Finite-Length Scaling and Finite-Length Shift for Low-Density Parity-Check Codes
Information Theory
2007-07-13 v1 Disordered Systems and Neural Networks
math.IT
Abstract
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.
Cite
@article{arxiv.cs/0410019,
title = {Finite-Length Scaling and Finite-Length Shift for Low-Density Parity-Check Codes},
author = {Abdelaziz Amraoui and Andrea Montanari and Tom Richardson and Rudiger Urbanke},
journal= {arXiv preprint arXiv:cs/0410019},
year = {2007}
}
Comments
42nd Allerton Conference on Communication, Control and Computing (invited paper)