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From Large Scale Rearrangements to Mode Coupling Phenomenology
Andrea Montanari, Guilhem Semerjian
We consider the equilibrium dynamics of Ising spin models with multi-spin interactions on sparse random graphs (Bethe lattices). Such models undergo a mean field glass transition u…
Life Above Threshold: From List Decoding to Area Theorem and MSE
Cyril Measson, Andrea Montanari, Tom Richardson +1
We consider communication over memoryless channels using low-density parity-check code ensembles above the iterative (belief propagation) threshold. What is the computational compl…
Finite-Length Scaling and Finite-Length Shift for Low-Density Parity-Check Codes
Abdelaziz Amraoui, Andrea Montanari, Tom Richardson +1
Consider communication over the binary erasure channel BEC using random low-density parity-check codes with finite-blocklength n from `standard' ensembles. We show that large error…
Tight bounds for LDPC and LDGM codes under MAP decoding
Andrea Montanari
A new method for analyzing low density parity check (LDPC) codes and low density generator matrix (LDGM) codes under bit maximum a posteriori probability (MAP) decoding is introduc…
Finite-Length Scaling for Iteratively Decoded LDPC Ensembles
Abdelaziz Amraoui, Andrea Montanari, Tom Richardson +1
In this paper we investigate the behavior of iteratively decoded low-density parity-check codes over the binary erasure channel in the so-called ``waterfall region." We show that t…
On the cooling-schedule dependence of the dynamics of mean-field glasses
Andrea Montanari, Federico Ricci-Tersenghi
The low temperature phase of discontinuous mean-field spin glasses is characterized by the appearance of an exponential number of metastable states. Which ones among these states d…