Open AccessHow to find good finite‐length codes: from art towards science
Author(s) -
Amraoui Abdelaziz,
Montanari Andrea,
Urbanke Ruediger
Publication year - 2007
Publication title -
european transactions on telecommunications
Language(s) - English
Resource type - Journals
eISSN - 1541-8251
pISSN - 1124-318X
DOI - 10.1002/ett.1182
Subject(s) - erasure , low density parity check code , binary erasure channel , binary number , erasure code , channel (broadcasting) , scaling , upper and lower bounds , transmission (telecommunications) , computer science , decoding methods , algorithm , tornado code , theoretical computer science , discrete mathematics , mathematics , channel capacity , error floor , arithmetic , telecommunications , mathematical analysis , geometry , programming language
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.