Under the auspices of the Computational Complexity Foundation (CCF)
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).