Renormalization group approach to error-correcting codes
We explain an algorithm that approximately but efficiently assesses the performance of belief propagation decoding for particular parity check error-correcting codes of large, but finite, blocklength. This algorithm is based on the renormalization group approach from physics: the idea is to continually replace an error-correcting code with a simpler error-correcting code that has nearly identical performance, until the code is reduced to a small enough size that its performance can be computed exactly.