Title :
LDPC codes from voltage graphs
Author :
Kelley, Christine A. ; Walker, Judy L.
Author_Institution :
Dept. of Math., Univ. of Nebraska-Lincoln, Lincoln, NE
Abstract :
Several well-known structure-based constructions of LDPC codes, for example codes based on permutation and circulant matrices and in particular, quasi-cyclic LDPC codes, can be interpreted via algebraic voltage assignments. We explain this connection and show how this idea from topological graph theory can be used to give simple proofs of many known properties of these codes. In addition, the notion of Abelian-inevitable cycle is introduced and the subgraphs giving rise to these cycles are classified. We also indicate how, by using more sophisticated voltage assignments, new classes of good LDPC codes may be obtained.
Keywords :
cyclic codes; graph theory; matrix algebra; parity check codes; Abelian-inevitable cycle; LDPC codes; algebraic voltage assignments; circulant matrices; permutation matrices; quasicyclic code; topological graph theory; Bridge circuits; Communication channels; Decoding; Graph theory; H infinity control; Mathematics; Parity check codes; Sparse matrices; Terminology; Voltage;
Conference_Titel :
Information Theory, 2008. ISIT 2008. IEEE International Symposium on
Conference_Location :
Toronto, ON
Print_ISBN :
978-1-4244-2256-2
Electronic_ISBN :
978-1-4244-2257-9
DOI :
10.1109/ISIT.2008.4595095
