Encoding and indexing of lattice codes is generalized from self-similar lattice codes to a
broader class of lattices. If coding lattice A c and sha** lattice A s satisfy A s⊆ A c, then A …

Low density parity check (LDPC) lattices were the first family of lattices equipped with
iterative decoding algorithms. We introduce quasi-cyclic LDPC (QC LDPC) lattices as a …

Lattice codes are elegant and powerful structures that not only achieve the capacity of the
additive white Gaussian noise (AWGN) channel but are also a key ingredient to many …

This paper deals with Low-Density Construction-A (LDA) lattices, which are obtained via
Construction A from non-binary low-density parity-check codes. More precisely, a proof is …

The problem of communicating over the additive white Gaussian noise (AWGN) channel
with lattice codes is addressed in this paper. Theoretically, Voronoi constellations have …

A new Goldreich-Goldwasser-Halevi (GGH) cryptosystem is proposed using Generalized
Low Density (GLD) lattices. These low density lattices can alleviate a major drawback of the …

We prove that the ensemble of random Generalized Low-Density (GLD) lattices can attain
the Poltyrev limit for an alphabet size increasing polylogarithmically with the lattice …

Today, there is a real need to strengthen the communication security to anticipate the
development of quantum computing and the eventual attacks arising from it. This work …

This paper contains a summary of the arguments used to show how to achieve capacity of
the AWGN channel with Voronoi constellations of LDA lattices under lattice decoding. No …

We consider real lattices built from error-correcting codes. After recalling the definition of a
lattice, we review Construction A over a prime field. Construction A combined with non …