Families of LDPC codes with constant error fraction corrected I am looking for families of error-correcting LDPC codes with a constant error fraction corrected by a decoding algorithm. 

For example, I know that Sipser and Spielman proved that there is an algorithm that can correct a constant fraction of errors for expander codes (in Expander codes, 1996). 

But, is there any equivalent theorem for other families of LDPC codes (like regular LDPC or irregular LDPC, for example)? References would be useful.

Thanks!
Here are a few examples:

There are the expander codes of Spielman (not to be confused with Sipser-Spielman):
http://www.cs.yale.edu/homes/spielman/Research/ITsuperc.pdf

There are the linear-time codes of Guruswami-Indyk:
https://www.cs.cmu.edu/~venkatg/pubs/papers/lin-zyablov.pdf

There are the expander codes of Zemor:
https://courses.engr.illinois.edu/cs598sgt/zemor.pdf