Title: High Rate LDPC Codes from Difference Covering Arrays,
Abstract: 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 LDPC coming from balanced incomplete block designs (BIBDs) and
from Latin squares over finite fields. However these constructions have
suffered from the limited orders for which these designs exist. Here we present
a construction of LDPC codes of length $4n^2 - 2n$ for all $n$ using the cyclic
group of order $2n$. These codes achieve high information rate (greater than
0.8) for $n \geq 8$, have girth at least 6 and have minimum distance 6 for $n$
odd.