MAP and BP GEXIT functions of low density parity check codes

Nicolas Macris

We consider communication over binary input memoryless symmetric channels with low density parity check codes. The relationship between maximum a posteriori and belief propagation GEXIT functions is investigated using a set of correlation inequalities of s ...

2006

Tensor estimation with structured priors

Nicolas Macris, Clément Dominique Luneau

We consider rank-one symmetric tensor estimation when the tensor is corrupted by gaussian noise and the spike forming the tensor is a structured signal coming from a generalized linear model. The latter is a mathematically tractable model of a non-trivial ...

2020

Exact Solution of a p-Spin Model and its Relationship to Error Correcting Codes

Nicolas Macris

2006

Applications of correlation inequalities to low density graphical codes

Nicolas Macris

EDP Sciences, Springer2006