Abstract
Quasi-cyclic (QC) extension is a recursive graph construction that preserves key design parameters of a “seed” graph, such as the distribution of the degrees of the nodes, while increasing graph size and girth. Algebraic QC extension graphs are described in which automorphisms of the seed graph are purposefully preserved in the extension. The girth of the extension graph will be as least as great as for the seed while the “design rate” of the code is the same. A two-stage QC extension is given for a (3,4) low-density parity-check (LDPC) code to illustrate.
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Tanner, R.M. (2002). On Graph Constructions for LDPC Codes by Quasi-Cyclic Extension. In: Blaum, M., Farrell, P.G., van Tilborg, H.C.A. (eds) Information, Coding and Mathematics. The Springer International Series in Engineering and Computer Science, vol 687. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3585-7_13
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DOI: https://doi.org/10.1007/978-1-4757-3585-7_13
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