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Nicolas Macris

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Related publications (64)

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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

Sharp Bounds for Optimal Decoding of Low Density Parity Check Codes

Nicolas Macris, Shrinivas Kudekar

Consider communication over a binary-input memoryless output-symmetric channel with low density parity check (LDPC) codes and maximum a posteriori (MAP) decoding. The replica method of spin glass theory allows to conjecture an analytic formula for the aver ...

2009

Efficient Quantum Algorithms for GHZ and W States, and Implementation on the IBM Quantum Computer

Alix Sébastien Thibaut Jeannerot, Nicolas Macris, Marc-André Dupertuis, Clément Christian Javerzac, Chun Lam Chan

Efficient deterministic algorithms are proposed with logarithmic step complexities for the generation of entangled GHZ(N) and W-N states useful for quantum networks, and an implementation on the IBM quantum computer up to N = 16 is demonstrated. Improved q ...

WILEY2019

Matrix Inference in Growing Rank Regimes

Nicolas Macris, Farzad Pourkamali

The inference of a large symmetric signal-matrix S ϵ RN × N corrupted by additive Gaussian noise, is considered for two regimes of growth of the rank M as a function of N. For sub-linear ranks M=Θ (Nα) with α in (0,1) the mutual information and minimum mea ...

2024

The adaptive interpolation method: a simple scheme to prove replica formulas in Bayesian inference

Nicolas Macris, Jean François Emmanuel Barbier

In recent years important progress has been achieved towards proving the validity of the replica predictions for the (asymptotic) mutual information (or free energy) in Bayesian inference problems. The proof techniques that have emerged appear to be quite ...

SPRINGER HEIDELBERG2019

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

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

Nicolas Macris, Marc Vuffray, Vahid Aref

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 Mutual Information in Random Linear Estimation Beyond i.i.d. Matrices

Nicolas Macris, Florent Gérard Krzakala, Jean François Emmanuel Barbier

There has been definite progress recently in proving the variational single-letter formula given by the heuristic replica method for various estimation problems. In particular, the replica formula for the mutual information in the case of noisy linear esti ...

IEEE2018

Mutual Information for Low-Rank Even-Order Symmetric Tensor Factorization

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 mutual information when the tensor is of even order. The proof uses the adaptive interpolation method, for which rank-on ...

IEEE2019

How to Prove the Maxwell Conjecture Via Spatial Coupling - A Proof of Concept

Rüdiger Urbanke, Nicolas Macris, Andrei Giurgiu

Investigations on spatially coupled codes have lead to the conjecture that, in the infinite size limit, the average input-output conditional entropy for spatially coupled low-density parity-check ensembles, over binary memoryless symmetric channels, equals ...

Ieee2012

Lossy source coding via spatially coupled LDGM ensembles

Rüdiger Urbanke, Nicolas Macris, Marc Vuffray, Vahid Aref

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

Rectangular rotational invariant estimator for high-rank matrix estimation

Nicolas Macris, Farzad Pourkamali

We consider estimating a matrix from noisy observations coming from an arbitrary additive bi-rotational invariant perturbation. We propose an estimator, which we conjecture is optimal among the class of rectangular rotational invariant estimators and can b ...

Oxford University Press2025

Decay of correlations for sparse graph error correcting codes

Nicolas Macris, Shrinivas Kudekar

The subject of this paper is transmission over a general class of binary-input memoryless symmetric channels using error correcting codes based on sparse graphs, namely, low-density generator-matrix and low-density parity-check codes. The optimal (or ideal ...

SIAM Publications2011

Mutual Information for the Stochastic Block Model by the Adaptive Interpolation Method

Nicolas Macris, Jean François Emmanuel Barbier, Chun Lam Chan

We rigorously derive a single-letter variational expression for the mutual information of the asymmetric two-groups stochastic block model in the dense graph regime. Existing proofs in the literature are indirect, as they involve mapping the model to a ran ...

IEEE2019

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

Spatial Coupling as a Proof Technique and Three Applications

Rüdiger Urbanke, Nicolas Macris, Andrei Giurgiu

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. The starting point is the observation that some asymptotic properties of gr ...

Ieee-Inst Electrical Electronics Engineers Inc2016

Griffiths Kelly Sherman correlation inequalities: a useful tool in the theory of error correcting codes

Nicolas Macris

It is shown that a correlation inequality of statistical mechanics can be applied to linear low-density parity-check codes. Thanks to this tool we prove that, under a natural assumption, the exponential growth rate of regular low-density parity-check (LDPC ...

Institute of Electrical and Electronics Engineers2007

Decay of Correlations in Low Density Parity Check Codes: Low Noise Regime

Nicolas Macris, Shrinivas Kudekar

Consider transmission over a binary additive white gaussian noise channel using a fixed low-density parity check code. We consider the posterior measure over the code bits and the corresponding correlation between two codebits, averaged over the noise real ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2009

Percolation in the signal to interference ratio graph

Patrick Thiran, Nicolas Macris, Olivier Dousse

Continuum percolation models in which pairs of points of a two-dimensional Poisson point process are connected if they are within some range to each other have been extensively studied. This paper considers a variation in which a connection between two poi ...

2006

Percolation in the signal to interference ratio graph

Patrick Thiran, Nicolas Macris, Olivier Dousse

2005