Codes on finite geometries

被引：115
|
作者：
Tang, H [1 ]
Xu, J
Lin, S
Abdel-Ghaffar, KAS
机构：
[1] PMC Sierra Inc, Sunnyvale, CA 97223 USA
[2] Marvell Semicond Inc, Sunnyvale, CA 94089 USA
[3] Univ Calif Davis, Dept Elect & Comp Engn, Davis, CA 95616 USA
来源：
IEEE TRANSACTIONS ON INFORMATION THEORY | 2005年 / 51卷 / 02期
基金：
美国国家科学基金会; 美国国家航空航天局;
关键词：
cyclic codes; Euclidean geometry; low-density parity-check (LDPC) codes; majority-logic decoding; projective geometry; quasi-cyclic codes; sum product algorithm;
D O I：
10.1109/TIT.2004.840867
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
New algebraic methods for constructing codes based on hyperplanes of two different dimensions in finite geometries are presented. The new construction methods result in a class of multistep majority-logic decodable codes and three classes of low-density parity-check (LDPC) codes. Decoding methods for the class of majority-logic decodable codes, and a class of codes that perform well with iterative decoding in spite of having many cycles of length 4 in their Tanner graphs, are presented. Most of the codes constructed can be either put in cyclic or quasi-cyclic form and hence their encoding can be implemented with linear shift registers.
引用
收藏
页码：572 / 596
页数：25
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