Title :
A transform approach for constructing quasi-cyclic Euclidean geometry LDPC codes
Author :
Diao, Qiuju ; Zhou, Wei ; Lin, Shu ; Abdel-Ghaffar, Khaled
Author_Institution :
Dept. of Electr. & Comput. Eng., Univ. of California, Davis, CA, USA
Abstract :
A method for constructing quasi-cyclic Euclidean geometry (QC-EG) LDPC codes in the Fourier transform domain is presented. Given a Euclidean geometry over a finite field of characteristic 2, base matrices in the Fourier transform domain are first constructed. Then the inverse Fourier transforms of these base matrices, combined with row and column permutations, result in low-density arrays of circulant permutation matrices and/or zero matrices. The null spaces of these low-density arrays give a family of QC-EG-LDPC codes. Codes in a special subclass have large minimum distances and their Tanner graphs contain no harmful trapping sets with sizes smaller than their minimum distances.
Keywords :
Fourier transforms; cyclic codes; graph theory; inverse transforms; matrix algebra; parity check codes; Fourier transform domain; QC-EG LDPC codes; QC-EG-LDPC codes; Tanner graphs; base matrices; circulant permutation matrices; column permutations; finite field; harmful trapping sets; inverse Fourier transforms; low-density arrays; null spaces; quasicyclic Euclidean geometry LDPC codes; row permutations; transform approach; zero matrices; Fourier transforms; Generators; Geometry; Null space; Parity check codes; Vectors;
Conference_Titel :
Information Theory and Applications Workshop (ITA), 2012
Conference_Location :
San Diego, CA
Print_ISBN :
978-1-4673-1473-2
DOI :
10.1109/ITA.2012.6181800
