Title: Algebraic constructions of LDPC codes with no short cycles

Authors: Ted Hurley, Paul McEvoy, Jakub Wenus

Addresses: Department of Mathematics, National University of Ireland Galway, Galway, Ireland. ' TechnologyFromIdeas, Old Kilmeaden Road, Waterford, Ireland. ' TechnologyFromIdeas, Old Kilmeaden Road, Waterford, Ireland

Abstract: An algebraic group ring method for constructing codes with no short cycles in the check matrix is derived. It is shown that the matrix of a group ring element has no short cycles if and only if the collection of group differences of this element has no repeats. When the method is applied to elements in the group ring with small support this gives a general method for constructing and analysing low density parity check (LDPC) codes with no short cycles from group rings. Examples of LDPC codes with no short cycles are constructed from group ring elements and these are simulated and compared with known LDPC codes, including those adopted for wireless standards.

Keywords: LDPC codes; short cycles; group rings; low density parity check codes; wireless standards; simulation.

DOI: 10.1504/IJICOT.2010.032544

International Journal of Information and Coding Theory, 2010 Vol.1 No.3, pp.285 - 297

Published online: 06 Apr 2010 *

Full-text access for editors Access for subscribers Purchase this article Comment on this article