Expander Codes and Their Applications
Alex Olshevsky

My project revolves around the constructions and performance of binary codes from bipartite graphs.
I am working with Alexander Barg.



Recent progress in construction of good binary code families is associated with codes from bipartite
graphs decodable by simple iterative procedures. This project is concerned with bipartite-graph codes
for which convergence of decoding algorithms is proved relying upon expanding properties of the underlying
graph.

The purpose of this project is to construct and establish performance of several specific examples of
expander codes. First, constructions of expander codes will need to be studied and implemented. Secondly,
the error probability of several codes from the family described needs to be simulated and compared
with another popular code family, the so-called low-density parity-check codes decoded by a message-passing
iterative algorithm, for which the error probability of decoding  is known and appears in the literature.



Some papers on expander codes: Some papers on Low-Density Parity Check Codes: