Finite-Length Scaling and Finite-Length Shift for Low-Density Parity-Check Codes
<|reference_start|>Finite-Length Scaling and Finite-Length Shift for Low-Density Parity-Check Codes: Consider communication over the binary erasure channel BEC using random low-density parity-check codes with finite-blocklength n from `standard' ensembles. We show that large error events is conveniently described within a scaling theory, and explain how to estimate heuristically their effect. Among other quantities, we consider the finite length threshold e(n), defined by requiring a block error probability P_B = 1/2. For ensembles with minimum variable degree larger than two, the following expression is argued to hold e(n) = e -e_1 n^{-2/3} +\Theta(n^{-1}) with a calculable shift} parameter e_1>0.<|reference_end|>
@article{amraoui2004finite-length,
    title={Finite-Length Scaling and Finite-Length Shift for Low-Density
  Parity-Check Codes},
    author={Abdelaziz Amraoui, Andrea Montanari, Tom Richardson and Rudiger
  Urbanke},
    journal={arXiv preprint arXiv:cs/0410019},
    year={2004},
    archivePrefix={arXiv},
    eprint={cs/0410019},
    primaryClass={cs.IT cond-mat.dis-nn math.IT}
}