# Introduction to coding theory (CMU, Spr 2010)

## March 24, 2010

### Lecture 16 summary

Filed under: Lecture summary — Venkat Guruswami @ 8:05 pm

We saw a sequential algorithm for expander codes based on successively flipping bits involved in more unsatisfied checks than satisfied checks, and proved that it corrects a constant fraction of errors (related to the size of the sets which expand by a factor of more than $3D/4$).  We then considered a generalization called Tanner codes and saw how weaker expansion suffices to argue about its distance. We discussed the expander mixing lemma and its use to lower bound the distance of Tanner codes whose factor graph is the edge-vertex incidence matrix of a spectral expander.