QA612 : Constructing LDPC codes from cubic symmetric graphs
Thesis > Central Library of Shahrood University > Mathematical Sciences > MSc > 2021
Authors:
[Author], Abdollah Alhevaz[Supervisor]
Abstarct: Low-density parity-check (LDPC) codes have been the subject of much interest due to the fact that they can perform near the Shannon limit. In this thesis, some kinds of constructions of LDPC codes from cubic (semi-)symmetric graphs are presented. The constructed codes are (3,3)-regular and the vast majority of the corresponding Tanner graphs have girth greater than four. Some properties of the obtained codes are analysed, and some bounds for the code parameters, specially for the dimension and the minimum distance, are presented. Furthermore, an exxpression for the variance of the syndrome weight of the constructed codes are given. Information on the LDPC codes constructed from bipartite cubic symmetric graphs with less than 200 vertices is presented as well. Some of the constructed codes are optimal, and some have an additional property of being self-orthogonal or linear codes with complementary dual (LCD codes).
Keywords:
#LDPC codes #Cubic graph #Arc-transitive graph #Bipartite graph. Keeping place: Central Library of Shahrood University
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