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Two Lectures on Iterative Coding and Statistical Mechanics
Andrea Montanari
These are the notes for two lectures delivered at the Les Houches summer school Mathematical Statistical Mechanics, held in July 2005. I review some basic notions on sparse graph e…
Reconstruction on trees and spin glass transition
Marc Mezard, Andrea Montanari
Consider an information source generating a symbol at the root of a tree network whose links correspond to noisy communication channels, and broadcasting it through the network. We…
The Generalized Area Theorem and Some of its Consequences
Cyril Measson, Andrea Montanari, Tom Richardson +1
There is a fundamental relationship between belief propagation and maximum a posteriori decoding. The case of transmission over the binary erasure channel was investigated in detai…
Why We Can Not Surpass Capacity: The Matching Condition
Cyril Measson, Andrea Montanari, Rudiger Urbanke
We show that iterative coding systems can not surpass capacity using only quantities which naturally appear in density evolution. Although the result in itself is trivial, the meth…
Belief Propagation Based Multi--User Detection
Andrea Montanari, Balaji Prabhakar, David Tse
We apply belief propagation (BP) to multi--user detection in a spread spectrum system, under the assumption of Gaussian symbols. We prove that BP is both convergent and allows to e…
On the dynamics of the glass transition on Bethe lattices
Andrea Montanari, Guilhem Semerjian
The Glauber dynamics of disordered spin models with multi-spin interactions on sparse random graphs (Bethe lattices) is investigated. Such models undergo a dynamical glass transiti…
How to Compute Loop Corrections to Bethe Approximation
Andrea Montanari, Tommaso Rizzo
We introduce a method for computing corrections to Bethe approximation for spin models on arbitrary lattices. Unlike cluster variational methods, the new approach takes into accoun…
Maxwell Construction: The Hidden Bridge between Iterative and Maximum a Posteriori Decoding
Cyril Measson, Andrea Montanari, Ruediger Urbanke
There is a fundamental relationship between belief propagation and maximum a posteriori decoding. A decoding algorithm, which we call the Maxwell decoder, is introduced and provide…