Regular and Irregular Gallager-Zype Error-Correcting Codes
Abstract
The performance of regular and irregular Gallager-type error(cid:173) correcting code is investigated via methods of statistical physics. The transmitted codeword comprises products of the original mes(cid:173) sage bits selected by two randomly-constructed sparse matrices; the number of non-zero row/column elements in these matrices constitutes a family of codes. We show that Shannon's channel capacity may be saturated in equilibrium for many of the regular codes while slightly lower performance is obtained for others which may be of higher practical relevance. Decoding aspects are con(cid:173) sidered by employing the TAP approach which is identical to the commonly used belief-propagation-based decoding. We show that irregular codes may saturate Shannon's capacity but with improved dynamical properties.
Cite
Text
Kabashima et al. "Regular and Irregular Gallager-Zype Error-Correcting Codes." Neural Information Processing Systems, 1999.Markdown
[Kabashima et al. "Regular and Irregular Gallager-Zype Error-Correcting Codes." Neural Information Processing Systems, 1999.](https://mlanthology.org/neurips/1999/kabashima1999neurips-regular/)BibTeX
@inproceedings{kabashima1999neurips-regular,
title = {{Regular and Irregular Gallager-Zype Error-Correcting Codes}},
author = {Kabashima, Yoshiyuki and Murayama, Tatsuto and Saad, David and Vicente, Renato},
booktitle = {Neural Information Processing Systems},
year = {1999},
pages = {272-278},
url = {https://mlanthology.org/neurips/1999/kabashima1999neurips-regular/}
}