Title :
Large Girth Non-Binary LDPC Codes Based on Finite Fields and Euclidean Geometries
Author :
Jiang, Xueqin ; Lee, Moon Ho
Author_Institution :
Inst. of Inf. & Commun., Chonbuk Nat. Univ., Chonju
fDate :
6/1/2009 12:00:00 AM
Abstract :
This letter presents an approach to the construction of non-binary low-density parity-check (LDPC) codes based on alpha-multiplied circulant permutation matrices and hyperplanes of two different dimensions in Euclidean geometries. Codes constructed by this method have large girth and high binary column weight when the order of Galois field is high. Simulation results show that these codes perform very well with fast Fourier transform (FFT) based sum-product algorithm (SPA).
Keywords :
Galois fields; binary codes; fast Fourier transforms; matrix algebra; parity check codes; Galois field; alpha-multiplied circulant permutation matrices; euclidean geometries; fast Fourier transform; large girth nonbinary LDPC codes; nonbinary low-density parity-check codes; sum-product algorithm; Algorithm design and analysis; Bit error rate; Fast Fourier transforms; Galois fields; Geometry; Iterative algorithms; Iterative decoding; Moon; Parity check codes; Sum product algorithm; $alpha$-multiplied circulant permutation matrices; $mu$ -flats; Euclidean geometry; Non-binary LDPC codes;
Journal_Title :
Signal Processing Letters, IEEE
DOI :
10.1109/LSP.2009.2016830
