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Design of capacity-approaching irregular low-density parity-check codes (2001)
| Venue: | IEEE TRANS. INFORM. THEORY |
| Citations: | 588 - 6 self |
BibTeX
@ARTICLE{Richardson01designof,
author = {Thomas J. Richardson and M. Amin Shokrollahi and Rüdiger L. Urbanke},
title = {Design of capacity-approaching irregular low-density parity-check codes},
journal = {IEEE TRANS. INFORM. THEORY},
year = {2001},
volume = {47},
pages = {619--637}
}
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Abstract
We design low-density parity-check (LDPC) codes that perform at rates extremely close to the Shannon capacity. The codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides. Our theoretical analysis of the codes is based on [1]. Assuming that the underlying communication channel is symmetric, we prove that the probability densities at the message nodes of the graph possess a certain symmetry. Using this symmetry property we then show that, under the assumption of no cycles, the message densities always converge as the number of iterations tends to infinity. Furthermore, we prove a stability condition which implies an upper bound on the fraction of errors that a belief-propagation decoder can correct when applied to a code induced from a bipartite graph with a given degree distribution. Our codes are found by optimizing the degree structure of the underlying graphs. We develop several strategies to perform this optimization. We also present some simulation results for the codes found which show that the performance of the codes is very close to the asymptotic theoretical bounds.
Keyphrases
capacity-approaching irregular low-density parity-check code degree pattern underlying graph message node theoretical analysis iteration tends degree structure underlying communication channel bipartite graph certain symmetry probability density belief-propagation decoder irregular bipartite graph low-density parity-check degree distribution several strategy shannon capacity stability condition asymptotic theoretical bound simulation result graph posse upper bound symmetry property
