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Optimal Bipartite Ramanujan Graphs from Balanced Incomplete Block Designs: Their Characterizations and Applications to Expander/LDPC Codes

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Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5527))

Abstract

We characterize optimal bipartite expander graphs and give necessary and sufficient conditions for optimality. We determine the expansion parameters of the BIBD graphs and show that they yield optimal expander graphs that are also bipartite Ramanujan graphs. In particular, we show that the bipartite graphs derived from finite projective and affine geometries yield optimal Ramanujan graphs. This in turn leads to a theoretical explanation of the good performance of a class of LDPC codes.

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Authors and Affiliations

  1. Institute for Mathematics, Technical University of Denmark, Denmark

    Tom Høholdt

  2. Department of Mathematics and Computer Science, University of Puerto Rico (UPR), Rio Piedras Campus, P.O. Box: 23355, San Juan, PR, 00931 - 3355, USA

    Heeralal Janwal

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  1. Tom Høholdt
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  2. Heeralal Janwal
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  1. Departament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Avinguda Països Catalans, 26, 43007, Tarragona, Spain

    Maria Bras-Amorós

  2. Department of Mathematics, The Technical University of Denmark, Building 303, 2800, Lyngby, Denmark

    Tom Høholdt

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Høholdt, T., Janwal, H. (2009). Optimal Bipartite Ramanujan Graphs from Balanced Incomplete Block Designs: Their Characterizations and Applications to Expander/LDPC Codes. In: Bras-Amorós, M., Høholdt, T. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2009. Lecture Notes in Computer Science, vol 5527. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02181-7_6

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  • DOI: https://doi.org/10.1007/978-3-642-02181-7_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02180-0

  • Online ISBN: 978-3-642-02181-7

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