How to find good finite‐length codes: from art towards science
Abdelaziz Amraoui, Andrea Montanari, Rudiger L. Urbanke · European Transactions on Telecommunications · 2007
Abstract We explain how to optimise 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 performance of optimised ensembles as observed in simulations is 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. Copyright © 2007 John Wiley & Sons, Ltd.