  The concept and existence of sphere-bound-achieving and capacity-achieving
lattices has been explained on AWGN channels by Forney. LDPC lattices,
introduced by Sadeghi, perform very well under iterative decoding algorithm. In
this work, we focus on an ensemble of regular LDPC lattices. We produce and
investigate an ensemble of LDPC lattices with known properties. It is shown
that these lattices are sphere-bound-achieving and capacity-achieving. As
byproducts we find the minimum distance, coding gain, kissing number and an
upper bound for probability of error for this special ensemble of regular LDPC
lattices.
