Renormalization Group Approach To Error-Correcting Codes

Abstract

We explain an algorithm that approximately but efficiently assesses 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. This assessment algorithm can be used as a subroutine in a more general algorithm to search for optimal error-correcting codes of specified blocklength and rate.