Finite-Length Scaling and Finite-Length Shift for Low-Density Parity-Check Codes

Abdelaziz Amraoui; Andrea Montanari; Tom Richardson; Rudiger Urbanke

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Finite-Length Scaling and Finite-Length Shift for Low-Density Parity-Check Codes

Abdelaziz Amraoui·Andrea Montanari·Tom Richardson·Rudiger Urbanke

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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} +Θ(n^{-1}) with a calculable shift} parameter e_1>0.

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Abdelaziz Amraoui, Andrea Montanari, Tom Richardson, Rudiger Urbanke. 2004-10-10. Finite-Length Scaling and Finite-Length Shift for Low-Density Parity-Check Codes. https://arxiv.org/abs/cs/0410019

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