Algebraic constructions of LDPC codes with no short cycles. (7th April 2010)

• Record Type: Journal Article
• Authors: Hurley, Ted; McEvoy, Paul; Wenus, Jakub
• Is Part Of: International journal of information and coding theory. Volume 1:Number 3(2010)
• Page Start: 285
• Page End: 297
• Publication Date: 2010-04-07
• Subjects: LDPC codes -- short cycles -- group rings -- low density parity check codes -- wireless standards -- simulation; Coding theory -- Periodicals; Information theory -- Periodicals; 003.54
• Languages: English
• ISSNs: 1753-7703

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.