A Class of Real Expander Codes Based on Projective- Geometrically Constructed Ramanujan Graphs

Summary Quite recently, codes based on real field are gaining momentum in terms of research and applications. In high-performance computing, these codes are being explored to provide fault tolerance under node failures. In this paper, we propose novel real cycle codes based on expander graphs. The requisite graphs are the Ramanujan graphs constructed using incidence matrices of the appropriate projective-geometric objects. The proposed codes are elegant in terms of reduced complexity encoding and very simple erasure correction. Further, the codes are guaranteed to correct three erasures. Apart from building the codes from the sound existing principles, necessary simulation results and justification of the useful properties are also presented in the paper.

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