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IEEE International Symposium on Information Theory (ISIT)

Analytic Determination of Scaling Parameters

Abdelaziz Amraoui, Andrea Montanari A, Rudiger L. Urbanke

Published Jul 1, 2006• 14 citations
Publisher

Abstract

We show that the finite-length scaling parameters for irregular LDPC codes when used over the binary erasure channel can be computed without resorting to "covariance evolution". We provide simple expressions that can be evaluated using solely the degree distributions and the characteristics of the fixed point of density evolution

DOI
10.1109/isit.2006.261779

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arXiv:0901.2838•IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2009•1 citation
We show that the finite-length scaling parameters for irregular LDPC codes when used over the binary erasure channel can be computed without resorting to "covariance evolution". We provide simple expressions that can be evaluated using solely the degree distributions and the characteristics of the fixed point of density evolution
We investigate the finite-length scaling methodology for irregular LDPC code ensembles when transmission takes place over the binary erasure channel (BEC). We first show how the necessary computations, namely the covariance evolution and the computation of the finite-length shift, can be accomplished in the irregular case. We then investigate how the obtained approximation can be used to predict the performance of irregular code ensembles and to optimize the degree distributions for finite-length codes.
The covariance evolution is a system of differential equations with respect to the covariance of the number of edges connecting to the nodes of each residual degree. Solving the covariance evolution, we can derive distributions of the number of check nodes of residual degree 1, which helps us to estimate the block error probability for finite-length LDPC code. Amraoui et al. resorted to numerical computations to solve the covariance evolution. In this paper, we give the analytical solution of the covariance evolution.