Error-correcting codes on scale-free networks

Abstract

We investigate the potential of scale-free networks as error-correcting codes. We find that irregular low-density parity-check codes with the highest performance known to date have degree distributions well fitted by a power-law function [Formula presented] with [Formula presented] close to 2, which suggests that codes built on scale-free networks with appropriate power exponents can be good error-correcting codes, with a performance possibly approaching the Shannon limit. We demonstrate for an erasure channel that codes with a power-law degree distribution of the form [Formula presented], with [Formula presented] and suitable selection of the parameters [Formula presented] and [Formula presented], indeed have very good error-correction capabilities. © 2004 The American Physical Society.