On LDPC Codes Based on Families of Expanding Graphs of Increasing Girth without Edge-Transitive Automorphism Groups

  • Monika Polak
  • Vasyl Ustimenko
Part of the Communications in Computer and Information Science book series (CCIS, volume 448)


We introduce new examples of Low Density Parity Check codes connected with the new families of regular graphs of bounded degree and increasing girth. Some new codes have an evident advantage in comparison with the D(n,q) based codes [9]. The new graphs are not edge transitive. So, they are not isomorphic to the Cayley graphs or those from the D(n,q) family, [14]. We use computer simulation to investigate spectral properties of graphs used for the construction of new codes. The experiment demonstrates existence of large spectral gaps in the case of each graph. We conjecture the existence of infinite families of Ramanujan graphs and expanders of bounded degree,existence of strongly Ramanujan graphs of unbounded degree. The lists of eigenvalues can be used for various practical applications of expanding graphs (Coding Theory, Networking, Image Processing). We show that new graphs can be used as a source of lists of cospectral pairs of graphs of bounded or unbounded degree.


expanding graphs Ramanujun graphs LDPC codes families of graphs of increasing girth spectral gap cospectral graphs 


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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Monika Polak
    • 1
  • Vasyl Ustimenko
    • 1
  1. 1.Institute of MathematicsMaria Curie-Sklodowska UniversityLublinPoland

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