This paper analyzes the asymptotic exponent of both the weight spectrum and the stopping set size spectrum for a class of generalized low-density parity-check (GLDPC) codes. Specifically, all variable nodes (VNs) are assumed to have the same degree (regular VN set), while the check node (CN) set is assumed to be composed of a mixture of different linear block codes (hybrid CN set). A simple expression for the exponent (which is also referred to as the growth rate or the spectral shape) is developed. This expression is consistent with previous results, including the case where the normalized weight or stopping set size tends to zero. Furthermore, it is shown how certain symmetry properties of the local weight distribution at the CNs induce a symmetry in the overall weight spectral shape function.
@article{arxiv.1005.4834,
title = {Spectral Shape of Check-Hybrid GLDPC Codes},
author = {Enrico Paolini and Mark F. Flanagan and Marco Chiani and Marc P. C. Fossorier},
journal= {arXiv preprint arXiv:1005.4834},
year = {2016}
}
Comments
6 pages, 3 figures. Presented at the IEEE ICC 2010, Cape Town, South Africa. A minor typo in equation (9) has been corrected