Finite-Length Scaling for Iteratively Decoded LDPC Ensembles

TL;DR

This paper studies the finite-length performance of iteratively decoded LDPC codes over the binary erasure channel, revealing a basic scaling law in the waterfall region and proposing its broader applicability for optimization.

Contribution

It introduces a simple scaling law for finite-length LDPC code performance in the waterfall region and suggests its general applicability beyond the studied case.

Findings

Performance curves follow a basic scaling law

Empirical evidence supports the conjecture of broader applicability

Scaling law can be used for fast finite-length optimization

Abstract

In this paper we investigate the behavior of iteratively decoded low-density parity-check codes over the binary erasure channel in the so-called ``waterfall region." We show that the performance curves in this region follow a very basic scaling law. We conjecture that essentially the same scaling behavior applies in a much more general setting and we provide some empirical evidence to support this conjecture. The scaling law, together with the error floor expressions developed previously, can be used for fast finite-length optimization.