A Scaling Law to Predict the Finite-Length Performance of Spatially-Coupled LDPC Codes

TL;DR

This paper introduces a scaling law to accurately predict the finite-length error performance of spatially-coupled LDPC codes over the binary erasure channel, bridging the gap between asymptotic theory and practical code design.

Contribution

It proposes a novel scaling law linking finite-length performance to asymptotic analysis, validated through extensive simulations.

Findings

Scaling law accurately predicts error probability across various parameters.

Predictions closely match simulation data.

Provides insights for practical code design.

Abstract

Spatially-coupled LDPC codes are known to have excellent asymptotic properties. Much less is known regarding their finite-length performance. We propose a scaling law to predict the error probability of finite-length spatially-coupled ensembles when transmission takes place over the binary erasure channel. We discuss how the parameters of the scaling law are connected to fundamental quantities appearing in the asymptotic analysis of these ensembles and we verify that the predictions of the scaling law fit well to the data derived from simulations over a wide range of parameters. The ultimate goal of this line of research is to develop analytic tools for the design of spatially-coupled LDPC codes under practical constraints.