Andrea Montanari and Ruediger Urbanke TIFR Tuesday, January 6th, 2008 Phase Transitions in ...

187 Pages·2009·1.97 MB·English

Phase Transitions in Coding, Communications, and
Inference
Andrea Montanari and Ruediger Urbanke
TIFR
Tuesday, January 6th, 2008
Outline
Outline
1) Thresholds in coding, the large size limit
 (definition and density evolution characterization)            
2) The inversion of limits (length to infty vs size to infty)
Outline
1) Thresholds in coding, the large size limit
 (definition and density evolution characterization)            
2) The inversion of limits (length to infty vs size to infty)                  

3) Phase transitions in measurements                   
 (compressed sensing versus message passing,
  dense versus sparse matrices)
4) Phase transitions in collaborative filtering        
 (the low-rank matrix model)
Model
Shannon ’48
Model
Shannon ’48
binary erasures channel
capacity: R≤1-ε
Model
Shannon ’48
binary symmetric channel
capacity: R≤1-h(ε)
Channel Coding
Channel Coding
C={000, 010, 101, 111} code
Channel Coding
C={000, 010, 101, 111} code
n ... blocklength