Iterative Decoding of Low-Density Parity Check Codes (A Survey)
  Much progress has been made on decoding algorithms for error-correcting codes in the last decade. In this article, we give an introduction to some fundamental results on iterative, message-passing algorithms for low-density parity check codes. For certain important stochastic channels, this line of work has enabled getting very close to Shannon capacity with algorithms that are extremely efficient (both in theory and practice). 
Venkatesan Guruswami