Maximizing the minimum distance of bipartite graph based low density parity check codes from two-step circulant covers
Raul Soto · California State University ScholarWorks (system-wide DSpace) · 2013
OF THE THESIS Maximizing the Minimum Distance of Bipartite Graph Based Low Density Parity Check Codes From Two-Step Circulant Covers by Raul Soto Master of Arts in Mathematics San Diego State University, 2013 Algebraic constructions of low-density parity-check (LDPC) codes are important for code designing because of their implementation advantages and properties that facilitate their analysis. This thesis presents a concise notation for LDPC codes that are constructed using a two-step circulant covering process. By implementing this process, instead of a single circulant cover, we are able to show improved minimum distance and girth properties. These improvements were verified by results from codes constructed from a two-step circulant cover of the 2× 3 complete bipartite graph.