This paper presents a combinatorial construction of low-density parity-check (LDPC) codes from difference covering arrays. While the original construction by Gallagher was by randomly allocating bits in a sparse parity-check matrix, over the past 20 years researchers have used a variety of more structured approaches to construct these codes, with the more recent constructions of well-structured...

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 applied to elements in the group ring with small support this gives a general method for constructing and analysing low density pa...

A) , (L J regular QC-LDPC code of length N is defined by a parity-check matrix L L p I p I p I p I p I p I p I p I p I H     (1) where 1 1    J j , 1 1    L l and   l j p I , represents the p p  circulant permutation matrix obtained by cyclically right-shifting the p p  identity matrix   0 I by l j p , positions, with. / L N p  For a specific QC-LDPC code we define the correspo...

Amongst the contributions to the theory of LDPC codes deriving from finite geometries ([13], [12], [9]), we present a study of the code C which has as parity-check matrix H the incidence matrix of the Hermitian curve of PG(2, q) and the q + 1-secant to it. The good performance of C with iterative decoding algorithm is showed by Johnson and Weller in [11]. In this paper we prove the ”double” cyc...