Codes from zero-divisors and units in group rings
International Journal of Information and Coding Theory
Discrete Applied Mathematics
Geometrically-structured maximum-girth LDPC block and convolutional codes
IEEE Journal on Selected Areas in Communications - Special issue on capaciyy approaching codes
A lattice-based systematic recursive construction of quasi-cyclic LDPC codes
IEEE Transactions on Communications
Algebraic constructions of LDPC codes with no short cycles
International Journal of Information and Coding Theory
Quasi-cyclic LDPC codes: an algebraic construction, rank analysis, and codes on Latin squares
IEEE Transactions on Communications
AAECC'06 Proceedings of the 16th international conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
AAECC'06 Proceedings of the 16th international conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Hi-index | 754.84 |
This correspondence presents three algebraic methods for constructing low-density parity-check (LDPC) codes. These methods are based on the structural properties of finite geometries. The first method gives a class of Gallager codes and a class of complementary Gallager codes. The second method results in two classes of circulant-LDPC codes, one in cyclic form and the other in quasi-cyclic form. The third method is a two-step hybrid method. Codes in these classes have a wide range of rates and minimum distances, and they perform well with iterative decoding.