Error-correcting codes on scale-free networks

We investigate the potential of scale-free networks as error-correcting codes. We find that irregular low-density parity-check codes with highest performance known to date have degree distributions well fitted by a power-law function $p(k)\sim k^{-\gamma}$ with $\gamma$ close to 2, which suggests that codes built on scale-free networks with appropriate power exponents can be good error-correcting codes, with performance possibly approaching the Shannon limit. We demonstrate for an erasure channel that codes with power-law degree distribution of the form $p(k)=C(k+\alpha)^{-\gamma}$, with $k \geq 2$ and suitable selection of the parameters $\alpha$ and $\gamma$, indeed have very good error-correction capabilities.