We estimate the variance of weight and stopping set distribution of regular LDPC ensembles. Using this estimate and the second moment method we obtain bounds on the probability that a randomly chosen code from regular LDPC ensemble has its weight distribution and stopping set distribution close to respective ensemble averages. We are able to show that a large fraction of total number of codes have their weight and stopping set distribution close to the average.
@article{arxiv.cs/0512066,
title = {On the Asymptotic Weight and Stopping Set Distribution of Regular LDPC Ensembles},
author = {Vishwambhar Rathi},
journal= {arXiv preprint arXiv:cs/0512066},
year = {2016}
}
Comments
Submitted to IEEE Trans on Information Theory (revised version). Minor comments from reviewers addressed