Generalized low-density (GLD) lattices

Abstract

We propose the construction of a new family of lattice sphere packings. Given a small-dimensional lattice, we start by building a first lattice in a large dimension by the direct sum of the small lattice. Then, the coordinates of the first large lattice are permuted to yield a second large-dimensional lattice. Finally, our generalized low-density (GLD) lattice is the intersection of the first and the second lattice. We restrict our construction in this paper to integer lattices. GLD lattices are the result of mixing classical lattice theory with modern coding theory. They are potential candidates not only for channel coding as coded modulations, but also for physical-layer network coding and for secure digital communications.

On the design of multi-dimensional irregular repeat-accumulate lattice codes

“…From Table II, it can be seen that our coding scheme outperforms all of these schemes for large codeword length, i.e., N ≥ 10, 000. When the codeword length is 1,000, our code is about 0.2 dB worse compared with LDA lattices [23] and GLD lattices [25] because of the probability of short cycles are higher when the codeword length is small. Since our goal is to design capacity-approaching lattice codes, thus we mainly focus on the codes with large codeword length, i.e., N ≥ 10, 000.…”

Diversity of low-density lattices

“…Other families of lattices built from sparse codes have been recently proposed, such as lattices from Construction A with non-binary low-density parity-check codes [11][12], referred to as LDA lattices. More recently, a powerful family of generalized low-density (GLD) lattices for the AWGN channel has been defined by the intersection of repeated and interleaved lattices [9].…”

“…Low-density lattice codes (LDLC) are a special class of lattices proposed by Sommer et al in [8] which can be decoded by iterative probabilistic message passing. Another family of iteratively decodable lattices has been published in [9], where authors described a generalized low-density construction. In the present work, we focus on LDLC without using any shaping region.…”