On the Asymptotic Weight and Stopping Set Distribution of Regular LDPC Ensembles
<|reference_start|>On the Asymptotic Weight and Stopping Set Distribution of Regular LDPC Ensembles: 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.<|reference_end|>
@article{rathi2005on,
    title={On the Asymptotic Weight and Stopping Set Distribution of Regular LDPC
  Ensembles},
    author={Vishwambhar Rathi},
    journal={arXiv preprint arXiv:cs/0512066},
    year={2005},
    doi={10.1109/TIT.2006.880065},
    archivePrefix={arXiv},
    eprint={cs/0512066},
    primaryClass={cs.IT math.IT}
}