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Nicolas Macris

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Publications associées (65)

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

Nicolas Macris, Rüdiger Urbanke, 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

Nicolas Macris, Rüdiger Urbanke, 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

Chains of mean-field models

Nicolas Macris, Rüdiger Urbanke, Seyed Hamed Hassani

We consider a collection of Curie-Weiss (CW) spin systems, possibly with a random field, each of which is placed along the positions of a one-dimensional chain. The CW systems are coupled together by a Kac-type interaction in the longitudinal direction of ...

2012

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

Tight Bounds on the Capacity of Binary Input random CDMA Systems

Nicolas Macris, Satish Babu Korada

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

Exact Solution of the Gauge Symmetric p-Spin Glass Model on a Complete Graph

Nicolas Macris, Satish Babu Korada

We consider a gauge symmetric version of the p-spin glass model on a complete graph. The gauge symmetry guarantees the absence of replica symmetry breaking and allows to fully use the interpolation scheme of Guerra to rigorously compute the free energy. In ...

2009

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

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

Concentration of Magnetization for Linear Block Codes

Nicolas Macris, Shrinivas Kudekar, Satish Babu Korada

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

Proof of replica formulas in the high noise regime for communication using LDGM codes

Nicolas Macris, Shrinivas Kudekar

We consider communication over a binary input memoryless output symmetric channel with low density generator matrix codes and optimal maximum a posteriori decoding. It is known that the problem of computing the average conditional entropy, over such code e ...

2008

Decay of Correlations: An Application to Low-Density Parity Check codes

Nicolas Macris, Shrinivas Kudekar

Recently the decay of correlations between bits of low density generator matrix (LDGM) codes have been investigated by using high temperature expansions from statistical physics \cite{KuMa07}. In this work we apply these ideas to a special class of low den ...

IEEE2008

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

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

Nicolas Macris, Satish Babu Korada

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

On the Capacity of a Code Division Multiple Access System

Nicolas Macris, Satish Babu Korada

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

Exact solution for the conditional entropy of Poissonian LDPC codes over the Binary Erasure Channel

Nicolas Macris, Shrinivas Kudekar, Satish Babu Korada

We consider communication over a binary erasure channel with low density parity check codes and optimal maximum a posteriori decoding. It is known that the problem of computing the average conditional entropy, over such code ensembles, in the asymptotic li ...

2007

Sharp Bounds on Generalized EXIT Functions

Nicolas Macris

2007

Percolation in the signal to interference ratio graph

Olivier Dousse, Patrick Thiran, Nicolas Macris

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

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

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

Nicolas Macris, Satish Babu Korada

2006

Sharp Bounds for MAP Decoding of General Irregular LDPC Codes

Nicolas Macris, Shrinivas Kudekar

2006

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