How to Find Good Finite-Length Codes: From Art Towards Science

TL;DR

This paper presents a method to optimize finite-length LDPC codes for the binary erasure channel using an analytic approximation that models large and small error events, aligning well with simulation results.

Contribution

It introduces a novel analytic approximation framework for finite-length LDPC code optimization, combining large-scale erasure modeling and minimal stopping set analysis.

Findings

Optimized LDPC ensembles match simulation results

The approximation accurately predicts finite-length code performance

Method potentially applicable to other channels

Abstract

We explain how to optimize finite-length LDPC codes for transmission over the binary erasure channel. Our approach relies on an analytic approximation of the erasure probability. This is in turn based on a finite-length scaling result to model large scale erasures and a union bound involving minimal stopping sets to take into account small error events. We show that the performances of optimized ensembles as observed in simulations are well described by our approximation. Although we only address the case of transmission over the binary erasure channel, our method should be applicable to a more general setting.