Title :
Codes on finite geometries
Author :
Tang, Heng ; Xu, Jun ; Lin, Shu ; Abdel-Ghaffar, Khaled A S
Author_Institution :
PMC-Sierra Inc., Portland, OR, USA
Abstract :
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.
Keywords :
cyclic codes; geometric codes; geometry; graph theory; iterative decoding; majority logic; parity check codes; shift registers; Euclidean geometry; LDPC; Tanner graphs; finite geometry; iterative decoding; linear shift registers; low-density parity-check codes; multistep majority-logic decodable codes; projective geometry; quasicyclic codes; sum product algorithm; Costs; Design engineering; Encoding; Galois fields; Geometry; High speed integrated circuits; Iterative decoding; Parity check codes; Shift registers; Sum product algorithm; Cyclic codes; Euclidean geometry; low-density parity-check (LDPC) codes; majority-logic decoding; projective geometry; quasi-cyclic codes; sum product algorithm;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2004.840867
